Optimal classical simulation of state-independent quantum contextuality

TL;DR

This paper rigorously determines the minimum classical memory required to simulate quantum state-independent contextuality, revealing that simulating certain quantum systems demands more than 4.5 bits of memory.

Contribution

It establishes the exact lower bounds on classical memory needed for simulating quantum contextuality in single systems, advancing understanding of quantum-classical computational differences.

Findings

Simulating two qubits with Peres-Mermin set requires about 4.585 bits.

Simulating a single qutrit with Yu-Oh set requires at least 5.740 bits.

Provides a rigorous framework for classical simulation of quantum contextuality.

Abstract

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 $\log_2 24 \approx 4.585$ bits, simulating a single qutrit tested with the Yu-Oh set requires, at least, $5.740$ bits.