Minimum Dimension of a Hilbert Space Needed to Generate a Quantum Correlation

Consider a two-party correlation that can be generated by performing local measurements on a bipartite quantum system. A question of fundamental importance is to understand how many resources, which we quantify by the dimension of the underlying quantum system, are needed to reproduce this correlati...

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Bibliographic Details
Published in:Physical review letters 2016-08, Vol.117 (6), p.060401-060401, Article 060401
Main Authors: Sikora, Jamie, Varvitsiotis, Antonios, Wei, Zhaohui
Format: Article
Language:English
Subjects:
Correlation
Correlation analysis
Hilbert space
Lower bounds
Quantum theory
Representations
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Summary:Consider a two-party correlation that can be generated by performing local measurements on a bipartite quantum system. A question of fundamental importance is to understand how many resources, which we quantify by the dimension of the underlying quantum system, are needed to reproduce this correlation. In this Letter, we identify an easy-to-compute lower bound on the smallest Hilbert space dimension needed to generate a given two-party quantum correlation. We show that our bound is tight on many well-known correlations and discuss how it can rule out correlations of having a finite-dimensional quantum representation. We show that our bound is multiplicative under product correlations and also that it can witness the nonconvexity of certain restricted-dimensional quantum correlations.
ISSN:0031-9007
1079-7114
DOI:10.1103/PhysRevLett.117.060401