Robustness of contextuality under different types of noise as quantifiers for parity-oblivious multiplexing tasks

TL;DR

This paper investigates how different types of noise affect the robustness of contextuality in parity-oblivious multiplexing tasks, providing quantitative measures and bounds for the nonclassical advantage in quantum information processing.

Contribution

It introduces analytical and numerical methods to estimate the robustness of contextuality under noise in POM scenarios and relates this robustness to success rates and information bounds.

Findings

Robustness to depolarisation indicates nonclassical advantage.

Minimisation of robustness to dephasing over all bases is a key quantifier.

A general relation links robustness of contextuality to success rate and information bounds.

Abstract

Generalised contextuality is the notion of nonclassicality powering up a myriad of quantum tasks, among which is the celebrated case of a two-party information processing task where classical information is compressed in a quantum channel, the parity-oblivious multiplexing (POM) task. The success rate is the standard quantifier of resourcefulness for this task, while robustness-based quantifiers are as operationally motivated and have known general properties. In this work, we leverage analytical and numerical tools to estimate robustness of contextuality in POM scenarios under different types of noise. We conclude that for the 3-to-1 case robustness of contextuality to depolarisation, as well as a minimisation of robustness of contextuality to dephasing over all bases, are good quantifiers for the nonclassical advantage of this scenario. Moreover, we obtain a general relation between robustness of contextuality to depolarisation and the success rate in any $n$-to-1 POM scenario and show how it can be used to bound the number of bits encoded in this task.