Limitations on sharing Bell nonlocality between sequential pairs of observers

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.

Network nonlocality sharing via weak measurements in the extended bilocal scenario

“…when θ 1,0 = θ 1,1 = π 4 for Alice [48,49]. In particular, network nonlocal sharing can also be divided into two different types of nonlocality sharing, passive and active network nonlocal sharing, according to the different motivations of the former observers Alice 1 and Charlie 1 .…”

“…Nonlocal sharing has attracted extensive attention [35][36][37][38][39][40][41][42][43][44][45][46][47][48][49][50], and lots of relevant results have been published ever since, such as active and passive nonlocal sharing [35], quantum steering sharing [47] and so on. However, almost all discussions are limited to the case of one-sided sequential measurements, that is, an entangled pair is distributed to one Alice and multiple [48,49]. Such discrepancy may give a hint to exhibit the different properties between network nonlocality and Bell nonlocality.…”

Generalising the Horodecki criterion to nonprojective qubit measurements

“…The observable is projective if and only if X ± are projection operators (i.e., X 2 ± = X ± ). We follow the notation used in [11,12] and represent the observable by the corresponding operator…”

“…In contrast, an observable with minimum strength S = 0 is trivial, with X = B½, corresponding to tossing a coin having biased outcome probabilities 1 2 (1 ± B). The strength and bias parameters also determine the maximum reversibility of measurements of X [11,12].…”

“…However, H(T ) does represent the maximum possible value of the CHSH parameter for the case of projective observables with unit strengths [7]. Moreover, the criterion H(T ) > 2 for the maximal violation of the CHSH inequality remains valid for nonprojective observables [11,13]. Indeed, it follows from the general convexity argument in [13], or more directly via the proof of equation (S31) in [11], that one has the tight upper bound…”