Abstract:We address the recently posed question as to whether the nonlocality of a single member of an entangled pair of spin 1/2 particles can be shared among multiple observers on the other wing who act sequentially and independently of each other. We first show that the optimality condition for the trade-off between information gain and disturbance in the context of weak or non-ideal measurements emerges naturally when one employs a one-parameter class of positive operator valued measures (POVMs). Using this formalism we then prove analytically that it is impossible to obtain violation of the Clauser-Horne-Shimony-Holt (CHSH) inequality by more than two Bobs in one of the two wings using unbiased input settings with an Alice in the other wing.

Quantum mechanics puts a restriction on the number of observers who can simultaneously steer another observer's system, known as the monogamy of steering. In this work we find the limit of the number of observers (Bobs) who can steer another party's (Alice's) system invoking a scenario where half of an entangled pair is shared between a single Alice in one wing and several Bobs on the other wing, who act sequentially and independently of each other. When all the observers measure two dichotomic observables, we find that two Bobs can steer Alice's system going beyond the monogamy restriction. We further show that three Bobs can steer Alice's system considering a three-settings linear steering inequality, and then conjecture that at most n Bobs can demonstrate steering of Alice's system when steering is probed through an n-settings linear steering inequality.

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Wigner's form of the local realist inequality is used to derive its temporal version for an oscillating two-level system involving two-time joint probabilities. Such an inequality may be regarded as a novel form of the Leggett-Garg inequality (LGI) constituting a necessary condition for macrorealism. The robustness of its quantum mechanical (QM) violation against unsharpness of measurement is investigated by using a suitable model of unsharp measurements. It is found that there exists a range of values of the sharpness parameter (characterizing precision of the relevant measurements) for which the usual LGI is satisfied by QM, but Wigner's form of the LGI (WLGI) is violated. This implies that for such unsharp measurements, the QM violation of macrorealism cannot be tested using the usual LGI, but can be tested using WLGI. In showing this, we take into account the general form of the usual LGI involving an arbitrary number of pairs of two-time correlation functions. Another recently proposed necessary condition for macrorealism, called 'no-signalling in time', is also probed, showing that its QM violation persists for arbitrarily unsharp measurements.