How to make a separable product state in a given sub-Hilbert space

How to make a separable product state in a given sub-Hilbert space Ask Question Asked today Modified today Viewed 6 times 0 Consider a Hilbert space of dimension d 2 𝑑 2 and bipartite entangled states therein. I would like to generate (numerically) a collection of separable pure states that all lie within a sub-space of the Hilbert space. The subspace has been specified by an orthonormal set of vectors which spans it, and none of the vectors in the spanning set is itself separable. For example, for a pair of qubits the total space is of dimension 4 4 and a subspace could be of dimension 3 or 2 (don't worry about dimension 1 1 .) The above is my main question. A couple of related issues are: can there be subspaces (of dimension above 1 1 ) which contain no separable pure states at all? And if the answer to that is "yes" then is there a test for that property? entanglementnumerical Share Improve this question Follow asked 1 hour ago Andrew Steane 1535 5 bronze badges Add a comment Know someone who can answer? Share a link to this question via email, Twitter, or Facebook. Your Answer Sign up or log in Sign up using Google Sign up using Email and Password Post as a guest Name Email Required, but never shown Post Your Answer By clicking “Post Your Answer”, you agree to our terms of service and acknowledge you have read our privacy policy. Start asking to get answers Find the answer to your question by asking. Ask question Explore related questions entanglementnumerical See similar questions with these tags. The Overflow Blog Domain expertise still wanted: the latest trends in AI-assisted knowledge for... 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