In the work by Silva et al. [Phys. Rev. Lett. 114, 250401 (2015)], the sharing of nonlocality by multiple observers was demonstrated through the quantum violation of Clauser-Horne-Shimony-Halt inequality. We provide a scheme for the sharing of nonlocality and nontrivial preparation contextuality sequentially through the quantum violation of a family of Bell's inequalities, where Alice and Bob perform ${2}^{n\ensuremath{-}1}$ and
n numbers of measurements of dichotomic observables, respectively. For this, we consider that Alice always performs projective measurement and multiple Bobs sequentially perform unsharp measurement. We show that when Bob's choices of measurement settings are unbiased, a maximum of two Bobs can sequentially share the nonlocality through the violation of our inequalities. Further, we show that the local bound of the aforementioned family of inequalities gets reduced if nontrivial preparation noncontextuality assumptions are further imposed. Then there is a chance to share the nontrivial preparation contextuality for a greater number of Bobs than that of nonlocality. We demonstrate that the nontrivial preparation contextuality can be sequentially shared by arbitrary numbers of Bob for unbiased choices of his measurement settings.
This paper illustrates a direct connection between quantum steering and non-trivial preparation contextuality. In two party-two measurement per party-two outcomes per measurement
(2−2−2) Bell scenario, any argument of Bell nonlocality is a proof of trivial preparation contextuality; however, the converse may not hold. If one of the parties (say, Alice) performs the measurements of more than two dichotomic observables, then it is possible to find a set of non-trivial functional relations between Alice's observables. We argue that the existence of a suitable set of such non-trivial relations between Alice's observables may warrant the unsteerability of quantum states at the end of another spatially separated party (say, Bob). Interestingly, such constraints can be read as non-trivial preparation non-contextuality assumptions in an ontological model. We further demonstrate two types of Bell inequalities that can be converted into linear steering inequalities using the aforementioned non-trivial conditions on Alice's observables. Such steering inequalities can also be considered as non-trivial preparation noncontextual inequalities. Since the local bound of the family of Bell expression gets reduced under the additional non-trivial conditions, it provides a test of quantum steering and nonlocality from the same family of Bell expressions depending upon its violation of the non-trivial preparation non-contextual or the local bound, thereby establishing a direct connection between quantum steering and non-trivial preparation contextuality.
Of late, there has been an upsurge of interest in studying the sequential sharing of various forms of quantum correlations, viz., nonlocality, preparation contextuality, coherence, and entanglement. In this work, we explore the sequential sharing of nonlocality in a quantum network. We first consider the simplest case of the two-input bilocality scenario that features two independent sources and three parties, including two edge parties and a central party. We demonstrate that, in the symmetric case when the sharing is considered for both the edge parties, the nonlocality can be shared by, at most, two sequential observers per edge party. However, in the asymmetric case, when the sharing across one edge party is considered, we show that, at most, six sequential observers can share the nonlocality in the network. We extend our investigation to the two-input
n-local scenario in the star-network configuration that features an arbitrary
n number of edge parties and one central party. In the asymmetric case, we demonstrate that the network nonlocality can be shared by an unbounded number of sequential observers across one edge party for a suitably large value of
n. Further, we generalize our study for an arbitrary
m input
n-local scenario in the star-network configuration. We show that, even for an arbitrary
m input scenario, the nonlocality can be shared by an unbounded number of sequential observers. However, increasing the input
m, one has to employ a larger number of edge parties
n than that of the two-input case to demonstrate the sharing of an unbounded number of sequential observers.
Abstract In a bipartite Bell scenario involving two local measurements per party and two outcomes per measurement, the measurement incompatibility in one wing is both necessary and sufficient to reveal the nonlocality. However, such a one-to-one correspondence fails when one of the observers performs more than two measurements. In such a scenario, the measurement incompatibility is necessary but not sufficient to reveal the nonlocality. In this work, within the formalism of general probabilistic theory (GPT), we demonstrate that unlike the nonlocality, the incompatibility of N arbitrary measurements in one wing is both necessary and sufficient for revealing the generalised contextuality for the sub-system in the other wing. Further, we formulate an elegant form of inequality for any GPT that is necessary for N-wise compatibility of N arbitrary observables. Moreover, we argue that any theory that violates the proposed inequality possess a degree of incompatibility that can be quantified through the amount of violation. We claim that it is the generalised contextuality that provides a restriction to the allowed degree of measurement incompatibility of any viable theory of nature and thereby super-select the quantum theory. Finally, we discuss the geometrical implications of our results.
Abstract The relations between Bell nonlocality and Kochen–Specker contextuality have been subject of research from many different perspectives in the last decades. Recently, some interesting results on these relations have been explored in the so-called generalized Bell scenarios, that is, scenarios where Bell spatial separation (or agency independence) coexist with (at least one of the) parties’ ability to perform compatible measurements at each round of the experiment. When this party has an n-cycle compatiblity setup, it was first claimed that Bell nonlocality could not be concomitantly observed with contextuality at this party’s local experiment. However, by a more natural reading of the definition of locality, it turns out that both Bell nonlocality and local contextuality can, in fact, be jointly present. In spite of it, in this work we prove that in the simplest of those scenarios there cannot be arbitrary amounts of both of these two resources together. That is, in these cases we show that the violation of any Bell inequality limits the possible violations of any local noncontextuality inequality. We also explore this trade-off relation using quantifiers of nonlocality and contextuality, discussing how such a relation can be understood in terms of a ‘global’ notion of contextuality, and we study possible extensions of this result to other scenarios.
Contextuality and measurement incompatibility are two fundamental aspects of nonclassicality, and their manifestations in observed quantum correlations are often deeply interconnected. Recently, measurement incompatibility has been studied in connection with nonlocality, particularly in terms of their robustness under various quantum channels. This line of investigation helps establish a connection between the channels that break nonlocality and those that break incompatibility. In this study, we focus on an asymmetric bipartite Bell scenario involving three and four inputs on Alice and Bob sides, respectively, with each of these inputs having dichotomous outcomes. Under the assumption of locality, the observed statistics in this asymmetric scenario obeys the Elegant Bell inequality (EBI). Here, we use a different version of the EBI that relies on the assumption of the preparation noncontextuality. By taking the violation of this noncontextual version of EBI as a witness of preparation contextuality we establish a connection between the channels that break contextuality and the channels that break triple-wise measurement incompatibility. Our results suggest that any channel which breaks EBI contextuality will also break Clauser-Horne-Shimony-Holt (CHSH) nonlocality; however, the reverse does not hold. We also show that a depolarising channel that breaks N-wise incompatibility can also break a certain form of contextuality, witnessed by a generalised inequality involving N measurements on one wing of a bipartite Bell scenario.