M1L6b.txt

#
# File:   content-mit-8422-1x-captions/M1L6b.txt
#
# Captions for 8.422x module
#
# This file has 54 caption lines.
#
# Do not add or delete any lines.  If there is text missing at the end, please add it to the last line.
#
#----------------------------------------

So we want to talk about some standard entangled states.
And the most basic state is a singlet state.
So if you have a state which is 01 minus 10 normalized,
this is an Einstein-Podolsky-Rosen state.
This needs now some explanation.
We have often encountered in [INAUDIBLE] states which are
simply a superposition of, if you interpret 01 as-- if you
interpret 01 as spin up or spin down,
you can [INAUDIBLE] quite often.
And I want to explain to you now what
is not an entangled state for the reasons of using
entanglement as as resource.
So first of all, I want to point out
this state is not a single photon because we
have entangled here two qubits.
Let me just contrast it.
If you have a single photon after beam splitter,
the single photon after beam splitter is in a superposition
of mode A, mode B 01 minus 10 divided by square root 2.
But now, 0 is the vacuum.
So we have not a system which can
be decomposed into two partial systems
A and B. You may even separate the system
and then manipulate you single qubits individually by putting
phase shifts on and doing other operations.
If you have this state, which is a superposition between having
a photon not having a vacuum and having a vacuum state,
the vacuum state itself is not a separate system.
You cannot take the vacuum and perform operations
on the vacuum.
So I know it has been confusing for me when I heard
about it for the first time.
We have, so to speak, here and entangled mode but not
an entangled state.
It's a singlet state.
It has some aspects of entanglement,
but it is not the entanglement we have defined as a resource.
So let me just repeat.
This may be an entangled mode, but to be in an entangled state
requires systems where you have two parts which
you can separate.
The second comment is we have situations
where we have two different parts,
but they can't be physically separated.
So part of our definition of entanglement as a resource
is that this state must be of two
physically distinct systems.
And we won't have parts which can be separately addressed,
manipulated, and measured.
In other words, if you weed out one part of an EPR pair,
the other part still exists.