diff --git a/dev/.documenter-siteinfo.json b/dev/.documenter-siteinfo.json index ea51b74..7b89cf7 100644 --- a/dev/.documenter-siteinfo.json +++ b/dev/.documenter-siteinfo.json @@ -1 +1 @@ -{"documenter":{"julia_version":"1.10.4","generation_timestamp":"2024-07-14T13:21:11","documenter_version":"1.5.0"}} \ No newline at end of file +{"documenter":{"julia_version":"1.10.4","generation_timestamp":"2024-07-16T16:33:21","documenter_version":"1.5.0"}} \ No newline at end of file diff --git a/dev/api/index.html b/dev/api/index.html index 88c8939..31389d7 100644 --- a/dev/api/index.html +++ b/dev/api/index.html @@ -1,2 +1,2 @@ -List of functions · Ket.jl

List of functions

Basic

Ket.ketFunction
ket([T=ComplexF64,] i::Integer, d::Integer = 2)

Produces a ket of dimension d with nonzero element i.

source
Ket.ketbraFunction
ketbra(v::AbstractVector)

Produces a ketbra of vector v.

source
Ket.projFunction
proj([T=ComplexF64,] i::Integer, d::Integer = 2)

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

source
Ket.pauliFunction
pauli([T=ComplexF64,], ind::Vector{<:Integer})

Constructs the Pauli matrices: 0 or "I" for the identity, 1 or "X" for the Pauli X operation, 2 or "Y" for the Pauli Y operator, and 3 or "Z" for the Pauli Z operator. Vectors of integers between 0 and 3 or strings of I, X, Y, Z automatically generate Kronecker products of the corresponding operators.

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

In-place version of gell_mann.

source
Ket.partial_traceFunction
partial_trace(X::AbstractMatrix, remove::Vector, dims::Vector)

Takes the partial trace of matrix X with subsystem dimensions dims over the subsystems in remove.

source
partial_trace(X::AbstractMatrix, remove::Integer, dims::Vector)

Takes the partial trace of matrix X with subsystem dimensions dims over the subsystem remove.

source
Ket.partial_transposeFunction
partial_transpose(X::AbstractMatrix, transp::Vector, dims::Vector)

Takes the partial transpose of matrix X with subsystem dimensions dims on the subsystems in transp.

source
partial_transpose(X::AbstractMatrix, transp::Integer, dims::Vector)

Takes the partial transpose of matrix X with subsystem dimensions dims on the subsystem transp.

source
Ket.permute_systemsFunction
permute_systems(X::AbstractVector, perm::Vector, dims::Vector)

Permutes the order of the subsystems of vector X with subsystem dimensions dims according to the permutation perm.

source
permute_systems(X::AbstractMatrix, perm::Vector, dims::Vector)

Permutes the order of the subsystems of the square matrix X, which is composed by square subsystems of dimensions dims, according to the permutation perm.

source
permute_systems(X::AbstractMatrix, perm::Vector, dims::Matrix)

Permutes the order of the subsystems of the matrix X, which is composed by subsystems of dimensions dims, according to the permutation perm. dims should be a n x 2 matrix where dims[i, 1] is the number of rows of subsystem i, and dims[i,2] is its number of columns.

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

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

source

Entropy

Ket.entropyFunction
entropy([base=2,] ρ::AbstractMatrix)

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

Reference: von Neumann entropy.

source
entropy([base=2,] p::AbstractVector)

Computes the Shannon entropy -Σᵢpᵢlog(pᵢ) of a non-negative vector p using a base base logarithm.

Reference: Entropy (information theory).

source
Ket.relative_entropyFunction
relative_entropy([base=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 base 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
relative_entropy([base=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 base 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.binary_relative_entropyFunction
binary_relative_entropy([base=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 base logarithm.

Reference: Relative entropy.

source
Ket.conditional_entropyFunction
conditional_entropy([base=2,] pAB::AbstractMatrix)

Computes the conditional Shannon entropy H(A|B) of the joint probability distribution pAB using a base base logarithm.

Reference: Conditional entropy.

source
conditional_entropy([base=2,], rho::AbstractMatrix, csys::AbstractVector, dims::AbstractVector)

Computes the conditional von Neumann entropy of rho with subsystem dimensions dims and conditioning systems csys, using a base base logarithm.

Reference: Conditional quantum entropy.

source

Entanglement

Ket.schmidt_decompositionFunction
schmidt_decomposition(ψ::AbstractVector, dims::AbstractVector{<:Integer})

Produces the Schmidt decomposition of ψ with subsystem dimensions dims. Returns the (sorted) Schmidt coefficients λ and isometries U, V such that kron(U', V')*ψ is of Schmidt form.

Reference: Schmidt decomposition.

source
schmidt_decomposition(ψ::AbstractVector, dims::AbstractVector{<:Integer})

Produces the Schmidt decomposition of ψ assuming equally-sized subsystems. Returns the (sorted) Schmidt coefficients λ and isometries U, V such that kron(U', V')*ψ is of Schmidt form.

Reference: Schmidt decomposition.

source

Measurements

Ket.sic_povmFunction
sic_povm([T=ComplexF64,] d::Integer)

Constructs a vector of 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_sicFunction
test_sic(vecs)

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

source
Ket.test_povmFunction
test_povm(A::Vector{<:AbstractMatrix{T}})

Checks if the measurement defined by A is valid (hermitian, semi-definite positive, and normalized).

source
Ket.dilate_povmFunction
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
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.povmFunction
povm(B::Vector{<:AbstractMatrix{T}})

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

source
povm(A::Array{T, 4}, n::Vector{Int64})

Converts a set of measurements 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.mubFunction
mub([T=ComplexF64,] 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

Nonlocality

Ket.chshFunction
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.local_boundFunction
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.

Reference: Araújo, Hirsch, and Quintino, arXiv:2005.13418.

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

Applies N sets of measurements 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.probability_tensorFunction
probability_tensor(rho::LA.Hermitian, all_Aax::Vector{Measurement}...)

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

source
Ket.fp2cgFunction
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

Norms

Ket.kyfan_normFunction
kyfan_norm(X::AbstractMatrix, k::Integer, p::Real = 2)

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

source
Ket.diamond_normFunction
diamond_norm(J::AbstractMatrix, dims::AbstractVector)

Computes the diamond norm of the supermap J given in the Choi-Jamiołkowski representation, with subsystem dimensions dims.

Reference: Diamond norm

source
diamond_norm(K::Vector{<:AbstractMatrix})

Computes the diamond norm of the CP map given by the Kraus operators K.

source

Random

Ket.random_stateFunction
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_unitaryFunction
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: Stewart, doi:10.1137/0717034.

source
Ket.random_povmFunction
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

States

Ket.state_phiplus_ketFunction
state_phiplus_ket([T=ComplexF64,] d::Integer = 2)

Produces the vector of the maximally entangled state Φ⁺ of local dimension d.

source
Ket.state_phiplusFunction
state_phiplus([T=ComplexF64,] d::Integer = 2; v::Real = 1)

Produces the maximally entangled state Φ⁺ of local dimension d with visibility v.

source
Ket.isotropicFunction
isotropic(v::Real, d::Integer = 2)

Produces the isotropic state of local dimension d with visibility v.

source
Ket.state_psiminus_ketFunction
state_psiminus_ket([T=ComplexF64,] d::Integer = 2)

Produces the vector of the maximally entangled state ψ⁻ of local dimension d.

source
Ket.state_psiminusFunction
state_psiminus([T=ComplexF64,] d::Integer = 2; v::Real = 1)

Produces the maximally entangled state ψ⁻ of local dimension d with visibility v.

source
Ket.state_ghz_ketFunction
state_ghz_ket([T=ComplexF64,] d::Integer = 2, N::Integer = 3; coeff = 1/√d)

Produces the vector of the GHZ state local dimension d.

source
Ket.state_ghzFunction
state_ghz([T=ComplexF64,] d::Integer = 2, N::Integer = 3; v::Real = 1, coeff = 1/√d)

Produces the GHZ state of local dimension d with visibility v.

source
Ket.state_w_ketFunction
state_w_ket([T=ComplexF64,] N::Integer = 3; coeff = 1/√d)

Produces the vector of the N-partite W state.

source
Ket.state_wFunction
state_w([T=ComplexF64,] N::Integer = 3; v::Real = 1, coeff = 1/√d)

Produces the N-partite W state with visibility v.

source
Ket.white_noiseFunction
white_noise(rho::AbstractMatrix, v::Real)

Returns v * rho + (1 - v) * id, where id is the maximally mixed state.

source
Ket.white_noise!Function
white_noise!(rho::AbstractMatrix, v::Real)

Modifies rho in place to tranform in into v * rho + (1 - v) * id where id is the maximally mixed state.

source

Supermaps

Ket.choiFunction
choi(K::Vector{<:AbstractMatrix})

Constructs the Choi-Jamiołkowski representation of the CP map given by the Kraus operators K. The convention used is that choi(K) = ∑ᵢⱼ |i⟩⟨j|⊗K|i⟩⟨j|K'

source

Internal functions

Ket._partitionFunction
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._fiducial_WHFunction
_fiducial_WH([T=ComplexF64,] 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._idxFunction
_idx(tidx::Vector, dims::Vector)

Converts a tensor index tidx = [i₁, i₂, ...] with subsystems dimensions dims to a standard index.

source
Ket._tidxFunction
_tidx(idx::Integer, dims::Vector)

Converts a standard index idx to a tensor index [i₁, i₂, ...] with subsystems dimensions dims.

source
+List of functions · Ket.jl

List of functions

Basic

Ket.ketFunction
ket([T=ComplexF64,] i::Integer, d::Integer = 2)

Produces a ket of dimension d with nonzero element i.

source
Ket.ketbraFunction
ketbra(v::AbstractVector)

Produces a ketbra of vector v.

source
Ket.projFunction
proj([T=ComplexF64,] i::Integer, d::Integer = 2)

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

source
Ket.pauliFunction
pauli([T=ComplexF64,], ind::Vector{<:Integer})

Constructs the Pauli matrices: 0 or "I" for the identity, 1 or "X" for the Pauli X operation, 2 or "Y" for the Pauli Y operator, and 3 or "Z" for the Pauli Z operator. Vectors of integers between 0 and 3 or strings of I, X, Y, Z automatically generate Kronecker products of the corresponding operators.

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

In-place version of gell_mann.

source
Ket.partial_traceFunction
partial_trace(X::AbstractMatrix, remove::Vector, dims::Vector)

Takes the partial trace of matrix X with subsystem dimensions dims over the subsystems in remove.

source
partial_trace(X::AbstractMatrix, remove::Integer, dims::Vector)

Takes the partial trace of matrix X with subsystem dimensions dims over the subsystem remove.

source
Ket.partial_transposeFunction
partial_transpose(X::AbstractMatrix, transp::Vector, dims::Vector)

Takes the partial transpose of matrix X with subsystem dimensions dims on the subsystems in transp.

source
partial_transpose(X::AbstractMatrix, transp::Integer, dims::Vector)

Takes the partial transpose of matrix X with subsystem dimensions dims on the subsystem transp.

source
Ket.permute_systemsFunction
permute_systems(X::AbstractVector, perm::Vector, dims::Vector)

Permutes the order of the subsystems of vector X with subsystem dimensions dims according to the permutation perm.

source
permute_systems(X::AbstractMatrix, perm::Vector, dims::Vector)

Permutes the order of the subsystems of the square matrix X, which is composed by square subsystems of dimensions dims, according to the permutation perm.

source
permute_systems(X::AbstractMatrix, perm::Vector, dims::Matrix)

Permutes the order of the subsystems of the matrix X, which is composed by subsystems of dimensions dims, according to the permutation perm. dims should be a n x 2 matrix where dims[i, 1] is the number of rows of subsystem i, and dims[i,2] is its number of columns.

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

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

source

Entropy

Ket.entropyFunction
entropy([base=2,] ρ::AbstractMatrix)

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

Reference: von Neumann entropy.

source
entropy([base=2,] p::AbstractVector)

Computes the Shannon entropy -Σᵢpᵢlog(pᵢ) of a non-negative vector p using a base base logarithm.

Reference: Entropy (information theory).

source
Ket.relative_entropyFunction
relative_entropy([base=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 base 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
relative_entropy([base=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 base 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.binary_relative_entropyFunction
binary_relative_entropy([base=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 base logarithm.

Reference: Relative entropy.

source
Ket.conditional_entropyFunction
conditional_entropy([base=2,] pAB::AbstractMatrix)

Computes the conditional Shannon entropy H(A|B) of the joint probability distribution pAB using a base base logarithm.

Reference: Conditional entropy.

source
conditional_entropy([base=2,], rho::AbstractMatrix, csys::AbstractVector, dims::AbstractVector)

Computes the conditional von Neumann entropy of rho with subsystem dimensions dims and conditioning systems csys, using a base base logarithm.

Reference: Conditional quantum entropy.

source

Entanglement

Ket.schmidt_decompositionFunction
schmidt_decomposition(ψ::AbstractVector, dims::AbstractVector{<:Integer})

Produces the Schmidt decomposition of ψ with subsystem dimensions dims. Returns the (sorted) Schmidt coefficients λ and isometries U, V such that kron(U', V')*ψ is of Schmidt form.

Reference: Schmidt decomposition.

source
schmidt_decomposition(ψ::AbstractVector, dims::AbstractVector{<:Integer})

Produces the Schmidt decomposition of ψ assuming equally-sized subsystems. Returns the (sorted) Schmidt coefficients λ and isometries U, V such that kron(U', V')*ψ is of Schmidt form.

Reference: Schmidt decomposition.

source

Measurements

Ket.sic_povmFunction
sic_povm([T=ComplexF64,] d::Integer)

Constructs a vector of 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_sicFunction
test_sic(vecs)

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

source
Ket.test_povmFunction
test_povm(A::Vector{<:AbstractMatrix{T}})

Checks if the measurement defined by A is valid (hermitian, semi-definite positive, and normalized).

source
Ket.dilate_povmFunction
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
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.povmFunction
povm(B::Vector{<:AbstractMatrix{T}})

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

source
povm(A::Array{T, 4}, n::Vector{Int64})

Converts a set of measurements 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.mubFunction
mub([T=ComplexF64,] 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

Nonlocality

Ket.chshFunction
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.local_boundFunction
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.

Reference: Araújo, Hirsch, and Quintino, arXiv:2005.13418.

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

Applies N sets of measurements 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.probability_tensorFunction
probability_tensor(rho::LA.Hermitian, all_Aax::Vector{Measurement}...)

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

source
Ket.fp2cgFunction
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

Norms

Ket.kyfan_normFunction
kyfan_norm(X::AbstractMatrix, k::Integer, p::Real = 2)

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

source
Ket.diamond_normFunction
diamond_norm(J::AbstractMatrix, dims::AbstractVector)

Computes the diamond norm of the supermap J given in the Choi-Jamiołkowski representation, with subsystem dimensions dims.

Reference: Diamond norm

source
diamond_norm(K::Vector{<:AbstractMatrix})

Computes the diamond norm of the CP map given by the Kraus operators K.

source

Random

Ket.random_stateFunction
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_unitaryFunction
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: Stewart, doi:10.1137/0717034.

source
Ket.random_povmFunction
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

States

Ket.state_phiplus_ketFunction
state_phiplus_ket([T=ComplexF64,] d::Integer = 2)

Produces the vector of the maximally entangled state Φ⁺ of local dimension d.

source
Ket.state_phiplusFunction
state_phiplus([T=ComplexF64,] d::Integer = 2; v::Real = 1)

Produces the maximally entangled state Φ⁺ of local dimension d with visibility v.

source
Ket.isotropicFunction
isotropic(v::Real, d::Integer = 2)

Produces the isotropic state of local dimension d with visibility v.

source
Ket.state_psiminus_ketFunction
state_psiminus_ket([T=ComplexF64,] d::Integer = 2)

Produces the vector of the maximally entangled state ψ⁻ of local dimension d.

source
Ket.state_psiminusFunction
state_psiminus([T=ComplexF64,] d::Integer = 2; v::Real = 1)

Produces the maximally entangled state ψ⁻ of local dimension d with visibility v.

source
Ket.state_ghz_ketFunction
state_ghz_ket([T=ComplexF64,] d::Integer = 2, N::Integer = 3; coeff = 1/√d)

Produces the vector of the GHZ state local dimension d.

source
Ket.state_ghzFunction
state_ghz([T=ComplexF64,] d::Integer = 2, N::Integer = 3; v::Real = 1, coeff = 1/√d)

Produces the GHZ state of local dimension d with visibility v.

source
Ket.state_w_ketFunction
state_w_ket([T=ComplexF64,] N::Integer = 3; coeff = 1/√d)

Produces the vector of the N-partite W state.

source
Ket.state_wFunction
state_w([T=ComplexF64,] N::Integer = 3; v::Real = 1, coeff = 1/√d)

Produces the N-partite W state with visibility v.

source
Ket.white_noiseFunction
white_noise(rho::AbstractMatrix, v::Real)

Returns v * rho + (1 - v) * id, where id is the maximally mixed state.

source
Ket.white_noise!Function
white_noise!(rho::AbstractMatrix, v::Real)

Modifies rho in place to tranform in into v * rho + (1 - v) * id where id is the maximally mixed state.

source

Supermaps

Ket.choiFunction
choi(K::Vector{<:AbstractMatrix})

Constructs the Choi-Jamiołkowski representation of the CP map given by the Kraus operators K. The convention used is that choi(K) = ∑ᵢⱼ |i⟩⟨j|⊗K|i⟩⟨j|K'

source

Internal functions

Ket._partitionFunction
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._fiducial_WHFunction
_fiducial_WH([T=ComplexF64,] 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._idxFunction
_idx(tidx::Vector, dims::Vector)

Converts a tensor index tidx = [i₁, i₂, ...] with subsystems dimensions dims to a standard index.

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Ket._tidxFunction
_tidx(idx::Integer, dims::Vector)

Converts a standard index idx to a tensor index [i₁, i₂, ...] with subsystems dimensions dims.

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diff --git a/dev/index.html b/dev/index.html index c9f43b3..938a19c 100644 --- a/dev/index.html +++ b/dev/index.html @@ -1,2 +1,2 @@ -Home · Ket.jl

Ket.jl

Dev

Toolbox for quantum information, nonlocality, and entanglement.

Highlights are the functions mub and sic_povm, that produce respectively MUBs and SIC-POVMs with arbitrary precision, local_bound that uses a parallelized algorithm to compute the local bound of a Bell inequality, and partial_trace and partial_transpose, that compute the partial trace and partial transpose in a way that can be used for optimization with JuMP. Also worth mentioning are the functions to produce uniformly-distributed random states, unitaries, and POVMs: random_state, random_unitary, random_povm. And the eponymous ket, of course.

For the full list of functions see the documentation.

+Home · Ket.jl

Ket.jl

Dev

Toolbox for quantum information, nonlocality, and entanglement.

Highlights are the functions mub and sic_povm, that produce respectively MUBs and SIC-POVMs with arbitrary precision, local_bound that uses a parallelized algorithm to compute the local bound of a Bell inequality, and partial_trace and partial_transpose, that compute the partial trace and partial transpose in a way that can be used for optimization with JuMP. Also worth mentioning are the functions to produce uniformly-distributed random states, unitaries, and POVMs: random_state, random_unitary, random_povm. And the eponymous ket, of course.

For the full list of functions see the documentation.