Sharing nonlocality and nontrivial preparation contextuality using the same family of Bell expressions

Kumari, Anupma; Pan, A. K.

doi:10.1103/physreva.100.062130

Cited by 68 publications

(53 citation statements)

References 24 publications

(46 reference statements)

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“…Since the presence of non-locality implies the possibility of steering and the presence of entanglement, our work shows that it is also possible to achieve both of these with arbitrarily many independent Bobs using only a single pair of entangled qubits. This goes against some of the results in [18,22,23], and suggests that it is worth rethinking others that study the space of such correlations [24] or look at other Bell in-equalities [25] or more parties [26,27] after removing the assumption that both measurements used by each party have the same sharpness.…”

Section: Discussionmentioning

confidence: 98%

Arbitrarily Many Independent Observers can Share the Nonlocality of a Single Maximally Entangled Qubit Pair

2020

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Alice and Bob each have half of a pair of entangled qubits. Bob measures his half and then passes his qubit to a second Bob who measures again and so on. The goal is to maximize the number of Bobs that can have an expected violation of the Clauser-Horne-Shimony-Holt (CHSH) Bell inequality with the single Alice. This scenario was introduced in [Phys. Rev. Lett. 114, 250401 (2015)] where the authors mentioned evidence that when the Bobs act independently and with unbiased inputs then at most two of them can expect to violate the CHSH inequality with Alice. Here we show that, contrary to this evidence, arbitrarily many independent Bobs can have an expected CHSH violation with the single Alice. Our proof is constructive and our measurement strategies can be generalized to work with a larger class of two-qubit states that includes all pure entangled two-qubit states. Since violation of a Bell inequality is necessary for device-independent tasks, our work represents a step towards an eventual understanding of the limitations on how much device-independent randomness can be robustly generated from a single pair of qubits.

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Section: Discussionmentioning

confidence: 98%

Arbitrarily Many Independent Observers can Share the Nonlocality of a Single Maximally Entangled Qubit Pair

2020

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“…(12) when the dimension of the system is lower than that is required for achieving the optimal quantum value (B n ) opt Q . One of us have shown [39] that the sharing of preparation contextuality can be demonstrated by arbitrary number of Bobs by using optimal quantum value (B n ) opt Q for d = 2 n/2 dimensional Hilbert space. Here, by providing the examples of n = 5 and n = 6, we have demonstrated that even for lower dimensional system the number of Bobs who can share the preparation contextuality remains same but the value of unshrapness parameter required is always higher in lower dimensional system.…”

Section: Summary and Discussionmentioning

confidence: 99%

Device-independent certification of the Hilbert-space dimension using a family of Bell expressions

Pan

Mahato

2020

Phys. Rev. A

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Dimension witness provides a device-independent certification of the minimal dimension required to reproduce the observed data without imposing assumptions on the functioning of the devices used to generate the experimental statistics. In this paper, we provide a family of Bell expressions where Alice and Bob perform 2 n−1 and n number of dichotomic measurements respectively which serve as the device-independent dimension witnesses of Hilbert space of 2 m dimensions with m = 1, 2..2 n/2. The family of Bell expressions considered here determines the success probability of a communication game known as n-bit parity-oblivious random access code. The parity obliviousness constraint is equivalent to preparation non-contextuality assumption in an ontological model of an operational theory. For any given n ≥ 3, if such a constraint is imposed on the encoding scheme of the random-access code, then the local bound of the Bell expression reduces to the preparation noncontextual bound. We provide explicit examples for n = 4, 5 case to demonstrate that the relevant Bell expressions certify the qubit and two-qubit system, and for n = 6 case, the relevant Bell expression certifies the qubit, two-qubit and three-qubit systems. We further demonstrate the sharing of quantum preparation contextuality by multiple Bobs sequentially to examine whether number of Bobs sharing the preparation contextuality is dependent on the dimension of the system. We provide explicit example of n = 5 and 6 to demonstrate that number of Bobs sequentially sharing the contextuality remains same for any of the 2 m dimensional systems.

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“…x 1 and y i x 2 by invoking the encoding scheme used in Random Access Codes (RACs) [43][44][45][46] as a tool. This will fix 1 or −1 values of (−1) y i x 1 and (−1) y i x 2 in Eq.…”

Section: Generalized Bilocality and N-locality Scenario In Star-netwo...mentioning

confidence: 99%

Generalized $n$-locality inequalities in star-network configuration and their optimal quantum violations

Munshi,

Pan

2021

Preprint

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Network Bell experiments reveal a form of nonlocality conceptually different from standard Bell nonlocality. Standard multiparty Bell experiments involve a single source shared by a set of observers. In contrast, network Bell experiments feature multiple independent sources, and each of them may distribute physical systems to a set of observers who perform randomly chosen measurements. The n-locality scenario in star-network configuration involves n number of edge observers (Alices), a central observer (Bob), and n number of independent sources having no prior correlation. Each Alice shares an independent state with the central observer Bob. Usually, in network Bell experiments, one considers that each party measures only two observables. In this work, we propose a non-trivial generalization of n-locality scenario in star-network configuration, where each Alice performs some integer m number of binary-outcome measurements, and the central party Bob performs 2 m−1 binary-outcome measurements. We derive a family of generalized n-locality inequalities for any arbitrary m. Using bluean elegant sum-of-squares approach, we derive the optimal quantum violation of the aforementioned inequalities can be attained when each and every Alice measures m number of mutually anticommuting observables. For m = 2 and 3, one obtains the optimal quantum value bluefor qubit system local to each Alice, and it is sufficient to consider the sharing of a two-qubit entangled state between each Alice and Bob. We further demonstrate that the optimal quantum violation of n-locality inequality for any arbitrary m can be obtained when every Alice shares m/2 copies of two-qubit maximally entangled state with the central party Bob. We also argue that for m > 3, a single copy of a two-qubit entangled state may not be enough to exhibit the violation of n-locality inequality but multiple copies of it can activate the quantum violation. We discuss the implications of our study and raise some open questions.

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Sharing nonlocality and nontrivial preparation contextuality using the same family of Bell expressions

Cited by 68 publications

References 24 publications

Arbitrarily Many Independent Observers can Share the Nonlocality of a Single Maximally Entangled Qubit Pair

Arbitrarily Many Independent Observers can Share the Nonlocality of a Single Maximally Entangled Qubit Pair

Device-independent certification of the Hilbert-space dimension using a family of Bell expressions

Generalized $n$-locality inequalities in star-network configuration and their optimal quantum violations

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