Optimality of any pair of incompatible rank-one projective measurements for some nontrivial Bell inequality

Alves, Gabriel Pereira; Kaniewski, Jędrzej

doi:10.1103/physreva.106.032219

Cited by 2 publications

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“…Two proposals in this direction have succeeded in designing different classes of Bell inequalities tailored to the broad family of multi-qubit graph states [17,18] and the first Bell inequalities maximally violated by the maximally entangled state of any local dimension [19]. The success of these methods was further confirmed by later applications to design the first self-testing Bell inequalities for graph states [20] (see also [21] for the first self-testing method for multi-qubit graph states which, however, is not directly based on violation of Bell inequalities), for genuinely entangled stabilizer subspaces [22,23] or maximally entangled two-qutrit states [24], as well as to derive many other classes of Bell inequalities tailored to two-qudit maximally entangled [25,26] or many-qudit Greenberger-Horne-Zeilinger (GHZ) states [27]. Some of these constructions were later exploited to provide self-testing schemes for the maximally entangled [25,28] or the GHZ states [29] of arbitrary local dimension.…”

Section: Introductionmentioning

confidence: 93%

“…It is worth stressing here that one of the key observations making the construction of [20] work is that for any graph there exists a choice of observables at any site, given by the above formulas, turning the quantum operators appearing in the expectation values of ( 27) into the stabilising operators G i ; in particular, it is a well-known fact that combinations of the Pauli matrices in equation ( 28) are proper quantum observables with eigenvalues ±1. Let us also mention that the replacement in equations ( 25) and (26) guarantees that the maximal quantum and classical values of the inequalities ( 27) can be determined basically by hand and that they differ for any graph state, implying that all these inequalities are nontrivial.…”

Section: Multiqubit Graph Statesmentioning

confidence: 99%

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Scalable Bell inequalities for graph states of arbitrary prime local dimension and self-testing

2023

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Bell nonlocality---the existence of quantum correlations that cannot be explained by classical means---is certainly one of the most striking features of quantum mechanics. Its range of applications in device-independent protocols is constantly growing. Many relevant quantum features can be inferred from violations of Bell inequalities, including entanglement detection and quantification, and state certification applicable to systems of arbitrary number of particles. A complete characterisation of nonlocal correlations for many-body systems is, however, a computationally intractable problem. Even if one restricts the analysis to specific classes of states, no general method to tailor Bell inequalities to be violated by a given state is known. In this work we provide a general construction of Bell expressions tailored to the graph states of any prime local dimension. These form a broad class of multipartite quantum states that have many applications in quantum information, including quantum error correction. We analytically determine their maximal quantum values, a number of high relevance for device-independent applications of Bell inequalities. Importantly, the number of expectation values to determine in order to test the violation of our inequalities scales only linearly with the system size, which we expect to be the optimal scaling one can hope for in this case. Finally, we show that these inequalities can be used for self-testing of multi-qutrit graph states such as the well-known four-qutrit absolutely maximally entangled state AME(4,3).

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Section: Introductionmentioning

confidence: 93%

Section: Multiqubit Graph Statesmentioning

confidence: 99%

Scalable Bell inequalities for graph states of arbitrary prime local dimension and self-testing

2023

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Unbounded Device-Independent Quantum Key Rates from Arbitrarily Small Nonlocality

Farkas

2024

Phys. Rev. Lett.

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Device-independent quantum key distribution allows for proving the security of a shared cryptographic key between two distant parties with potentially untrusted devices. The security proof is based on the measurement outcome statistics (correlation) of a Bell experiment, and security is guaranteed by the laws of quantum theory. While it is known that the observed correlation must be Bell nonlocal in order to prove security, recent results show that Bell nonlocality is in general not sufficient for standard device-independent quantum key distribution. In this work, we show that conversely, there is no lower bound on the amount of nonlocality that is sufficient for device-independent quantum key distribution. Even more so, we show that from certain correlations that exhibit arbitrarily small nonlocality, one can still extract unbounded device-independent key rates. Therefore, a quantitative relation between device-independent key rates and Bell nonlocality cannot be drawn in general. Our main technique comprises a rigorous connection between self-testing and device-independent quantum key distribution, applied to a recently discovered family of Bell inequalities with arbitrarily many measurement outcomes. Published by the American Physical Society 2024

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Optimality of any pair of incompatible rank-one projective measurements for some nontrivial Bell inequality

Cited by 2 publications

References 20 publications

Scalable Bell inequalities for graph states of arbitrary prime local dimension and self-testing

Scalable Bell inequalities for graph states of arbitrary prime local dimension and self-testing

Unbounded Device-Independent Quantum Key Rates from Arbitrarily Small Nonlocality

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