All entangled pure quantum states violate the bilocality inequality

Gisin, Nicolas; Mei, Quanxin; Tavakoli, Armin; Renou, Marc-Olivier; Brunner, Nicolás

doi:10.1103/physreva.96.020304

Cited by 94 publications

(84 citation statements)

References 33 publications

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“…Note added in proof. During the preparation of this manuscript which contains results of a master thesis [36], we became aware of an independent work [37] preprinted in February 2017.…”

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confidence: 99%

Maximal qubit violation of n-locality inequalities in a star-shaped quantum network

et al. 2017

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Bell's theorem was a cornerstone for our understanding of quantum theory, and the establishment of Bell non-locality played a crucial role in the development of quantum information. Recently, its extension to complex networks has been attracting a growing attention, but a deep characterization of quantum behaviour is still missing for this novel context. In this work we analyze quantum correlations arising in the bilocality scenario, that is a tripartite quantum network where the correlations between the parties are mediated by two independent sources of states. First, we prove that non-bilocal correlations witnessed through a Bell-state measurement in the central node of the network form a subset of those obtainable by means of a separable measurement. This leads us to derive the maximal violation of the bilocality inequality that can be achieved by arbitrary two-qubit quantum states and arbitrary projective separable measurements. We then analyze in details the relation between the violation of the bilocality inequality and the CHSH inequality. Finally, we show how our method can be extended to n-locality scenario consisting of n two-qubit quantum states distributed among n + 1 nodes of a star-shaped network.

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“…Note added in proof. During the preparation of this manuscript which contains results of a master thesis [36], we became aware of an independent work [37] preprinted in February 2017.…”

mentioning

confidence: 99%

Maximal qubit violation of n-locality inequalities in a star-shaped quantum network

et al. 2017

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“…As regards the quantum networks the feasibility and construction have been fully verified both theoretically [10][11][12][13][14][15][16][17][18] and experimentally [19]. To better transmit quantum information via a quantum network, related quantum network communication technologies must be explored.…”

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confidence: 99%

Efficient quantum state transmission via perfect quantum network coding

Chen

et al. 2018

Sci. China Inf. Sci.

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Quantum network coding with the assistance of auxiliary resources can achieve perfect transmission of the quantum state. This paper suggests a novel perfect network coding scheme to efficiently solve the quantum k-pair problem, in which only a few assisting resources are introduced. Specifically, only one pair of maximally entangled state needs to be pre-shared between two intermediate nodes, and only O(k) of classical information is transmitted though the network. Moreover, the classical communication used in our protocol does not cause transmission congestion, providing better adaptability to large-scale quantum k-pair networks. Through relevant analyses and comparisons, we demonstrate that our proposed scheme saves resources and has good application value, thereby showing its high efficiency. Furthermore, the proposed scheme achieves 1-max flow quantum communication, and the achievable rate region result is extended from its counterpart over the butterfly network.

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“…In the Bell scenario, a paradigmatic example is the Horodecki criterion [36], testing whether a given two-qubit quantum state can violate the Clauser-Horne-Shimony-Holt (CHSH) inequality [37]. Extensions of it to more general scenarios [38,39] and other Bell-like causal structures are also known [40,41]. In scenarios involving communication, for instance in quantum teleportation, it is known that all entangled states can lead to nonclassical correlations [42].…”

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confidence: 99%

Criteria for nonclassicality in the prepare-and-measure scenario

Poderini

Brito

Nery

et al. 2020

Phys. Rev. Research

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Quantum communication networks involving the preparation, sharing, and measurement of quantum states are ubiquitous in quantum information. Of particular relevance within this context is to understand under which conditions a given quantum resource can give rise to correlations incompatible with a classical explanation. Here we consider the so-called prepare-and-measure scenario, in which a quantum or classical message with bounded dimension is transmitted between two parties. In this scenario we derive criteria witnessing whether a set of quantum states can lead or not to nonclassical correlations. Based on that, we show that quantum resources that can only give rise to classical correlations in the simplest prepare-and-measure scenario can have their nonclassicality witnessed if we increase the number of preparations or measurements.

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All entangled pure quantum states violate the bilocality inequality

Cited by 94 publications

References 33 publications

Maximal qubit violation of n-locality inequalities in a star-shaped quantum network

Maximal qubit violation of n-locality inequalities in a star-shaped quantum network

Efficient quantum state transmission via perfect quantum network coding

Criteria for nonclassicality in the prepare-and-measure scenario

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