Optimal quantum preparation contextuality in $n$-bit parity-oblivious multiplexing task

TL;DR

This paper investigates the relationship between quantum preparation contextuality and success probabilities in n-bit parity-oblivious multiplexing tasks, establishing that optimal quantum success depends on Bell inequality violations.

Contribution

It demonstrates that the optimal success probability in n-bit POM tasks is determined by Bell inequality violations and clarifies how contextuality limits quantum advantages.

Findings

Optimal success probability linked to Bell inequality violation

Quantum contextuality constrains quantum advantage in POM tasks

Extension of results to n-bit POM beyond 2-bit case

Abstract

In [ PRL, 102, 010401 (2009)], Spekkens et al., have shown that quantum preparation contextuality can power the parity-oblivious multiplexing (POM) task. The bound on the optimal success probability of $n$-bit POM task performed with the classical resources was shown to be the \textit{same} as in a preparation non-contextual theory. This non-contextual bound is violated if the task is performed with quantum resources. While in $2$-bit POM task the optimal quantum success probability is achieved, in 3-bit case optimality was left as an open question. In this paper, we show that the quantum success probability of a $n$-bit POM task is solely dependent on a suitable $2^{n-1}\times n$ Bell's inequality and optimal violation of it optimizes the success probability of the said POM task. Further, we discuss how the degree of quantum preparation contextuality restricts the amount of quantum violations of Bell's inequalities, and consequently the success probability of a POM task.