Recycling qubits for the generation of Bell nonlocality between independent sequential observers

TL;DR

This paper investigates how to recycle entangled qubits to generate Bell nonlocality among multiple independent observers, deriving tradeoff relations, monogamy constraints, and schemes for multi-observer Bell tests.

Contribution

It introduces new tradeoff relations and monogamy constraints for Bell nonlocality recycling, and extends schemes for multi-observer Bell tests using recycled entanglement.

Findings

Derived tradeoff relations between measurement bias, strength, and reversibility.

Established monogamy relations for Bell nonlocality among sequential observers.

Proposed schemes for multi-observer Bell tests with recycled entanglement.

Abstract

There is currently much interest in the recycling of entangled systems, for use in quantum information protocols by sequential observers. In this work, we study the sequential generation of Bell nonlocality via recycling one or both components of two-qubit states. We first give a description of two-valued qubit measurements in terms of measurement bias, strength, and reversibility, and derive useful tradeoff relations between them. Then, we derive one-sided monogamy relations for unbiased observables, that strengthen the recent Conjecture in [S. Cheng {\it et al.}, Phys. Rev. A \textbf{104}, L060201 (2021) ] that if the first pair of observers violate Bell nonlocality then a subsequent independent pair cannot, and give semi-analytic results for the best possible monogamy relation. We also extend the construction in [P. J. Brown and R. Colbeck, Phys. Rev. Lett. \textbf{125}, 090401 (2020)] to obtain (i)~a broader class of two-qubit states that allow the recycling of one qubit by a given number of observers on one side, and (ii)~a scheme for generating Bell nonlocality between arbitrarily many independent observers on each side, via the two-sided recycling of multiqubit states. Our results are based on a formalism that is applicable to more general problems in recycling entanglement, and hence is expected to aid progress in this field.