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Memory cost for simulating all quantum correlations from the Peres-Mermin scenario. (English) Zbl 1372.81013

Summary: Sequences of compatible quantum measurements can be contextual and any simulation with a classical model conforming with the quantum predictions needs to use internal memory. M. Kleinmann et al. [“Memory cost of quantum contextuality”, New J. Phys. 13, Article ID 113011; 20 p. (2011; doi:10.1088/1367-2630/13/11/113011)] showed that simulating sequences from the Peres-Mermin scenario requires at least three different internal states in order not to contradict the deterministic predictions of quantum theory. We extend this analysis to probabilistic quantum predictions and ask how much memory is required to simulate correlations generated for sequences of compatible observables by any quantum state. We find that even in this comprehensive approach only three internal states are required for a perfect simulation of quantum correlations in the Peres-Mermin scenario.

MSC:

81P13 Contextuality in quantum theory
81P45 Quantum information, communication, networks (quantum-theoretic aspects)
81P05 General and philosophical questions in quantum theory
81P15 Quantum measurement theory, state operations, state preparations

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