Quantcast
  • 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.

News

Please welcome our new moderators!

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

Attributions

(propose a free ad)

Site Statistics

122 submissions , 103 unreviewed
3,497 questions , 1,172 unanswered
4,544 answers , 19,342 comments
1,470 users with positive rep
408 active unimported users
More ...

States diagonal in the tensor product of Bell states.

+ 6 like - 0 dislike
23 views

Bell-diagonal states are 2-qubit states that are diagonal in the Bell basis. Since those states lie in $\mathbb{C}^{2} \otimes \mathbb{C}^{2}$, the Peres-Horodecki criterion is a sufficient condition to show separability and it's also pretty easy to check: $\rho = \sum_{i \in [0,3]}\lambda_i|\psi_{i}\rangle\langle\psi_{i}| $ is PPT (or separable) if and only if $Tr(\rho) \geq 2\lambda_i \geq 0$ for every $i$. (Here {$|\psi_{i}\rangle$} are the Bell states)

In my research I am dealing with a generalization of those states. In particular, my question is about states in $\mathbb{C}^{2^d} \otimes \mathbb{C}^{2^d}$ that are diagonal in the basis given by the $d$-fold tensor product of Bell states.

For example, for $d=2$, the states I am considering are diagonal in the basis: $$ |\psi_{0}\rangle\otimes|\psi_{0}\rangle,|\psi_{0}\rangle\otimes|\psi_{1}\rangle, \ldots,|\psi_{3}\rangle\otimes|\psi_{3}\rangle. $$

I am wondering the following:

are there some nice criteria already known to check when these states are PPT or separable?

Notice that those states are in general different from the states diagonal in what is called the generalized Bell basis in literature.

This post has been migrated from (A51.SE)
asked Mar 30, 2012 in Theoretical Physics by Alessandro Cosentino (30 points) [ no revision ]
retagged Mar 18, 2014 by dimension10

1 Answer

+ 4 like - 0 dislike

Try Theorem 12 in (the arXiv version) of http://arxiv.org/abs/quant-ph/0411098. What I call "lattice states" there should exactly be the class of states you are interested in.

This post has been migrated from (A51.SE)
answered Apr 2, 2012 by Marco (260 points) [ no revision ]
thanks Marco! this is what I was looking for.

This post has been migrated from (A51.SE)

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:
p$\varnothing$ysicsOverflow
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).
To avoid this verification in future, please log in or register.




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

Your rights
...