Sharing non-locality and non-trivial preparation contextuality using same family of Bell expressions

TL;DR

This paper presents a scheme for sequential sharing of non-locality and preparation contextuality using a family of Bell inequalities, showing that multiple observers can share these quantum correlations under specific measurement conditions.

Contribution

It introduces a new method to share non-locality and preparation contextuality sequentially with multiple observers using a family of Bell inequalities and unsharp measurements.

Findings

Maximum two Bobs can share non-locality sequentially with unbiased measurements.

More Bobs can share preparation contextuality than non-locality.

Preparation contextuality can be shared by an arbitrary number of Bobs under certain conditions.

Abstract

In [Phys. Rev. Lett. 114, 250401 (2015)] the sharing of non-locality by multiple observers was demonstrated through the quantum violation of Clauser-Horne-Shimony-Halt inequality. In this paper we provide a scheme for sharing of non-locality and non-trivial preparation contextuality sequentially through the quantum violation of a family of Bell's inequalities where Alice and Bob perform $2^{n-1}$ and $n$ numbers of measurements of dichotomic observables respectively. For this, we consider that Alice always performs projective measurement and multiple Bobs sequentially perform unsharp measurement. We show that when Bob's choices of measurement settings are unbiased, maximum two Bobs can sequentially share the non-locality through the violation of our inequalities. Further, we show that the local bound of the aforementioned family of inequalities gets reduced if non-trivial preparation non-contextuality assumptions are further imposed. Then there is a chance to share the non-trivial preparation contextuality for more number of Bobs than that of non-locality. We demonstrate that the non-trivial preparation contextuality can be sequentially shared by arbitrary numbers of Bob for unbiased choices of his measurement settings.