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arXiv:1411.0828 · Physical Review A

Expanding the principle of local distinguishability

Claudio Carmeli, Teiko Heinosaari, Jussi Schultz, Alessandro Toigo

Published Apr 17, 2015• 2 citations
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Abstract

The principle of local distinguishability states that an arbitrary physical state of a bipartite system can be determined by the combined statistics of local measurements performed on the subsystems. A necessary and sufficient requirement for the local measurements is that each one must be able to distinguish between all pairs of states of the respective subsystems. We show that, if the task is changed into the determination of an arbitrary bipartite pure state, then at least in certain cases it is possible to restrict to local measurements which can distinguish all pure states but not all states. Moreover, we show that, if the local measurements are such that the purity of the bipartite state can be verified from the statistics without any prior assumption, then in these special cases also this property is carried over to the composite measurement. These surprising facts give evidence that the principle of local distinguishability may be expanded beyond its usual applicability.

DOI
10.1103/physreva.91.042121

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The principle of local distinguishability states that an arbitrary physical state of a bipartite system can be determined by the combined statistics of local measurements performed on the subsystems. A necessary and sufficient requirement for the local measurements is that each one must be able to distinguish between all pairs of states of the respective subsystems. We show that, if the task is changed into the determination of an arbitrary bipartite pure state, then at least in certain cases it is possible to restrict to local measurements which can distinguish all pure states but not all states. Moreover, we show that, if the local measurements are such that the purity of the bipartite state can be verified from the statistics without any prior assumption, then in these special cases also this property is carried over to the composite measurement. These surprising facts give evidence that the principle of local distinguishability may be expanded beyond its usual applicability.
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A new criterion necessary and sufficient for the separability of pure bipartite systems for arbitrary finite dimensions is demonstrated; and the corresponding finer quantitative measures or characterizations of entanglement (beyond mere separability or non-separability determination) are discussed. Based on this criterion, we proved that the well-known Peres-Horodecki positivity-of-partial-transform criterion is also necessary and sufficient for separability in the case of pure bipartite systems. The maximum value of entanglement, and the corresponding maximally-entangled states are also worked out in detail.