0
$\begingroup$

Suppose A,B,C are Hilbert space, and P,Q be density matrices defined on $A\times B$, and $B\times C$ respectively. Relation $Tr_A P=Tr_C Q$ holds(i.e., partial trace of the two matrix are the same in the common space.) Is there a density matrix $R$ on $A\times B\times C$ such that $Tr_{C}R=P$, and $Tr_{A}R=Q$?

$\endgroup$

closed as off-topic by Norbert Schuch, user36790, rob, Gert, Bosoneando Oct 7 '16 at 11:28

This question appears to be off-topic. The users who voted to close gave this specific reason:

  • "Homework-like questions should ask about a specific physics concept and show some effort to work through the problem. We want our questions to be useful to the broader community, and to future users. See our meta site for more guidance on how to edit your question to make it better" – Norbert Schuch, Community, rob, Gert, Bosoneando
If this question can be reworded to fit the rules in the help center, please edit the question.

  • $\begingroup$ Cross-posted all over the place: physics.stackexchange.com/q/284414/24498, cstheory.stackexchange.com/q/36726/5038, math.stackexchange.com/q/1955870/14578, cs.stackexchange.com/q/64286/755. Please do not post the same question on multiple sites. Each community should have an honest shot at answering without anybody's time being wasted. $\endgroup$ – D.W. Oct 6 '16 at 17:07
  • $\begingroup$ @D.W. I disagree. First, it isn't the job of the asker to be as "fair as possible to each site". Second, I don't see how it's really a slight against one community if the question is answered first somewhere else; the whole setup of stackexchange depends on the idea that it's good to have multiple answers to the same question, even if one comes after the other. Finally, this is the first I'm hearing of this "policy" in any community. $\endgroup$ – Omnomnomnom Oct 8 '16 at 14:36
  • $\begingroup$ @Omnomnomnom, I understand. The Stack Exchange policy is documented at the link that I gave, and it is clear: cross-posting the same question on multiple SE sites is not allowed. You're free to disagree; I respect that. A site can always choose to adopt a different policy for their own site, so if you disagree, one approach is to take it to meta and propose a different policy for your site and see if the community agrees with you or not. Failing that, the Stack Exchange network-wide policy applies. I realize many people haven't heard of this policy. $\endgroup$ – D.W. Oct 8 '16 at 20:18
5
$\begingroup$

No. Consider e.g. $P$ and $Q$ to be the maximally entangled state $|\omega\rangle = (|00\rangle+|11\rangle)/\sqrt{2}$, $P=Q=|\omega\rangle\langle\omega|$. Then, the monogamy of entanglement tells us that there can be no such state $R$.

(Obviously, there are also cases where this possible, since you can always start from $R$ and derive $P$ and $Q$ from there.)

$\endgroup$

Not the answer you're looking for? Browse other questions tagged or ask your own question.