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arXiv:1501.01746 · Physics Letters A

State-independent contextuality sets for a qutrit

Zhen‐Peng Xu, Jing‐Ling Chen, Hong-Yi Su

Published Apr 21, 2015• 12 citations
arXivHTMLPDF
DOI
10.1016/j.physleta.2015.04.024

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Simulating quantum contextuality with classical systems requires memory. A fundamental yet open question is what is the minimum memory needed and, therefore, the precise sense in which quantum systems outperform classical ones. Here, we make rigorous the notion of classically simulating quantum state-independent contextuality (QSIC) in the case of a single quantum system submitted to an infinite sequence of measurements randomly chosen from a finite QSIC set. We obtain the minimum memory needed to simulate arbitrary QSIC sets via classical systems under the assumption that the simulation should not contain any oracular information. In particular, we show that, while classically simulating two qubits tested with the Peres-Mermin set requires log_{2}24≈4.585 bits, simulating a single qutrit tested with the Yu-Oh set requires, at least, 5.740 bits.
Recent experiments have demonstrated ququart state-independent quantum contextuality and qutrit state-dependent quantum contextuality. So far, the most basic form of quantum contextuality pointed out by Kochen and Specker, and Bell, has eluded experimental confirmation. Here we present an experimentally feasible test to observe qutrit state-independent quantum contextuality using single photons in a three-path setup. In addition, we show that if the same measurements are performed on two entangled qutrits, rather than sequentially on the same qutrit, then the noncontextual inequality becomes a Bell inequality. We show that this connection also applies to other recently introduced noncontextual inequalities.
We propose a test of quantum contextuality for a single three-level system that uses nine projective measurements. It has the form of an inequality that has to be satisfied by any noncontextual theory. We show that for any qutrit state, except for the maximally mixed state, one can always find a set of nine observables for which the corresponding inequality is violated. This inequality is a test of contextuality that may offer insight into the relation between state-dependent and state-independent contextuality tests present in the literature.