Abstract
According to usual definitions, entangled states cannot be given a separable decomposition in terms of products of local density operators. If we relax the requirement that the local operators be positive, then an entangled quantum state may admit a separable decomposition in terms of more general sets of single-system operators. This form of separability can be used to construct classical models and simulation methods when only a restricted set of measurements is available. With these motivations in mind, we ask what are the smallest sets of local operators such that a pure bipartite entangled quantum state becomes separable? We find that in the case of maximally entangled states there are many inequivalent solutions, including for example the sets of phase point operators that arise in the study of discrete Wigner functions. We therefore provide a new way of interpreting these operators, and more generally, provide an alternative method for constructing local hidden variable models for entangled quantum states under subsets of quantum measurements.
Highlights
AND OVERVIEWIn recent years a variety of work has examined the nature of quantum entanglement by considering quantum systems as examples of more general structures
This motivates the question: if we want to use such generalised separable decompositions for the construction of local hidden variable (LHV) models or for efficient classical simulation algorithms, what such decompositions are useful? This question motivated a problem that we considered in a previous work [8]: what are the smallest sets of operators such that a given entangled quantum state admits a separable decomposition? In this work we will generalise the results of [8] to a much wider family of states
In order for a separable decomposition to be useful for constructing LHV models in this way, we would like the local operators appearing in the decomposition to be generalised positive for as large a set of measurements as possible
Summary
In recent years a variety of work has examined the nature of quantum entanglement by considering quantum systems as examples of more general structures. One of the observations underlying the present work is that by allowing local state spaces to contain non-quantum operators, an entangled quantum state may admit a separable decomposition that can be considered to be unentangled if the measurements available are restricted. This motivates the question: if we want to use such generalised separable decompositions for the construction of LHV models or for efficient classical simulation algorithms, what such decompositions are useful?
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