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Entanglement Theory Quantum Correlations Open Quantum Systems Decoherence Quantum Simulation

Local Records and Global Entanglement: A Unique Multi-Partite Generalization of the Schmidt Decomposition

arXiv

Authors: C. Jess Riedel

Year

2013

Paper ID

32203

Status

Preprint

Abstract Read

~2 min

Abstract Words

124

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N/A

Abstract

We show that there is a unique maximal decomposition of a pure multi-partite (N>2) quantum state into a sum of states which are "locally orthogonal" in the sense that the local reduced state for a term in the sum lives in its own orthogonal subspace for each subsystem. Observers can make local measurements on any subsystem and determine which "branch" they are on. The Shannon entropy of the resulting branch weights defines a new measure of global, GHZ-like entanglement, which is insensitive to local pairwise entangling operations and vanishes when there is no piece of information recorded at every subsystem. In the bi-partite N=2 case, this decomposition reduces to the (not necessarily unique) Schmidt decomposition and the entropy reduces to the entropy of entanglement

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We show that there is a unique maximal decomposition of a pure multi-partite (N>2) quantum state into a sum of states which are "locally orthogonal" in the sense that the local...

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References & Citation Signals

[1] DOI https://doi.org/arXiv:1310.4473 [2] arXiv https://arxiv.org/abs/1310.4473 [3] Publisher https://arxiv.org/abs/1310.4473

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