• Register
PhysicsOverflow is a next-generation academic platform for physicists and astronomers, including a community peer review system and a postgraduate-level discussion forum analogous to MathOverflow.

Welcome to PhysicsOverflow! PhysicsOverflow is an open platform for community peer review and graduate-level Physics discussion.

Please help promote PhysicsOverflow ads elsewhere if you like it.


New printer friendly PO pages!

Migration to Bielefeld University was successful!

Please vote for this year's PhysicsOverflow ads!

Please do help out in categorising submissions. Submit a paper to PhysicsOverflow!

... see more

Tools for paper authors

Submit paper
Claim Paper Authorship

Tools for SE users

Search User
Reclaim SE Account
Request Account Merger
Nativise imported posts
Claim post (deleted users)
Import SE post

Users whose questions have been imported from Physics Stack Exchange, Theoretical Physics Stack Exchange, or any other Stack Exchange site are kindly requested to reclaim their account and not to register as a new user.

Public \(\beta\) tools

Report a bug with a feature
Request a new functionality
404 page design
Send feedback


(propose a free ad)

Site Statistics

204 submissions , 162 unreviewed
5,030 questions , 2,184 unanswered
5,344 answers , 22,705 comments
1,470 users with positive rep
816 active unimported users
More ...

  CHSH violation and entanglement of quantum states

+ 11 like - 0 dislike

How is the violation of the usual CHSH inequality by a quantum state related to the entanglement of that quantum state?

Say we know that exist Hermitian and unitary operators $A_{0}$, $A_{1}$, $B_{0}$ and $B_{1}$ such that $$\mathrm{tr} ( \rho ( A_{0}\otimes B_{0} + A_{0} \otimes B_{1} + A_{1}\otimes B_{0} - A_{1} \otimes B_{1} )) = 2+ c > 2,$$ then we know that the state $\rho$ must be entangled. But what else do we know? If we know the form of the operators $A_{j}$ and $B_{j}$, then there is certainly more to be said (see e.g. http://prl.aps.org/abstract/PRL/v87/i23/e230402 ). However, what if I do not want to assume anything about the measurements performed?

Can the value of $c$ be used to give a rigourous lower bound on any of the familar entanglement measures, such as log-negativity or relative entropy of entanglement?

Clearly, one could argue in a slightly circular fashion and define an entanglement measure as the maximal possible CHSH violation over all possible measurements. But is there anything else one can say?

This post has been migrated from (A51.SE)
asked Nov 18, 2011 in Theoretical Physics by Earl (405 points) [ no revision ]
Your questions is answered here: [arXiv:0907.2170](http://arxiv.org/abs/0907.2170). BTW, _device-independent_ is the key phrase to search for.

This post has been migrated from (A51.SE)
@PiotrMigdal Thanks for your comment. I had not thought of goggling for "device-independent" and was not aware of that paper. It seems to answer my question, though I'm still going through some of the details.

This post has been migrated from (A51.SE)
@PiotrMigdal: Perhaps you should post that as an answer.

This post has been migrated from (A51.SE)

1 Answer

+ 5 like - 0 dislike

In a paper C.-E. Bardyn et al., PRA 80(6): 062327 (2009), arXiv:0907.2170, they discuss constrains on the state, given how much the CHSH equality is violated ($S=2+c$), but without putting any assumptions on the operator used.

In general people consider schemes, when operators (for a Bell-type measurement) are random or one or more parties cannot be trusted. One of the key phrases is device-independent and maybe also loophole-free (as even a slight misalignment of operators may change the results dramatically).

This post has been migrated from (A51.SE)
answered Nov 21, 2011 by Piotr Migdal (1,260 points) [ no revision ]

Your answer

Please use answers only to (at least partly) answer questions. To comment, discuss, or ask for clarification, leave a comment instead.
To mask links under text, please type your text, highlight it, and click the "link" button. You can then enter your link URL.
Please consult the FAQ for as to how to format your post.
This is the answer box; if you want to write a comment instead, please use the 'add comment' button.
Live preview (may slow down editor)   Preview
Your name to display (optional):
Privacy: Your email address will only be used for sending these notifications.
Anti-spam verification:
If you are a human please identify the position of the character covered by the symbol $\varnothing$ in the following word:
Then drag the red bullet below over the corresponding character of our banner. When you drop it there, the bullet changes to green (on slow internet connections after a few seconds).
Please complete the anti-spam verification

user contributions licensed under cc by-sa 3.0 with attribution required

Your rights