Talk:Separable state

Could someone write a better introduction for this article? The current version is meaningless to a reader who lacks prior expertise in the subject. Durova 01:56, 1 December 2005 (UTC)

If I understand you correctly, you want someone to explain what separable states are to someone with no knowledge of quantum informatics? Putting the horse before the carriage, if you ask me. Vegalabs 15:11, 20 December 2005 (EST)

Serparability problem

Is the separability problem in quantum mechanics identical to the Grobner basis problem in algebraic geometry? The idea is that the subspaces of the Segre embedding are linear subspaces, and Buchberger's algorithm is used to find those subspaces. Right? Or maybe I'm crazy. linas 21:32, 1 July 2006 (UTC)

linas, i think you might be referring application of projective algebraic geometry to find subspaces that are not completely entangled. i believe the result is that any subspace of a certain dimension would fail to be completely entangled. this is related to the range criterion. it is a necessary condition for separability, not sufficient. a problem that is equivalent to the separability problem is the classification of positive maps. Mct mht 02:02, 2 July 2006 (UTC)

Finite Sum

If a state is separable, does that mean than it can be written as a finite sum of projectors onto product states, or is it that this sum need not be finite as long as it converges? —Preceding unsigned comment added by 129.97.127.183 (talk) 21:37, 12 May 2008 (UTC)

Huh?

I removed the following text, because it makes no sense (to me):

A standard example of an (un-normalized) entangled state is

$|\psi \rangle ={\begin{bmatrix}1\\0\\0\\1\end{bmatrix}}\in H\otimes H$

where H is the Hilbert space of dimension 2.

Maybe there's something there, but its wildly out-of-context, and thus non-sensical. User:Linas (talk) 20:11, 17 November 2013 (UTC)

separability problem

The article mentions this problem is NP-hard, but if I understand the concept of separability, a state can be shown separable by "factoring" it into a tensor product of simpler states and writing down the factors. That would mean separability is in NP, so should the article say NP-complete instead of NP-hard? I won't make the edit myself since I might be misunderstanding something. 173.228.123.121 (talk) 09:04, 18 March 2018 (UTC)

Shouldn't this page be merged with "Quantum entanglement"

I meant to add some more information to this page, but then realised there's already plenty in Quantum entanglement. If there a specific reason why these are separate pages? How can we possibly talk about separability without talking about entanglement, and vice versa? Luca (talk) 09:28, 30 December 2021 (UTC)