Discrimination of Non-Local Correlations

Clicks: 180
ID: 19640
2019
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Abstract
In view of the importance of quantum non-locality in cryptography, quantum computation, and communication complexity, it is crucial to decide whether a given correlation exhibits non-locality or not. As proved by Pitowski, this problem is NP-complete, and is thus computationally intractable unless NP is equal to P. In this paper, we first prove that the Euclidean distance of given correlations from the local polytope can be computed in polynomial time with arbitrary fixed error, granted the access to a certain oracle; namely, given a fixed error, we derive two upper bounds on the running time. The first bound is linear in the number of measurements. The second bound scales with the number of measurements to the sixth power. The former holds only for a very high number of measurements, and is never observed in the performed numerical tests. We, then, introduce a simple algorithm for simulating the oracle. In all of the considered numerical tests, the simulation of the oracle contributes with a multiplicative factor to the overall running time and, thus, does not affect the sixth-power law of the oracle-assisted algorithm.
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montina2019discriminationentropy Use this key to autocite in the manuscript while using SciMatic Manuscript Manager or Thesis Manager
Authors Montina, Alberto;Wolf, Stefan;
Journal entropy
Year 2019
DOI
DOI not found
URL
https://www.mdpi.com/1099-4300/21/2/104
Keywords Keywords not found

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