Limitations on sharing Bell nonlocality between sequential pairs of observers

TL;DR

This paper demonstrates that under common measurement assumptions, two qubits cannot be recycled to generate Bell nonlocality between multiple independent observers on each side, revealing fundamental limitations on sequential quantum correlations.

Contribution

The paper provides strong analytic and numerical evidence for limitations on sharing Bell nonlocality sequentially, introducing monogamy relations and exploring measurement bias effects.

Findings

Two-qubit recycling for Bell nonlocality is fundamentally limited.

Monogamy relations prevent two-sided recycling under mild assumptions.

Biased measurements can enable limited two-sided recycling in specific cases.

Abstract

We give strong analytic and numerical evidence that, under mild measurement assumptions, two qubits cannot both be recycled to generate Bell nonlocality between multiple independent observers on each side. This is surprising, as under the same assumptions it is possible to recycle just one of the qubits an arbitrarily large number of times [P. J. Brown and R. Colbeck, Phys. Rev. Lett. 125, 090401 (2020)]. We derive corresponding 'one-sided monogamy relations' that rule out two-sided recycling for a wide range of parameters, based on a general tradeoff relation between the strengths and maximum reversibilities of qubit measurements. We also show if the assumptions are relaxed to allow sufficiently biased measurement selections, then there is a narrow range of measurement strengths that allows two-sided recycling for two observers on each side, and propose an experimental test. Our methods may be readily applied to other types of quantum correlations, such as steering and entanglement, and hence to general information protocols involving sequential measurements.