Computing finite-dimensional bipartite quantum separability

Abstract

Ever since entanglement was identified as a computational and cryptographic resource, effort has been made to find an efficient way to tell whether a given density matrix represents an unentangled, or separable, state. Essentially, this is the quantum separability problem. Chapters 1 to 3 motivate a new interior-point algorithm which, given the expected values of a subset of an orthogonal basis of observables of an otherwise unknown quantum state, searches for an entanglement witness in the span of the subset of observables. When all the expected values are known, the algorithm solves the separability problem. In Chapter 4, I give the motivation for the algorithm and show how it can be used in a particular physical scenario to detect entanglement (or decide separability) of an unknown quantum state using as few quantum resources as possible. I then explain the intuitive idea behind the algorithm and relate it to the standard algorithms of its kind. I end the chapter with a comparison of the complexities of the algorithms surveyed in Chapter 3. Finally, in Chapter 5, I present the details of the algorithm and discuss its performance relative to standard methods.

Replaced orginal archive submission with PhD thesis, which subsumes and mildly corrects it

References in corpus (7)

• A complete family of separability criteria
• Separable Multipartite Mixed States - Operational Asymptotically Necessary and Sufficient Conditions
• A Robust Semidefinite Programming Approach to the Separability Problem
• Continuous optimal ensembles I: A geometrical characterization of robustly separable quantum states
• A note on continuous ensemble expansions of quantum states
• Continuous optimal ensembles II. Reducing the separability condition to numerical equations
• An asymptotical separability criterion for bipartite density operators