Oblivious communication game, self-testing of projective and non-projective measurements and certification of randomness

TL;DR

This paper introduces a two-party quantum communication game linked to Bell expressions, enabling device-independent self-testing of quantum states and measurements, and certifying randomness through parity-oblivious conditions.

Contribution

It presents a novel parity-oblivious communication game that connects Bell inequalities with self-testing and randomness certification, extending to arbitrary measurement counts.

Findings

Optimal quantum strategies self-test maximally entangled states.

Device-independent certification of trine-set POVMs and randomness.

Generalization to arbitrary odd number of measurements.

Abstract

We provide an interesting two-party parity oblivious communication game whose success probability is solely determined by the Bell expression. The parity-oblivious condition in an operational quantum theory implies the preparation non-contextuality in an ontological model of it. We find that the aforementioned Bell expression has two upper bounds in an ontological model; the usual local bound and a non-trivial preparation non-contextual bound arising from the non-trivial parity-oblivious condition, which is smaller that the local bound. We first demonstrate the communication game when both Alice and Bob perform three measurements of dichotomic observables in their respective sites. The optimal quantum value of the Bell expression in this scenario enables us to device-independently self-test the maximally entangled state and trine-set of observables, three-outcome qubit positive-operator-valued-measures (POVMs) and 1.58 bit of local randomness. Further, we generalize the above communication game in that both Alice and Bob perform the same but arbitrary (odd) number ($n> 3$) of measurements. Based on the optimal quantum value of the relevant Bell expression for any arbitrary $n$, we have also demonstrated device-independent self-testing of state and measurements.