Memory cost of quantum contextuality with Pauli observables

TL;DR

This paper quantifies the minimal classical memory required to simulate quantum contextuality for specific sets of Pauli observables, revealing that some quantum correlations demand more memory than the system's classical capacity.

Contribution

It provides exact lower bounds on the classical memory needed to simulate quantum contextuality for certain Pauli observable sets, extending previous work.

Findings

Memory cost for Mermin's pentagram: ~2.32 bits.

Memory cost for all 15 two-qubit Pauli observables: ~2.58 bits.

Memory requirements can exceed classical system capacity.

Abstract

Classically simulating the quantum contextual correlations produced by sequences of ideal measurements of compatible observables requires the measured system to have an internal memory. Computing the minimum amount of memory needed is, in general, challenging. Here, building upon the work of Kleinmann et al. [New J. Phys. 13, 113011 (2011)], we prove that the memory cost for simulating the contextuality produced by the $10$ three-qubit observables of Mermin's pentagram is only $\log_2(5) \approx 2.32$ bits, but the memory cost for simulating the contextuality produced by all $15$ two-qubit Pauli observables is, at least, $\log_2(6) \approx 2.58$ bits, thus exceeding the classical capacity of the system on which the measurements are performed. We also add results on the memory for simulating some subsets of quantum predictions.