diff --git a/dev/.documenter-siteinfo.json b/dev/.documenter-siteinfo.json new file mode 100644 index 0000000..5f2d5bd --- /dev/null +++ b/dev/.documenter-siteinfo.json @@ -0,0 +1 @@ +{"documenter":{"julia_version":"1.10.3","generation_timestamp":"2024-05-20T17:55:16","documenter_version":"1.4.1"}} \ No newline at end of file diff --git a/dev/api/index.html b/dev/api/index.html new file mode 100644 index 0000000..8f6fb02 --- /dev/null +++ b/dev/api/index.html @@ -0,0 +1,2 @@ + +API reference · Ket.jl

API reference

Ket._fiducial_WH — Method
_fiducial_WH(d::Integer)

Computes the fiducial Weyl-Heisenberg vector of dimension d.

Reference: Appleby, Yadsan-Appleby, Zauner, arXiv:1209.1813 http://www.gerhardzauner.at/sicfiducials.html

source
Ket._partition — Method
partition(n::Integer, k::Integer)

If n ≥ k partitions the set 1:n into k parts as equally sized as possible. Otherwise partitions it into n parts of size 1.

source
Ket.binary_relative_entropy — Method
binary_relative_entropy([b=2,] p::Real, q::Real)

Computes the binary relative entropy D(p||q) = p log(p/q) + (1-p) log((1-p)/(1-q)) between two probabilities p and q using a base b logarithm.

Reference: Relative entropy.

source
Ket.chsh — Method
chsh([T=Float64,] d::Integer = 2)

CHSH-d nonlocal game in full probability notation. If T is an integer type the game is unnormalized.

Reference: Buhrman and Massar, arXiv:quant-ph/0409066.

source
Ket.cleanup! — Method
cleanup!(M::AbstractArray{T}; tol = Base.rtoldefault(real(T)))

Zeroes out real or imaginary parts of M that are smaller than tol.

source
Ket.correlation_tensor — Method
correlation_tensor(p::AbstractArray{T, N2}; marg::Bool = true)

Applies N sets of POVMs onto a state rho to form a probability array. Convert a 2x...x2xmx...xm probability array into

  • a mx...xm correlation array (no marginals)
  • a (m+1)x...x(m+1) correlation array (marginals).
source
Ket.dilate_povm — Method
dilate_povm(E::Vector{<:AbstractMatrix})

Does the Naimark dilation of a POVM given as a vector of matrices. This always works, but is wasteful if the POVM elements are not full rank.

source
Ket.dilate_povm — Method
dilate_povm(vecs::Vector{Vector{T}})

Does the Naimark dilation of a rank-1 POVM given as a vector of vectors. This is the minimal dilation.

source
Ket.entropy — Method
entropy([b=2,] ρ::AbstractMatrix)

Computes the von Neumann entropy -tr(ρ log ρ) of a positive semidefinite operator ρ using a base b logarithm.

Reference: von Neumann entropy.

source
Ket.fp2cg — Method
fp2cg(V::Array{T,4}) where {T <: Real}

Takes a bipartite Bell functional V in full probability notation and transforms it to Collins-Gisin notation.

source
Ket.gell_mann! — Method
gell_mann!(res::AbstractMatrix{T}, i::Integer, j::Integer, d::Integer = 3)

In-place version of gell_mann.

source
Ket.isotropic — Method

Produces the isotropic state of local dimension d with visibility v

source
Ket.ket — Method
ket([T=ComplexF64,] i::Integer, d::Integer)

Produces a ket of dimension d with nonzero element i.

source
Ket.ketbra — Method
ketbra(v::AbstractVector)

Produces a ketbra of vector v.

source
Ket.kyfan_norm — Function
kyfan_norm(X::AbstractMatrix, k::Int, p::Real = 2)

Computes Ky-Fan (k,p) norm of matrix X.

source
Ket.local_bound — Method
local_bound(G::Array{T,4})

Computes the local bound of a bipartite Bell functional G, written in full probability notation as a 4-dimensional array.

source
Ket.mub — Method
mub(d::Integer)

Construction of the standard complete set of MUBs. The output contains 1+minᵢ pᵢ^rᵢ bases, where d = ∏ᵢ pᵢ^rᵢ.

Reference: Durt, Englert, Bengtsson, Życzkowski, arXiv:1004.3348.

source
Ket.phiplus — Method

Produces the maximally entangled state Φ⁺ of local dimension d

source
Ket.povm — Method
povm(A::Array{T, 4}, n::Vector{Int64})

Converts a set of POVMs in the common tensor format into a matrix of matrices. The second argument is fixed by the size of A but can also contain custom number of outcomes.

source
Ket.povm — Method
povm(B::Vector{<:AbstractMatrix{T}})

Creates a set of (projective) POVMs from a set of bases given as unitary matrices.

source
Ket.probability_tensor — Method
probability_tensor(Aax::Vector{POVM{T}})

Applies N sets of POVMs onto a state rho to form a probability array.

source
Ket.proj — Method
proj([T=ComplexF64,] i::Integer, d::Integer)

Produces a projector onto the basis state i in dimension d.

source
Ket.psiminus — Method

Produces the maximally entangled state ψ⁻ of local dimension d

source
Ket.random_povm — Method
random_povm([T=ComplexF64,] d::Integer, n::Integer, r::Integer)

Produces a random POVM of dimension d with n outcomes and rank min(k, d).

Reference: Heinosaari et al., arXiv:1902.04751.

source
Ket.random_state — Method
random_state([T=ComplexF64,] d::Integer, k::Integer = d)

Produces a uniformly distributed random quantum state in dimension d with rank k.

Reference: Życzkowski and Sommers, arXiv:quant-ph/0012101.

source
Ket.random_unitary — Method
random_unitary([T=ComplexF64,] d::Integer)

Produces a Haar-random unitary matrix in dimension d. If T is a real type the output is instead a Haar-random (real) orthogonal matrix.

Reference: Mezzadri, arXiv:math-ph/0609050.

source
Ket.relative_entropy — Method
relative_entropy([b=2,] ρ::AbstractMatrix, σ::AbstractMatrix)

Computes the (quantum) relative entropy tr(ρ (log ρ - log σ)) between positive semidefinite matrices ρ and σ using a base b logarithm. Note that the support of ρ must be contained in the support of σ but for efficiency this is not checked.

Reference: Quantum relative entropy.

source
Ket.relative_entropy — Method
relative_entropy([b=2,] p::AbstractVector, q::AbstractVector)

Computes the relative entropy D(p||q) = Σᵢpᵢlog(pᵢ/qᵢ) between two non-negative vectors p and q using a base b logarithm. Note that the support of p must be contained in the support of q but for efficiency this is not checked.

Reference: Relative entropy.

source
Ket.sic_povm — Method
sic_povm(d::Integer)

Constructs a vector of d² vectors |vᵢ⟩ such that |vᵢ⟩⟨vᵢ| forms a SIC-POVM of dimension d. This construction is based on the Weyl-Heisenberg fiducial.

Reference: Appleby, Yadsan-Appleby, Zauner, arXiv:1209.1813

source
Ket.test_sic — Method
test_sic(vecs)

Tests whether vecs is a vector of d² vectors |vᵢ⟩ such that |vᵢ⟩⟨vᵢ| forms a SIC-POVM of dimension d.

source
Ket.tsirelson_bound — Method
tsirelson_bound(CG::Matrix, scenario::Vector, level::Integer)

Upper bounds the Tsirelson bound of a bipartite Bell funcional game CG, written in Collins-Gisin notation. scenario is vector detailing the number of inputs and outputs, in the order [oa, ob, ia, ib]. level is an integer determining the level of the NPA hierarchy.

This function requires Moment. It is only available if you first do "import MATLAB" or "using MATLAB".

source
diff --git a/dev/assets/documenter.js b/dev/assets/documenter.js new file mode 100644 index 0000000..c6562b5 --- /dev/null +++ b/dev/assets/documenter.js @@ -0,0 +1,1050 @@ +// Generated by Documenter.jl +requirejs.config({ + paths: { + 'highlight-julia': 'https://cdnjs.cloudflare.com/ajax/libs/highlight.js/11.8.0/languages/julia.min', + 'headroom': 'https://cdnjs.cloudflare.com/ajax/libs/headroom/0.12.0/headroom.min', + 'jqueryui': 'https://cdnjs.cloudflare.com/ajax/libs/jqueryui/1.13.2/jquery-ui.min', + 'katex-auto-render': 'https://cdnjs.cloudflare.com/ajax/libs/KaTeX/0.16.8/contrib/auto-render.min', + 'jquery': 'https://cdnjs.cloudflare.com/ajax/libs/jquery/3.7.0/jquery.min', + 'headroom-jquery': 'https://cdnjs.cloudflare.com/ajax/libs/headroom/0.12.0/jQuery.headroom.min', + 'katex': 'https://cdnjs.cloudflare.com/ajax/libs/KaTeX/0.16.8/katex.min', + 'highlight': 'https://cdnjs.cloudflare.com/ajax/libs/highlight.js/11.8.0/highlight.min', + 'highlight-julia-repl': 'https://cdnjs.cloudflare.com/ajax/libs/highlight.js/11.8.0/languages/julia-repl.min', + }, + shim: { + "highlight-julia": { + "deps": [ + "highlight" + ] + }, + "katex-auto-render": { + "deps": [ + "katex" + ] + }, + "headroom-jquery": { + "deps": [ + "jquery", + "headroom" + ] + }, + "highlight-julia-repl": { + "deps": [ + "highlight" + ] + } +} +}); +//////////////////////////////////////////////////////////////////////////////// +require(['jquery', 'katex', 'katex-auto-render'], function($, katex, renderMathInElement) { +$(document).ready(function() { + renderMathInElement( + document.body, + { + "delimiters": [ + { + "left": "$", + "right": "$", + "display": false + }, + { + "left": "$$", + "right": "$$", + "display": true + }, + { + "left": "\\[", + "right": "\\]", + "display": true + } + ] +} + + ); +}) + +}) +//////////////////////////////////////////////////////////////////////////////// +require(['jquery', 'highlight', 'highlight-julia', 'highlight-julia-repl'], function($) { +$(document).ready(function() { + hljs.highlightAll(); +}) + +}) +//////////////////////////////////////////////////////////////////////////////// +require(['jquery'], function($) { + +let timer = 0; +var isExpanded = true; + +$(document).on("click", ".docstring header", function () { + let articleToggleTitle = "Expand docstring"; + + debounce(() => { + if ($(this).siblings("section").is(":visible")) { + $(this) + .find(".docstring-article-toggle-button") + .removeClass("fa-chevron-down") + .addClass("fa-chevron-right"); + } else { + $(this) + .find(".docstring-article-toggle-button") + .removeClass("fa-chevron-right") + .addClass("fa-chevron-down"); + + articleToggleTitle = "Collapse docstring"; + } + + $(this) + .find(".docstring-article-toggle-button") + .prop("title", articleToggleTitle); + $(this).siblings("section").slideToggle(); + }); +}); + +$(document).on("click", ".docs-article-toggle-button", function (event) { + let articleToggleTitle = "Expand docstring"; + let navArticleToggleTitle = "Expand all docstrings"; + let animationSpeed = event.noToggleAnimation ? 0 : 400; + + debounce(() => { + if (isExpanded) { + $(this).removeClass("fa-chevron-up").addClass("fa-chevron-down"); + $(".docstring-article-toggle-button") + .removeClass("fa-chevron-down") + .addClass("fa-chevron-right"); + + isExpanded = false; + + $(".docstring section").slideUp(animationSpeed); + } else { + $(this).removeClass("fa-chevron-down").addClass("fa-chevron-up"); + $(".docstring-article-toggle-button") + .removeClass("fa-chevron-right") + .addClass("fa-chevron-down"); + + isExpanded = true; + articleToggleTitle = "Collapse docstring"; + navArticleToggleTitle = "Collapse all docstrings"; + + $(".docstring section").slideDown(animationSpeed); + } + + $(this).prop("title", navArticleToggleTitle); + $(".docstring-article-toggle-button").prop("title", articleToggleTitle); + }); +}); + +function debounce(callback, timeout = 300) { + if (Date.now() - timer > timeout) { + callback(); + } + + clearTimeout(timer); + + timer = Date.now(); +} + +}) +//////////////////////////////////////////////////////////////////////////////// +require([], function() { +function addCopyButtonCallbacks() { + for (const el of document.getElementsByTagName("pre")) { + const button = document.createElement("button"); + button.classList.add("copy-button", "fa-solid", "fa-copy"); + button.setAttribute("aria-label", "Copy this code block"); + button.setAttribute("title", "Copy"); + + el.appendChild(button); + + const success = function () { + button.classList.add("success", "fa-check"); + button.classList.remove("fa-copy"); + }; + + const failure = function () { + button.classList.add("error", "fa-xmark"); + button.classList.remove("fa-copy"); + }; + + button.addEventListener("click", function () { + copyToClipboard(el.innerText).then(success, failure); + + setTimeout(function () { + button.classList.add("fa-copy"); + button.classList.remove("success", "fa-check", "fa-xmark"); + }, 5000); + }); + } +} + +function copyToClipboard(text) { + // clipboard API is only available in secure contexts + if (window.navigator && window.navigator.clipboard) { + return window.navigator.clipboard.writeText(text); + } else { + return new Promise(function (resolve, reject) { + try { + const el = document.createElement("textarea"); + el.textContent = text; + el.style.position = "fixed"; + el.style.opacity = 0; + document.body.appendChild(el); + el.select(); + document.execCommand("copy"); + + resolve(); + } catch (err) { + reject(err); + } finally { + document.body.removeChild(el); + } + }); + } +} + +if (document.readyState === "loading") { + document.addEventListener("DOMContentLoaded", addCopyButtonCallbacks); +} else { + addCopyButtonCallbacks(); +} + +}) +//////////////////////////////////////////////////////////////////////////////// +require(['jquery', 'headroom', 'headroom-jquery'], function($, Headroom) { + +// Manages the top navigation bar (hides it when the user starts scrolling down on the +// mobile). +window.Headroom = Headroom; // work around buggy module loading? +$(document).ready(function () { + $("#documenter .docs-navbar").headroom({ + tolerance: { up: 10, down: 10 }, + }); +}); + +}) +//////////////////////////////////////////////////////////////////////////////// +require(['jquery'], function($) { + +$(document).ready(function () { + let meta = $("div[data-docstringscollapsed]").data(); + + if (meta?.docstringscollapsed) { + $("#documenter-article-toggle-button").trigger({ + type: "click", + noToggleAnimation: true, + }); + } +}); + +}) +//////////////////////////////////////////////////////////////////////////////// +require(['jquery'], function($) { + +/* +To get an in-depth about the thought process you can refer: https://hetarth02.hashnode.dev/series/gsoc + +PSEUDOCODE: + +Searching happens automatically as the user types or adjusts the selected filters. +To preserve responsiveness, as much as possible of the slow parts of the search are done +in a web worker. Searching and result generation are done in the worker, and filtering and +DOM updates are done in the main thread. The filters are in the main thread as they should +be very quick to apply. This lets filters be changed without re-searching with minisearch +(which is possible even if filtering is on the worker thread) and also lets filters be +changed _while_ the worker is searching and without message passing (neither of which are +possible if filtering is on the worker thread) + +SEARCH WORKER: + +Import minisearch + +Build index + +On message from main thread + run search + find the first 200 unique results from each category, and compute their divs for display + note that this is necessary and sufficient information for the main thread to find the + first 200 unique results from any given filter set + post results to main thread + +MAIN: + +Launch worker + +Declare nonconstant globals (worker_is_running, last_search_text, unfiltered_results) + +On text update + if worker is not running, launch_search() + +launch_search + set worker_is_running to true, set last_search_text to the search text + post the search query to worker + +on message from worker + if last_search_text is not the same as the text in the search field, + the latest search result is not reflective of the latest search query, so update again + launch_search() + otherwise + set worker_is_running to false + + regardless, display the new search results to the user + save the unfiltered_results as a global + update_search() + +on filter click + adjust the filter selection + update_search() + +update_search + apply search filters by looping through the unfiltered_results and finding the first 200 + unique results that match the filters + + Update the DOM +*/ + +/////// SEARCH WORKER /////// + +function worker_function(documenterSearchIndex, documenterBaseURL, filters) { + importScripts( + "https://cdn.jsdelivr.net/npm/minisearch@6.1.0/dist/umd/index.min.js" + ); + + let data = documenterSearchIndex.map((x, key) => { + x["id"] = key; // minisearch requires a unique for each object + return x; + }); + + // list below is the lunr 2.1.3 list minus the intersect with names(Base) + // (all, any, get, in, is, only, which) and (do, else, for, let, where, while, with) + // ideally we'd just filter the original list but it's not available as a variable + const stopWords = new Set([ + "a", + "able", + "about", + "across", + "after", + "almost", + "also", + "am", + "among", + "an", + "and", + "are", + "as", + "at", + "be", + "because", + "been", + "but", + "by", + "can", + "cannot", + "could", + "dear", + "did", + "does", + "either", + "ever", + "every", + "from", + "got", + "had", + "has", + "have", + "he", + "her", + "hers", + "him", + "his", + "how", + "however", + "i", + "if", + "into", + "it", + "its", + "just", + "least", + "like", + "likely", + "may", + "me", + "might", + "most", + "must", + "my", + "neither", + "no", + "nor", + "not", + "of", + "off", + "often", + "on", + "or", + "other", + "our", + "own", + "rather", + "said", + "say", + "says", + "she", + "should", + "since", + "so", + "some", + "than", + "that", + "the", + "their", + "them", + "then", + "there", + "these", + "they", + "this", + "tis", + "to", + "too", + "twas", + "us", + "wants", + "was", + "we", + "were", + "what", + "when", + "who", + "whom", + "why", + "will", + "would", + "yet", + "you", + "your", + ]); + + let index = new MiniSearch({ + fields: ["title", "text"], // fields to index for full-text search + storeFields: ["location", "title", "text", "category", "page"], // fields to return with results + processTerm: (term) => { + let word = stopWords.has(term) ? null : term; + if (word) { + // custom trimmer that doesn't strip @ and !, which are used in julia macro and function names + word = word + .replace(/^[^a-zA-Z0-9@!]+/, "") + .replace(/[^a-zA-Z0-9@!]+$/, ""); + + word = word.toLowerCase(); + } + + return word ?? null; + }, + // add . as a separator, because otherwise "title": "Documenter.Anchors.add!", would not + // find anything if searching for "add!", only for the entire qualification + tokenize: (string) => string.split(/[\s\-\.]+/), + // options which will be applied during the search + searchOptions: { + prefix: true, + boost: { title: 100 }, + fuzzy: 2, + }, + }); + + index.addAll(data); + + /** + * Used to map characters to HTML entities. + * Refer: https://github.com/lodash/lodash/blob/main/src/escape.ts + */ + const htmlEscapes = { + "&": "&", + "<": "<", + ">": ">", + '"': """, + "'": "'", + }; + + /** + * Used to match HTML entities and HTML characters. + * Refer: https://github.com/lodash/lodash/blob/main/src/escape.ts + */ + const reUnescapedHtml = /[&<>"']/g; + const reHasUnescapedHtml = RegExp(reUnescapedHtml.source); + + /** + * Escape function from lodash + * Refer: https://github.com/lodash/lodash/blob/main/src/escape.ts + */ + function escape(string) { + return string && reHasUnescapedHtml.test(string) + ? string.replace(reUnescapedHtml, (chr) => htmlEscapes[chr]) + : string || ""; + } + + /** + * Make the result component given a minisearch result data object and the value + * of the search input as queryString. To view the result object structure, refer: + * https://lucaong.github.io/minisearch/modules/_minisearch_.html#searchresult + * + * @param {object} result + * @param {string} querystring + * @returns string + */ + function make_search_result(result, querystring) { + let search_divider = `
`; + let display_link = + result.location.slice(Math.max(0), Math.min(50, result.location.length)) + + (result.location.length > 30 ? "..." : ""); // To cut-off the link because it messes with the overflow of the whole div + + if (result.page !== "") { + display_link += ` (${result.page})`; + } + + let textindex = new RegExp(`${querystring}`, "i").exec(result.text); + let text = + textindex !== null + ? result.text.slice( + Math.max(textindex.index - 100, 0), + Math.min( + textindex.index + querystring.length + 100, + result.text.length + ) + ) + : ""; // cut-off text before and after from the match + + text = text.length ? escape(text) : ""; + + let display_result = text.length + ? "..." + + text.replace( + new RegExp(`${escape(querystring)}`, "i"), // For first occurrence + '$&' + ) + + "..." + : ""; // highlights the match + + let in_code = false; + if (!["page", "section"].includes(result.category.toLowerCase())) { + in_code = true; + } + + // We encode the full url to escape some special characters which can lead to broken links + let result_div = ` + +
+
${escape(result.title)}
+
${result.category}
+
+

+ ${display_result} +

+
+ ${display_link} +
+ + ${search_divider} + `; + + return result_div; + } + + self.onmessage = function (e) { + let query = e.data; + let results = index.search(query, { + filter: (result) => { + // Only return relevant results + return result.score >= 1; + }, + }); + + // Pre-filter to deduplicate and limit to 200 per category to the extent + // possible without knowing what the filters are. + let filtered_results = []; + let counts = {}; + for (let filter of filters) { + counts[filter] = 0; + } + let present = {}; + + for (let result of results) { + cat = result.category; + cnt = counts[cat]; + if (cnt < 200) { + id = cat + "---" + result.location; + if (present[id]) { + continue; + } + present[id] = true; + filtered_results.push({ + location: result.location, + category: cat, + div: make_search_result(result, query), + }); + } + } + + postMessage(filtered_results); + }; +} + +// `worker = Threads.@spawn worker_function(documenterSearchIndex)`, but in JavaScript! +const filters = [ + ...new Set(documenterSearchIndex["docs"].map((x) => x.category)), +]; +const worker_str = + "(" + + worker_function.toString() + + ")(" + + JSON.stringify(documenterSearchIndex["docs"]) + + "," + + JSON.stringify(documenterBaseURL) + + "," + + JSON.stringify(filters) + + ")"; +const worker_blob = new Blob([worker_str], { type: "text/javascript" }); +const worker = new Worker(URL.createObjectURL(worker_blob)); + +/////// SEARCH MAIN /////// + +// Whether the worker is currently handling a search. This is a boolean +// as the worker only ever handles 1 or 0 searches at a time. +var worker_is_running = false; + +// The last search text that was sent to the worker. This is used to determine +// if the worker should be launched again when it reports back results. +var last_search_text = ""; + +// The results of the last search. This, in combination with the state of the filters +// in the DOM, is used compute the results to display on calls to update_search. +var unfiltered_results = []; + +// Which filter is currently selected +var selected_filter = ""; + +$(document).on("input", ".documenter-search-input", function (event) { + if (!worker_is_running) { + launch_search(); + } +}); + +function launch_search() { + worker_is_running = true; + last_search_text = $(".documenter-search-input").val(); + worker.postMessage(last_search_text); +} + +worker.onmessage = function (e) { + if (last_search_text !== $(".documenter-search-input").val()) { + launch_search(); + } else { + worker_is_running = false; + } + + unfiltered_results = e.data; + update_search(); +}; + +$(document).on("click", ".search-filter", function () { + if ($(this).hasClass("search-filter-selected")) { + selected_filter = ""; + } else { + selected_filter = $(this).text().toLowerCase(); + } + + // This updates search results and toggles classes for UI: + update_search(); +}); + +/** + * Make/Update the search component + */ +function update_search() { + let querystring = $(".documenter-search-input").val(); + + if (querystring.trim()) { + if (selected_filter == "") { + results = unfiltered_results; + } else { + results = unfiltered_results.filter((result) => { + return selected_filter == result.category.toLowerCase(); + }); + } + + let search_result_container = ``; + let modal_filters = make_modal_body_filters(); + let search_divider = `
`; + + if (results.length) { + let links = []; + let count = 0; + let search_results = ""; + + for (var i = 0, n = results.length; i < n && count < 200; ++i) { + let result = results[i]; + if (result.location && !links.includes(result.location)) { + search_results += result.div; + count++; + links.push(result.location); + } + } + + if (count == 1) { + count_str = "1 result"; + } else if (count == 200) { + count_str = "200+ results"; + } else { + count_str = count + " results"; + } + let result_count = `
${count_str}
`; + + search_result_container = ` +
+ ${modal_filters} + ${search_divider} + ${result_count} +
+ ${search_results} +
+
+ `; + } else { + search_result_container = ` +
+ ${modal_filters} + ${search_divider} +
0 result(s)
+
+
No result found!
+ `; + } + + if ($(".search-modal-card-body").hasClass("is-justify-content-center")) { + $(".search-modal-card-body").removeClass("is-justify-content-center"); + } + + $(".search-modal-card-body").html(search_result_container); + } else { + if (!$(".search-modal-card-body").hasClass("is-justify-content-center")) { + $(".search-modal-card-body").addClass("is-justify-content-center"); + } + + $(".search-modal-card-body").html(` +
Type something to get started!
+ `); + } +} + +/** + * Make the modal filter html + * + * @returns string + */ +function make_modal_body_filters() { + let str = filters + .map((val) => { + if (selected_filter == val.toLowerCase()) { + return `${val}`; + } else { + return `${val}`; + } + }) + .join(""); + + return ` +
+ Filters: + ${str} +
`; +} + +}) +//////////////////////////////////////////////////////////////////////////////// +require(['jquery'], function($) { + +// Modal settings dialog +$(document).ready(function () { + var settings = $("#documenter-settings"); + $("#documenter-settings-button").click(function () { + settings.toggleClass("is-active"); + }); + // Close the dialog if X is clicked + $("#documenter-settings button.delete").click(function () { + settings.removeClass("is-active"); + }); + // Close dialog if ESC is pressed + $(document).keyup(function (e) { + if (e.keyCode == 27) settings.removeClass("is-active"); + }); +}); + +}) +//////////////////////////////////////////////////////////////////////////////// +require(['jquery'], function($) { + +$(document).ready(function () { + let search_modal_header = ` +
+
+

+ + + + +

+
+
+ +
+
+ `; + + let initial_search_body = ` +
Type something to get started!
+ `; + + let search_modal_footer = ` + + `; + + $(document.body).append( + ` + + ` + ); + + document.querySelector(".docs-search-query").addEventListener("click", () => { + openModal(); + }); + + document + .querySelector(".close-search-modal") + .addEventListener("click", () => { + closeModal(); + }); + + $(document).on("click", ".search-result-link", function () { + closeModal(); + }); + + document.addEventListener("keydown", (event) => { + if ((event.ctrlKey || event.metaKey) && event.key === "/") { + openModal(); + } else if (event.key === "Escape") { + closeModal(); + } + + return false; + }); + + // Functions to open and close a modal + function openModal() { + let searchModal = document.querySelector("#search-modal"); + + searchModal.classList.add("is-active"); + document.querySelector(".documenter-search-input").focus(); + } + + function closeModal() { + let searchModal = document.querySelector("#search-modal"); + let initial_search_body = ` +
Type something to get started!
+ `; + + searchModal.classList.remove("is-active"); + document.querySelector(".documenter-search-input").blur(); + + if (!$(".search-modal-card-body").hasClass("is-justify-content-center")) { + $(".search-modal-card-body").addClass("is-justify-content-center"); + } + + $(".documenter-search-input").val(""); + $(".search-modal-card-body").html(initial_search_body); + } + + document + .querySelector("#search-modal .modal-background") + .addEventListener("click", () => { + closeModal(); + }); +}); + +}) +//////////////////////////////////////////////////////////////////////////////// +require(['jquery'], function($) { + +// Manages the showing and hiding of the sidebar. +$(document).ready(function () { + var sidebar = $("#documenter > .docs-sidebar"); + var sidebar_button = $("#documenter-sidebar-button"); + sidebar_button.click(function (ev) { + ev.preventDefault(); + sidebar.toggleClass("visible"); + if (sidebar.hasClass("visible")) { + // Makes sure that the current menu item is visible in the sidebar. + $("#documenter .docs-menu a.is-active").focus(); + } + }); + $("#documenter > .docs-main").bind("click", function (ev) { + if ($(ev.target).is(sidebar_button)) { + return; + } + if (sidebar.hasClass("visible")) { + sidebar.removeClass("visible"); + } + }); +}); + +// Resizes the package name / sitename in the sidebar if it is too wide. +// Inspired by: https://github.com/davatron5000/FitText.js +$(document).ready(function () { + e = $("#documenter .docs-autofit"); + function resize() { + var L = parseInt(e.css("max-width"), 10); + var L0 = e.width(); + if (L0 > L) { + var h0 = parseInt(e.css("font-size"), 10); + e.css("font-size", (L * h0) / L0); + // TODO: make sure it survives resizes? + } + } + // call once and then register events + resize(); + $(window).resize(resize); + $(window).on("orientationchange", resize); +}); + +// Scroll the navigation bar to the currently selected menu item +$(document).ready(function () { + var sidebar = $("#documenter .docs-menu").get(0); + var active = $("#documenter .docs-menu .is-active").get(0); + if (typeof active !== "undefined") { + sidebar.scrollTop = active.offsetTop - sidebar.offsetTop - 15; + } +}); + +}) +//////////////////////////////////////////////////////////////////////////////// +require(['jquery'], function($) { + +// Theme picker setup +$(document).ready(function () { + // onchange callback + $("#documenter-themepicker").change(function themepick_callback(ev) { + var themename = $("#documenter-themepicker option:selected").attr("value"); + if (themename === "auto") { + // set_theme(window.matchMedia('(prefers-color-scheme: dark)').matches ? 'dark' : 'light'); + window.localStorage.removeItem("documenter-theme"); + } else { + // set_theme(themename); + window.localStorage.setItem("documenter-theme", themename); + } + // We re-use the global function from themeswap.js to actually do the swapping. + set_theme_from_local_storage(); + }); + + // Make sure that the themepicker displays the correct theme when the theme is retrieved + // from localStorage + if (typeof window.localStorage !== "undefined") { + var theme = window.localStorage.getItem("documenter-theme"); + if (theme !== null) { + $("#documenter-themepicker option").each(function (i, e) { + e.selected = e.value === theme; + }); + } + } +}); + +}) +//////////////////////////////////////////////////////////////////////////////// +require(['jquery'], function($) { + +// update the version selector with info from the siteinfo.js and ../versions.js files +$(document).ready(function () { + // If the version selector is disabled with DOCUMENTER_VERSION_SELECTOR_DISABLED in the + // siteinfo.js file, we just return immediately and not display the version selector. + if ( + typeof DOCUMENTER_VERSION_SELECTOR_DISABLED === "boolean" && + DOCUMENTER_VERSION_SELECTOR_DISABLED + ) { + return; + } + + var version_selector = $("#documenter .docs-version-selector"); + var version_selector_select = $("#documenter .docs-version-selector select"); + + version_selector_select.change(function (x) { + target_href = version_selector_select + .children("option:selected") + .get(0).value; + window.location.href = target_href; + }); + + // add the current version to the selector based on siteinfo.js, but only if the selector is empty + if ( + typeof DOCUMENTER_CURRENT_VERSION !== "undefined" && + $("#version-selector > option").length == 0 + ) { + var option = $( + "" + ); + version_selector_select.append(option); + } + + if (typeof DOC_VERSIONS !== "undefined") { + var existing_versions = version_selector_select.children("option"); + var existing_versions_texts = existing_versions.map(function (i, x) { + return x.text; + }); + DOC_VERSIONS.forEach(function (each) { + var version_url = documenterBaseURL + "/../" + each + "/"; + var existing_id = $.inArray(each, existing_versions_texts); + // if not already in the version selector, add it as a new option, + // otherwise update the old option with the URL and enable it + if (existing_id == -1) { + var option = $( + "" + ); + version_selector_select.append(option); + } else { + var option = existing_versions[existing_id]; + option.value = version_url; + option.disabled = false; + } + }); + } + + // only show the version selector if the selector has been populated + if (version_selector_select.children("option").length > 0) { + version_selector.toggleClass("visible"); + } +}); + +}) diff --git a/dev/assets/themes/documenter-dark.css b/dev/assets/themes/documenter-dark.css new file mode 100644 index 0000000..1d71701 --- /dev/null +++ b/dev/assets/themes/documenter-dark.css @@ -0,0 +1,7 @@ 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h1,html.theme--documenter-dark .content h2,html.theme--documenter-dark .content h3,html.theme--documenter-dark .content h4,html.theme--documenter-dark .content h5,html.theme--documenter-dark .content h6{color:#f2f2f2;font-weight:600;line-height:1.125}html.theme--documenter-dark .content h1{font-size:2em;margin-bottom:0.5em}html.theme--documenter-dark .content h1:not(:first-child){margin-top:1em}html.theme--documenter-dark .content h2{font-size:1.75em;margin-bottom:0.5714em}html.theme--documenter-dark .content h2:not(:first-child){margin-top:1.1428em}html.theme--documenter-dark .content h3{font-size:1.5em;margin-bottom:0.6666em}html.theme--documenter-dark .content h3:not(:first-child){margin-top:1.3333em}html.theme--documenter-dark .content h4{font-size:1.25em;margin-bottom:0.8em}html.theme--documenter-dark .content h5{font-size:1.125em;margin-bottom:0.8888em}html.theme--documenter-dark .content h6{font-size:1em;margin-bottom:1em}html.theme--documenter-dark .content 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.docs-logo>img.is-5by4{padding-top:80%}html.theme--documenter-dark .image.is-4by3,html.theme--documenter-dark #documenter .docs-sidebar .docs-logo>img.is-4by3{padding-top:75%}html.theme--documenter-dark .image.is-3by2,html.theme--documenter-dark #documenter .docs-sidebar .docs-logo>img.is-3by2{padding-top:66.6666%}html.theme--documenter-dark .image.is-5by3,html.theme--documenter-dark #documenter .docs-sidebar .docs-logo>img.is-5by3{padding-top:60%}html.theme--documenter-dark .image.is-16by9,html.theme--documenter-dark #documenter .docs-sidebar .docs-logo>img.is-16by9{padding-top:56.25%}html.theme--documenter-dark .image.is-2by1,html.theme--documenter-dark #documenter .docs-sidebar .docs-logo>img.is-2by1{padding-top:50%}html.theme--documenter-dark .image.is-3by1,html.theme--documenter-dark #documenter .docs-sidebar .docs-logo>img.is-3by1{padding-top:33.3333%}html.theme--documenter-dark .image.is-4by5,html.theme--documenter-dark #documenter .docs-sidebar 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.hljs-string{color:#38a}.hljs-emphasis{font-style:italic}.hljs-strong{font-weight:bold}.gap-4{gap:1rem} diff --git a/dev/assets/themeswap.js b/dev/assets/themeswap.js new file mode 100644 index 0000000..9f5eebe --- /dev/null +++ b/dev/assets/themeswap.js @@ -0,0 +1,84 @@ +// Small function to quickly swap out themes. Gets put into the tag.. +function set_theme_from_local_storage() { + // Initialize the theme to null, which means default + var theme = null; + // If the browser supports the localstorage and is not disabled then try to get the + // documenter theme + if (window.localStorage != null) { + // Get the user-picked theme from localStorage. May be `null`, which means the default + // theme. + theme = window.localStorage.getItem("documenter-theme"); + } + // Check if the users preference is for dark color scheme + var darkPreference = + window.matchMedia("(prefers-color-scheme: dark)").matches === true; + // Initialize a few variables for the loop: + // + // - active: will contain the index of the theme that should be active. Note that there + // is no guarantee that localStorage contains sane values. If `active` stays `null` + // we either could not find the theme or it is the default (primary) theme anyway. + // Either way, we then need to stick to the primary theme. + // + // - disabled: style sheets that should be disabled (i.e. all the theme style sheets + // that are not the currently active theme) + var active = null; + var disabled = []; + var primaryLightTheme = null; + var primaryDarkTheme = null; + for (var i = 0; i < document.styleSheets.length; i++) { + var ss = document.styleSheets[i]; + // The tag of each style sheet is expected to have a data-theme-name attribute + // which must contain the name of the theme. The names in localStorage much match this. + var themename = ss.ownerNode.getAttribute("data-theme-name"); + // attribute not set => non-theme stylesheet => ignore + if (themename === null) continue; + // To distinguish the default (primary) theme, it needs to have the data-theme-primary + // attribute set. + if (ss.ownerNode.getAttribute("data-theme-primary") !== null) { + primaryLightTheme = themename; + } + // Check if the theme is primary dark theme so that we could store its name in darkTheme + if (ss.ownerNode.getAttribute("data-theme-primary-dark") !== null) { + primaryDarkTheme = themename; + } + // If we find a matching theme (and it's not the default), we'll set active to non-null + if (themename === theme) active = i; + // Store the style sheets of inactive themes so that we could disable them + if (themename !== theme) disabled.push(ss); + } + var activeTheme = null; + if (active !== null) { + // If we did find an active theme, we'll (1) add the theme--$(theme) class to + document.getElementsByTagName("html")[0].className = "theme--" + theme; + activeTheme = theme; + } else { + // If we did _not_ find an active theme, then we need to fall back to the primary theme + // which can either be dark or light, depending on the user's OS preference. + var activeTheme = darkPreference ? primaryDarkTheme : primaryLightTheme; + // In case it somehow happens that the relevant primary theme was not found in the + // preceding loop, we abort without doing anything. + if (activeTheme === null) { + console.error("Unable to determine primary theme."); + return; + } + // When switching to the primary light theme, then we must not have a class name + // for the tag. 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The names in localStorage much match this. + var themename = ss.ownerNode.getAttribute("data-theme-name"); + // attribute not set => non-theme stylesheet => ignore + if (themename === null) continue; + // we'll disable all the stylesheets, except for the active one + ss.disabled = !(themename == activeTheme); + } +} +set_theme_from_local_storage(); diff --git a/dev/assets/warner.js b/dev/assets/warner.js new file mode 100644 index 0000000..3f6f5d0 --- /dev/null +++ b/dev/assets/warner.js @@ -0,0 +1,52 @@ +function maybeAddWarning() { + // DOCUMENTER_NEWEST is defined in versions.js, DOCUMENTER_CURRENT_VERSION and DOCUMENTER_STABLE + // in siteinfo.js. + // If either of these are undefined something went horribly wrong, so we abort. + if ( + window.DOCUMENTER_NEWEST === undefined || + window.DOCUMENTER_CURRENT_VERSION === undefined || + window.DOCUMENTER_STABLE === undefined + ) { + return; + } + + // Current version is not a version number, so we can't tell if it's the newest version. Abort. + if (!/v(\d+\.)*\d+/.test(window.DOCUMENTER_CURRENT_VERSION)) { + return; + } + + // Current version is newest version, so no need to add a warning. + if (window.DOCUMENTER_NEWEST === window.DOCUMENTER_CURRENT_VERSION) { + return; + } + + // Add a noindex meta tag (unless one exists) so that search engines don't index this version of the docs. + if (document.body.querySelector('meta[name="robots"]') === null) { + const meta = document.createElement("meta"); + meta.name = "robots"; + meta.content = "noindex"; + + document.getElementsByTagName("head")[0].appendChild(meta); + } + + const div = document.createElement("div"); + div.classList.add("outdated-warning-overlay"); + const closer = document.createElement("button"); + closer.classList.add("outdated-warning-closer", "delete"); + closer.addEventListener("click", function () { + document.body.removeChild(div); + }); + const href = window.documenterBaseURL + "/../" + window.DOCUMENTER_STABLE; + div.innerHTML = + 'This documentation is not for the latest stable release, but for either the development version or an older release.
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Ket.jl

Dev

Toolbox for quantum information, nonlocality, and entanglement

diff --git a/dev/objects.inv b/dev/objects.inv new file mode 100644 index 0000000..fe95e9c Binary files /dev/null and b/dev/objects.inv differ diff --git a/dev/search_index.js b/dev/search_index.js new file mode 100644 index 0000000..246a385 --- /dev/null +++ b/dev/search_index.js @@ -0,0 +1,3 @@ +var documenterSearchIndex = {"docs": +[{"location":"api/#API-reference","page":"API reference","title":"API reference","text":"","category":"section"},{"location":"api/","page":"API reference","title":"API reference","text":"Modules = [Ket]","category":"page"},{"location":"api/#Ket._fiducial_WH-Union{Tuple{T}, Tuple{Type{T}, Integer}} where T","page":"API reference","title":"Ket._fiducial_WH","text":"_fiducial_WH(d::Integer)\n\nComputes the fiducial Weyl-Heisenberg vector of dimension d.\n\nReference: Appleby, Yadsan-Appleby, Zauner, arXiv:1209.1813 http://www.gerhardzauner.at/sicfiducials.html\n\n\n\n\n\n","category":"method"},{"location":"api/#Ket._partition-Union{Tuple{T}, Tuple{T, T}} where T<:Integer","page":"API reference","title":"Ket._partition","text":"partition(n::Integer, k::Integer)\n\nIf n ≥ k partitions the set 1:n into k parts as equally sized as possible. Otherwise partitions it into n parts of size 1.\n\n\n\n\n\n","category":"method"},{"location":"api/#Ket.anti_isotropic-Union{Tuple{Type{T}}, Tuple{T}, Tuple{Type{T}, Real}, Tuple{Type{T}, Real, Integer}} where T<:Number","page":"API reference","title":"Ket.anti_isotropic","text":"Produces the anti-isotropic state of local dimension d with visibility v\n\n\n\n\n\n","category":"method"},{"location":"api/#Ket.binary_entropy-Tuple{Real, Real}","page":"API reference","title":"Ket.binary_entropy","text":"binary_entropy([b=2,] p::Real)\n\nComputes the Shannon entropy -p log(p) - (1-p)log(1-p) of a probability p using a base b logarithm.\n\nReference: Entropy (information theory).\n\n\n\n\n\n","category":"method"},{"location":"api/#Ket.binary_relative_entropy-Tuple{Real, Real, Real}","page":"API reference","title":"Ket.binary_relative_entropy","text":"binary_relative_entropy([b=2,] p::Real, q::Real)\n\nComputes the binary relative entropy D(p||q) = p log(p/q) + (1-p) log((1-p)/(1-q)) between two probabilities p and q using a base b logarithm.\n\nReference: Relative entropy.\n\n\n\n\n\n","category":"method"},{"location":"api/#Ket.cglmp-Union{Tuple{T}, Tuple{Type{T}, Integer}} where T","page":"API reference","title":"Ket.cglmp","text":"cglmp([T=Float64,] d::Integer)\n\nCGLMP nonlocal game in full probability notation. If T is an integer type the game is unnormalized.\n\nReferences: arXiv:quant-ph/0106024 for the original game, and arXiv:2005.13418 for the form presented here.\n\n\n\n\n\n","category":"method"},{"location":"api/#Ket.chsh-Union{Tuple{Type{T}}, Tuple{T}, Tuple{Type{T}, Integer}} where T","page":"API reference","title":"Ket.chsh","text":"chsh([T=Float64,] d::Integer = 2)\n\nCHSH-d nonlocal game in full probability notation. If T is an integer type the game is unnormalized.\n\nReference: Buhrman and Massar, arXiv:quant-ph/0409066.\n\n\n\n\n\n","category":"method"},{"location":"api/#Ket.cleanup!-Union{Tuple{AbstractArray{T}}, Tuple{T}} where T<:Number","page":"API reference","title":"Ket.cleanup!","text":"cleanup!(M::AbstractArray{T}; tol = Base.rtoldefault(real(T)))\n\nZeroes out real or imaginary parts of M that are smaller than tol.\n\n\n\n\n\n","category":"method"},{"location":"api/#Ket.clock-Union{Tuple{T}, Tuple{Type{T}, Integer}, Tuple{Type{T}, Integer, Integer}} where T<:Number","page":"API reference","title":"Ket.clock","text":"clock([T=ComplexF64,] d::Integer, p::Integer = 1)\n\nConstructs the clock operator Z of dimension d to the power p.\n\nReference: Generalized Clifford algebra\n\n\n\n\n\n","category":"method"},{"location":"api/#Ket.correlation_tensor-Union{Tuple{AbstractArray{T, N2}}, Tuple{T}, Tuple{N2}} where {N2, T<:Number}","page":"API reference","title":"Ket.correlation_tensor","text":"correlation_tensor(p::AbstractArray{T, N2}; marg::Bool = true)\n\nApplies N sets of POVMs onto a state rho to form a probability array. Convert a 2x...x2xmx...xm probability array into\n\na mx...xm correlation array (no marginals)\na (m+1)x...x(m+1) correlation array (marginals).\n\n\n\n\n\n","category":"method"},{"location":"api/#Ket.dilate_povm-Tuple{Vector{<:AbstractMatrix}}","page":"API reference","title":"Ket.dilate_povm","text":"dilate_povm(E::Vector{<:AbstractMatrix})\n\nDoes the Naimark dilation of a POVM given as a vector of matrices. This always works, but is wasteful if the POVM elements are not full rank.\n\n\n\n\n\n","category":"method"},{"location":"api/#Ket.dilate_povm-Union{Tuple{Array{Vector{T}, 1}}, Tuple{T}} where T<:Union{Real, Complex}","page":"API reference","title":"Ket.dilate_povm","text":"dilate_povm(vecs::Vector{Vector{T}})\n\nDoes the Naimark dilation of a rank-1 POVM given as a vector of vectors. This is the minimal dilation.\n\n\n\n\n\n","category":"method"},{"location":"api/#Ket.entropy-Tuple{Real, AbstractMatrix}","page":"API reference","title":"Ket.entropy","text":"entropy([b=2,] ρ::AbstractMatrix)\n\nComputes the von Neumann entropy -tr(ρ log ρ) of a positive semidefinite operator ρ using a base b logarithm.\n\nReference: von Neumann entropy.\n\n\n\n\n\n","category":"method"},{"location":"api/#Ket.entropy-Tuple{Real, AbstractVector}","page":"API reference","title":"Ket.entropy","text":"entropy([b=2,] p::AbstractVector)\n\nComputes the Shannon entropy -Σᵢpᵢlog(pᵢ) of a non-negative vector p using a base b logarithm.\n\nReference: Entropy (information theory).\n\n\n\n\n\n","category":"method"},{"location":"api/#Ket.fp2cg-Union{Tuple{AbstractArray{T, 4}}, Tuple{T}} where T<:Real","page":"API reference","title":"Ket.fp2cg","text":"fp2cg(V::Array{T,4}) where {T <: Real}\n\nTakes a bipartite Bell functional V in full probability notation and transforms it to Collins-Gisin notation.\n\n\n\n\n\n","category":"method"},{"location":"api/#Ket.gell_mann!-Union{Tuple{T}, Tuple{AbstractMatrix{T}, Integer, Integer}, Tuple{AbstractMatrix{T}, Integer, Integer, Integer}} where T<:Number","page":"API reference","title":"Ket.gell_mann!","text":"gell_mann!(res::AbstractMatrix{T}, i::Integer, j::Integer, d::Integer = 3)\n\nIn-place version of gell_mann.\n\n\n\n\n\n","category":"method"},{"location":"api/#Ket.gell_mann-Union{Tuple{Type{T}}, Tuple{T}, Tuple{Type{T}, Integer}} where T<:Number","page":"API reference","title":"Ket.gell_mann","text":"gell_mann([T=ComplexF64,], d::Integer = 3)\n\nConstructs the set G of generalized Gell-Mann matrices in dimension d such that G[1] = I and G[i]*G[j] = 2 δ_ij.\n\nReference: Generalizations of Pauli matrices\n\n\n\n\n\n","category":"method"},{"location":"api/#Ket.gell_mann-Union{Tuple{T}, Tuple{Type{T}, Integer, Integer}, Tuple{Type{T}, Integer, Integer, Integer}} where T<:Number","page":"API reference","title":"Ket.gell_mann","text":"gell_mann([T=ComplexF64,], i::Integer, j::Integer, d::Integer = 3)\n\nConstructs the set i,jth Gell-Mann matrix of dimension d.\n\nReference: Generalizations of Pauli matrices\n\n\n\n\n\n","category":"method"},{"location":"api/#Ket.isotropic-Union{Tuple{Type{T}}, Tuple{T}, Tuple{Type{T}, Real}, Tuple{Type{T}, Real, Integer}} where T<:Number","page":"API reference","title":"Ket.isotropic","text":"Produces the isotropic state of local dimension d with visibility v\n\n\n\n\n\n","category":"method"},{"location":"api/#Ket.ket-Union{Tuple{T}, Tuple{Type{T}, Integer, Integer}} where T<:Number","page":"API reference","title":"Ket.ket","text":"ket([T=ComplexF64,] i::Integer, d::Integer)\n\nProduces a ket of dimension d with nonzero element i.\n\n\n\n\n\n","category":"method"},{"location":"api/#Ket.ketbra-Tuple{AbstractVector}","page":"API reference","title":"Ket.ketbra","text":"ketbra(v::AbstractVector)\n\nProduces a ketbra of vector v.\n\n\n\n\n\n","category":"method"},{"location":"api/#Ket.kyfan_norm","page":"API reference","title":"Ket.kyfan_norm","text":"kyfan_norm(X::AbstractMatrix, k::Int, p::Real = 2)\n\nComputes Ky-Fan (k,p) norm of matrix X.\n\n\n\n\n\n","category":"function"},{"location":"api/#Ket.local_bound-Union{Tuple{Array{T, 4}}, Tuple{T}} where T<:Real","page":"API reference","title":"Ket.local_bound","text":"local_bound(G::Array{T,4})\n\nComputes the local bound of a bipartite Bell functional G, written in full probability notation as a 4-dimensional array.\n\n\n\n\n\n","category":"method"},{"location":"api/#Ket.mub-Union{Tuple{T}, Tuple{Type{T}, Integer}} where T<:Number","page":"API reference","title":"Ket.mub","text":"mub(d::Integer)\n\nConstruction of the standard complete set of MUBs. The output contains 1+minᵢ pᵢ^rᵢ bases, where d = ∏ᵢ pᵢ^rᵢ.\n\nReference: Durt, Englert, Bengtsson, Życzkowski, arXiv:1004.3348.\n\n\n\n\n\n","category":"method"},{"location":"api/#Ket.phiplus-Union{Tuple{Type{T}}, Tuple{T}, Tuple{Type{T}, Integer}} where T<:Number","page":"API reference","title":"Ket.phiplus","text":"Produces the maximally entangled state Φ⁺ of local dimension d\n\n\n\n\n\n","category":"method"},{"location":"api/#Ket.povm-Union{Tuple{Array{T, 4}}, Tuple{T}, Tuple{Array{T, 4}, Vector{Int64}}} where T<:Number","page":"API reference","title":"Ket.povm","text":"povm(A::Array{T, 4}, n::Vector{Int64})\n\nConverts a set of POVMs in the common tensor format into a matrix of matrices. The second argument is fixed by the size of A but can also contain custom number of outcomes.\n\n\n\n\n\n","category":"method"},{"location":"api/#Ket.povm-Union{Tuple{Vector{<:AbstractMatrix{T}}}, Tuple{T}} where T<:Number","page":"API reference","title":"Ket.povm","text":"povm(B::Vector{<:AbstractMatrix{T}})\n\nCreates a set of (projective) POVMs from a set of bases given as unitary matrices.\n\n\n\n\n\n","category":"method"},{"location":"api/#Ket.probability_tensor-Union{Tuple{N}, Tuple{T2}, Tuple{T1}, Tuple{LinearAlgebra.Hermitian{T1, Matrix{T1}}, Vararg{Array{Array{LinearAlgebra.Hermitian{T2, Matrix{T2}}, 1}, 1}, N}}} where {T1<:Number, T2<:Number, N}","page":"API reference","title":"Ket.probability_tensor","text":"probability_tensor(Aax::Vector{POVM{T}})\n\nApplies N sets of POVMs onto a state rho to form a probability array.\n\n\n\n\n\n","category":"method"},{"location":"api/#Ket.proj-Union{Tuple{T}, Tuple{Type{T}, Integer, Integer}} where T<:Number","page":"API reference","title":"Ket.proj","text":"proj([T=ComplexF64,] i::Integer, d::Integer)\n\nProduces a projector onto the basis state i in dimension d.\n\n\n\n\n\n","category":"method"},{"location":"api/#Ket.psiminus-Union{Tuple{Type{T}}, Tuple{T}, Tuple{Type{T}, Integer}} where T<:Number","page":"API reference","title":"Ket.psiminus","text":"Produces the maximally entangled state ψ⁻ of local dimension d\n\n\n\n\n\n","category":"method"},{"location":"api/#Ket.random_povm-Union{Tuple{T}, Tuple{Type{T}, Integer, Integer}, Tuple{Type{T}, Integer, Integer, Integer}} where T<:Number","page":"API reference","title":"Ket.random_povm","text":"random_povm([T=ComplexF64,] d::Integer, n::Integer, r::Integer)\n\nProduces a random POVM of dimension d with n outcomes and rank min(k, d).\n\nReference: Heinosaari et al., arXiv:1902.04751.\n\n\n\n\n\n","category":"method"},{"location":"api/#Ket.random_probability-Union{Tuple{T}, Tuple{Type{T}, Integer}} where T","page":"API reference","title":"Ket.random_probability","text":"random_probability([T=Float64,] d::Integer)\n\nProduces a random probability vector of dimension d uniformly distributed on the simplex.\n\nReference: Dirichlet distribution\n\n\n\n\n\n","category":"method"},{"location":"api/#Ket.random_state-Union{Tuple{T}, Tuple{Type{T}, Integer}, Tuple{Type{T}, Integer, Integer}} where T","page":"API reference","title":"Ket.random_state","text":"random_state([T=ComplexF64,] d::Integer, k::Integer = d)\n\nProduces a uniformly distributed random quantum state in dimension d with rank k.\n\nReference: Życzkowski and Sommers, arXiv:quant-ph/0012101.\n\n\n\n\n\n","category":"method"},{"location":"api/#Ket.random_state_vector-Union{Tuple{T}, Tuple{Type{T}, Integer}} where T","page":"API reference","title":"Ket.random_state_vector","text":"random_state_vector([T=ComplexF64,] d::Integer)\n\nProduces a Haar-random quantum state vector in dimension d.\n\nReference: Życzkowski and Sommers, arXiv:quant-ph/0012101.\n\n\n\n\n\n","category":"method"},{"location":"api/#Ket.random_unitary-Union{Tuple{T}, Tuple{Type{T}, Integer}} where T<:Number","page":"API reference","title":"Ket.random_unitary","text":"random_unitary([T=ComplexF64,] d::Integer)\n\nProduces a Haar-random unitary matrix in dimension d. If T is a real type the output is instead a Haar-random (real) orthogonal matrix.\n\nReference: Mezzadri, arXiv:math-ph/0609050.\n\n\n\n\n\n","category":"method"},{"location":"api/#Ket.relative_entropy-Union{Tuple{S}, Tuple{T}, Tuple{Real, AbstractMatrix{T}, AbstractMatrix{S}}} where {T, S<:Number}","page":"API reference","title":"Ket.relative_entropy","text":"relative_entropy([b=2,] ρ::AbstractMatrix, σ::AbstractMatrix)\n\nComputes the (quantum) relative entropy tr(ρ (log ρ - log σ)) between positive semidefinite matrices ρ and σ using a base b logarithm. Note that the support of ρ must be contained in the support of σ but for efficiency this is not checked.\n\nReference: Quantum relative entropy.\n\n\n\n\n\n","category":"method"},{"location":"api/#Ket.relative_entropy-Union{Tuple{S}, Tuple{T}, Tuple{Real, AbstractVector{T}, AbstractVector{S}}} where {T, S<:Real}","page":"API reference","title":"Ket.relative_entropy","text":"relative_entropy([b=2,] p::AbstractVector, q::AbstractVector)\n\nComputes the relative entropy D(p||q) = Σᵢpᵢlog(pᵢ/qᵢ) between two non-negative vectors p and q using a base b logarithm. Note that the support of p must be contained in the support of q but for efficiency this is not checked.\n\nReference: Relative entropy.\n\n\n\n\n\n","category":"method"},{"location":"api/#Ket.schatten_norm-Tuple{AbstractMatrix, Real}","page":"API reference","title":"Ket.schatten_norm","text":"schatten_norm(X::AbstractMatrix, p::Real)\n\nComputes Schatten p-norm of matrix X.\n\n\n\n\n\n","category":"method"},{"location":"api/#Ket.shift-Union{Tuple{T}, Tuple{Type{T}, Integer}, Tuple{Type{T}, Integer, Integer}} where T<:Number","page":"API reference","title":"Ket.shift","text":"shift([T=ComplexF64,] d::Integer, p::Integer = 1)\n\nConstructs the shift operator X of dimension d to the power p.\n\nReference: Generalized Clifford algebra\n\n\n\n\n\n","category":"method"},{"location":"api/#Ket.sic_povm-Union{Tuple{T}, Tuple{Type{T}, Integer}} where T","page":"API reference","title":"Ket.sic_povm","text":"sic_povm(d::Integer)\n\nConstructs a vector of d² vectors |vᵢ⟩ such that |vᵢ⟩⟨vᵢ| forms a SIC-POVM of dimension d. This construction is based on the Weyl-Heisenberg fiducial.\n\nReference: Appleby, Yadsan-Appleby, Zauner, arXiv:1209.1813\n\n\n\n\n\n","category":"method"},{"location":"api/#Ket.test_mub-Union{Tuple{Array{Matrix{T}, 1}}, Tuple{T}} where T<:Number","page":"API reference","title":"Ket.test_mub","text":"Check whether the input is indeed mutually unbiased\n\n\n\n\n\n","category":"method"},{"location":"api/#Ket.test_sic-Union{Tuple{Array{Vector{T}, 1}}, Tuple{T}} where T<:Number","page":"API reference","title":"Ket.test_sic","text":"test_sic(vecs)\n\nTests whether vecs is a vector of d² vectors |vᵢ⟩ such that |vᵢ⟩⟨vᵢ| forms a SIC-POVM of dimension d.\n\n\n\n\n\n","category":"method"},{"location":"api/#Ket.trace_norm-Tuple{AbstractMatrix}","page":"API reference","title":"Ket.trace_norm","text":"trace_norm(X::AbstractMatrix)\n\nComputes trace norm of matrix X. \n\n\n\n\n\n","category":"method"},{"location":"api/#Ket.tsirelson_bound-Tuple{Matrix{<:Real}, Vector{<:Integer}, Integer}","page":"API reference","title":"Ket.tsirelson_bound","text":"tsirelson_bound(CG::Matrix, scenario::Vector, level::Integer)\n\nUpper bounds the Tsirelson bound of a bipartite Bell funcional game CG, written in Collins-Gisin notation. scenario is vector detailing the number of inputs and outputs, in the order [oa, ob, ia, ib]. level is an integer determining the level of the NPA hierarchy.\n\nThis function requires Moment. It is only available if you first do \"import MATLAB\" or \"using MATLAB\".\n\n\n\n\n\n","category":"method"},{"location":"","page":"Home","title":"Home","text":"EditURL = \"https://github.com/araujoms/Ket.jl/blob/master/README.md\"","category":"page"},{"location":"#Ket.jl","page":"Home","title":"Ket.jl","text":"","category":"section"},{"location":"","page":"Home","title":"Home","text":"(Image: Dev)","category":"page"},{"location":"","page":"Home","title":"Home","text":"Toolbox for quantum information, nonlocality, and entanglement","category":"page"}] +} diff --git a/dev/siteinfo.js b/dev/siteinfo.js new file mode 100644 index 0000000..3343491 --- /dev/null +++ b/dev/siteinfo.js @@ -0,0 +1 @@ +var DOCUMENTER_CURRENT_VERSION = "dev"; diff --git a/index.html b/index.html new file mode 100644 index 0000000..1a6cc11 --- /dev/null +++ b/index.html @@ -0,0 +1,2 @@ + + diff --git a/versions.js b/versions.js new file mode 100644 index 0000000..4ec0f8f --- /dev/null +++ b/versions.js @@ -0,0 +1,5 @@ +var DOC_VERSIONS = [ + "dev", +]; +var DOCUMENTER_NEWEST = "dev"; +var DOCUMENTER_STABLE = "dev";