Smallest disentangling state spaces for general entangled bipartite quantum states

TL;DR

This paper constructs minimal local operator sets enabling separable decompositions of bipartite entangled quantum states, extending previous work and relating to ensemble decomposition theorems.

Contribution

It introduces the smallest local operator sets for separable decompositions, including variants with local state space constraints, generalizing prior results.

Findings

Constructed minimal local operator sets for bipartite states

Extended results to local state space containing quantum states

Linked to theorems on ensemble decompositions of positive operators

Abstract

Entangled quantum states can be given a separable decomposition if we relax the restriction that the local operators be quantum states. Motivated by the construction of classical simulations and local hidden variable models, we construct `smallest' local sets of operators that achieve this. In other words, given an arbitrary bipartite quantum state we construct convex sets of local operators that allow for a separable decomposition, but that cannot be made smaller while continuing to do so. We then consider two further variants of the problem where the local state spaces are required to contain the local quantum states, and obtain solutions for a variety of cases including a region of pure states around the maximally entangled state. The methods involve calculating certain forms of cross norm. Two of the variants of the problem have a strong relationship to theorems on ensemble decompositions of positive operators, and our results thereby give those theorems an added interpretation. The results generalise those obtained in our previous work on this topic [New J. Phys. 17, 093047 (2015)].