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arXiv:2102.11574 · Physical Review A

Limitations on sharing Bell nonlocality between sequential pairs of observers

Shuming Cheng, Lijun Liu, Travis J. Baker, Michael J. W. Hall

Published Dec 9, 2021• 51 citations
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Abstract

The authors demonstrate that, under mild measurement assumptions, two qubits cannot both be recycled to generate Bell nonlocality between multiple independent observers on each side. The authors also derive corresponding ``one-sided monogamy relations'' that rule out two-sided recycling for a wide range of parameters and propose a possible experimental test.

DOI
10.1103/physreva.104.l060201

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The authors demonstrate that, under mild measurement assumptions, two qubits cannot both be recycled to generate Bell nonlocality between multiple independent observers on each side. The authors also derive corresponding ``one-sided monogamy relations'' that rule out two-sided recycling for a wide range of parameters and propose a possible experimental test.
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 by Cheng et al. [Phys. Rev. A 104, L060201 (2021)] that if the first pair of observers violate Bell nonlocality then a subsequent independent pair cannot, and give semianalytic results for the best possible monogamy relation. We also extend the construction by Brown and Colbeck [Phys. Rev. Lett. 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.
Two spatially separated observers, Alice and Bob, share a bipartite two-qubit entangled state and perform measurements to witness entanglement. After their measurements, they pass their qubits to a subsequent pair of observers who try to perform the same task independently, and so on. Here we ask: what is the maximum number of such pairs that can perform this task successfully? It has previously been conjectured that not more than one pair of observers can detect Clauser-Horne-Shimony-Holt ``Bell-nonlocal'' correlations in this setup. We prove that, on the contrary, entanglement can be witnessed by arbitrarily many pairs of observers. The dissimilar nature between entanglement and Bell-nonlocal correlations is therefore uncovered in a rather radical way, when considering sequentially acting pairs of observers. We prove this statement to be true when the initial shared state is any pure entangled state, a class of Bell-nonlocal mixed states, or a class of Bell-local entangled states.
Abstract The recycling of quantum correlations has attracted widespread attention both theoretically and experimentally. Previous works show that bilateral sharing of nonlocality is impossible under mild measurement strategy and 2-qubit entangled state can be used to witness entanglement arbitrary many times by sequential and independent pairs of observers. However, less is known about the bilateral sharing of EPR steering yet. Here, we aim at investigating the EPR steering sharing between sequential pairs of observers. We show that an unbounded number of sequential Alice-Bob pairs can share the EPR steering as long as the initially shared state is an entangled two-qubit pure state. The claim is also true for particular class of mixed entangled states.
As a way of saving quantum resources, recycling of Bell nonlocality has been experimentally studied, but restricted to sequential unsharp measurements. However, it has been theoretically shown recently that projective measurements are sufficient for recycling nonlocality [Phys. Rev. Lett. \textbf{129}, 230402 (2022)]. Here, we go beyond unsharp measurement scenarios and experimentally demonstrate the recycling of nonlocal resources with projective measurements. By verifying the violation of Clauser-Horne-Shimony-Holt (CHSH) inequality, we find that three independent parties can recycle the Bell nonlocality of a two-qubit state, whether it is maximally or partially entangled. Furthermore, in the double violation region, the optimal trade-off for partially entangled states can be 11 standard deviations better than that for maximally entangled states. Our results experimentally eliminate the common misconception that projective measurements are incompatible with the recycling of quantum correlations. In addition, our nonlocality recycling setup does not require entanglement assistance, which is much more experimentally friendly, thus paving the way for the reuse of other kinds of quantum correlations.
A well-known property of quantum nonlocality is monogamy. However, recent research by Silva \emph{et al.} shows that multiple observers can share the nonlocality by using weak measurements [Phys. Rev. Lett. 114, 250401 (2015)]. There is an open question left in their result: whether the nonlocality of a single particle from an entangled pair can be shared among more than two observers that act sequentially and independently of each other? In this work, we analytical and numerical shows that it is possible to observe a triple violation of CHSH inequality between Alice and three Bobs when the measurements of each of the several observers at one side are unbiased with respect to the previous observers. This result overturns the conclusions and proofs of previous related work on this issue which has been widely shared in the scientific community before.
Unsharp measurements are widely seen as the key resource for recycling the nonlocality of an entangled state shared between several sequential observers. Contrasting this, we here show that nonlocality can be recycled using only standard, projective, qubit measurements. Focusing on the Clauser-Horne-Shimony-Holt inequality and allowing parties to share classical randomness, we determine the optimal trade-off in the magnitude of Bell violations for a maximally entangled state. We then find that nonmaximally entangled states make possible larger sequential violations, which contrasts the standard Clauser-Horne-Shimony-Holt scenario. Furthermore, we show that nonlocality can be recycled using projective qubit measurements even when no shared classical randomness is available. We discuss the implications of our results for experimental implementations of sequential nonlocality.