Parity Oblivious d-Level Random Access Codes and Class of Noncontextuality Inequalities

TL;DR

This paper introduces d-level parity-oblivious random access codes, derives noncontextuality inequalities for all d, and demonstrates quantum violations, highlighting the operational significance of preparation contextuality in higher-dimensional quantum systems.

Contribution

It formulates new d-level parity-oblivious random access codes and derives universal noncontextuality inequalities, showing quantum violations for various dimensions.

Findings

Quantum theory violates the noncontextual bounds for d=3.

Quantum violations are demonstrated for higher dimensions.

Preparation contextuality is operationally useful in higher-level quantum systems.

Abstract

One of the fundamental results in quantum foundations is the Kochen-Specker no-go theorem. For the quantum theory, the no-go theorem excludes the possibility of a class of hidden variable models where value attribution is context independent. Recently, the notion of contextuality has been generalized for different operational procedures and it has been shown that preparation contextuality of mixed quantum states can be a useful resource in an information-processing task called parity-oblivious multiplexing. Here, we introduce a new class of information processing tasks, namely d-level parity oblivious random access codes and obtain bounds on the success probabilities of performing such tasks in any preparation noncontextual theory. These bounds constitute noncontextuality inequalities for any value of d. For d=3, using a set of mutually asymmetric biased bases we show that the corresponding noncontextual bound is violated by quantum theory. We also show quantum violation of the inequalities for some other higher values of d. This reveals operational usefulness of preparation contextuality of higher level quantum systems.