Measurement contextuality and Planck's constant

Presenting Author: Lucas Kocia, National Institute of Standards and Technology, Maryland
Contributing Author(s): Peter Love

Contextuality is a necessary resource for universal quantum computation and non-contextual quantum mechanics can be simulated efficiently by classical computers in many cases. Orders of Planck's constant, hbar, can also be used to characterize the classical-quantum divide by expanding quantities of interest in powers of hbar. We show that contextual measurements in finite-dimensional systems\ have formulations within the Wigner-Weyl-Moyal (WWM) formalism that require higher than order hbar^0 terms to be included in order to violate the classical bounds on their expectation values. As a result, we show that contextuality as a resource is equivalent to orders of hbar as a resource within the WWM formalism. This explains why qubits can only exhibit state-independent contextuality under Pauli observables as in the Peres-Mermin square while odd-dimensional qudits can also exhibit state-dependent contextuality. In particular, we find that qubit Pauli observables lack an order hbar^0 contribution in their Weyl symbol and so exhibit contextuality regardless of the state being measured. As a result, the WWM formalism is shown to be an excellent candidate for use in the development of classical algorithms for quantum simulation that treat contextuality, or higher orders of hbar, as a resource.

Read this article online: https://arxiv.org/abs/1711.08066

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