Semi-device-independent certification of entanglement in superdense coding

Moreno, George; Nery, Ranieri; Gois, Carlos de; Rabelo, Rafael; Chaves, Rafael

doi:10.1103/physreva.103.022426

Cited by 14 publications

(15 citation statements)

References 52 publications

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“…Yet, in contrast to the simpler Bell and PM scenarios, the correlations that can be established in this more general scenario have received much less attention. When communication is quantum, some studies have been made on protocols similar to quantum dense coding [8,9]. When communication is classical, notable previous works have focused on reducing the communication complexity of specific functions [10][11][12][13] and on Bell scenarios featuring superluminal communication [14,15].…”

Section: Introductionmentioning

confidence: 99%

Entanglement in prepare-and-measure scenarios: many questions, a few answers

Pauwels,

Tavakoli,

Woodhead

et al. 2021

Preprint

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Entanglement and quantum communication are paradigmatic resources in quantum information science leading to correlations between systems that have no classical analogue. Correlations due to entanglement when communication is absent have for long been studied in Bell scenarios. Correlations due to quantum communication when entanglement is absent have been studied extensively in prepare-and-measure scenarios in the last decade. Here, following up on a recent companion paper [arXiv:2103.10748], we set out to understand and investigate correlations in scenarios that involve both entanglement and communication, focusing on entanglement-assisted prepare-and-measure scenarios. We establish several elementary relations between standard classical and quantum communication and their entanglement-assisted counterparts. In particular, while it was already known that bits or qubits assisted by two-qubit entanglement between the sender and receiver constitute a stronger resource than bare bits or qubits, we show that higher-dimensional entanglement further enhance the power of bits or qubits. We also provide a characterisation of generalised dense coding protocols, a natural subset of entanglement-assisted quantum communication protocols, finding that they can be understood as standard quantum communication protocols in real-valued Hilbert space. Though such dense coding protocols can convey up to two bits of information, we provide evidence, perhaps counter-intuitively, that resources with a small information capacity, such as a bare qutrits, can sometimes produce stronger correlations. Along the way we leave several conjectures and conclude with a list of interesting open problems.

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Section: Introductionmentioning

confidence: 99%

Entanglement in prepare-and-measure scenarios: many questions, a few answers

Pauwels,

Tavakoli,

Woodhead

et al. 2021

Preprint

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“…We answer this in the positive by employing our information-based SDP relaxations to bound W for the latter case. To enable this computation on a standard desktop computer, we have exploited the symmetries of the function (47) to reduce the number of variables in the final SDP matrix 8 . We find the bound…”

Section: B Qudits Can Outperform Ea Classical Ditsmentioning

confidence: 99%

Correlations in entanglement-assisted prepare-and-measure scenarios

Tavakoli,

Pauwels,

Woodhead

et al. 2021

Preprint

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We investigate the correlations that can arise between Alice and Bob in prepare-and-measure communication scenarios where the source (Alice) and the measurement device (Bob) can share prior entanglement. The paradigmatic example of such a scenario is the quantum dense coding protocol, where the communication capacity of a qudit can be doubled if a two-qudit entangled state is shared between Alice and Bob. We provide examples of correlations that actually require more general protocols based on higher-dimensional entangled states. This motivates us to investigate the set of correlations that can be obtained from communicating either a classical or a quantum d-dimensional system in the presence of an unlimited amount of entanglement. We show how such correlations can be characterized by a hierarchy of semidefinite programming relaxations by reducing the problem to a non-commutative polynomial optimization problem. We also introduce an alternative relaxation hierarchy based on the notion of informationally-restricted quantum correlations, which, though it represents a strict (non-converging) relaxation scheme, is less computationally demanding. As an application, we introduce device-independent tests of the dimension of classical and quantum systems that, in contrast to previous results, do not make the implicit assumption that Alice and Bob share no entanglement. We also establish several relations between communication with and without entanglement as resources for creating correlations.

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“…8 . More recently, the combination of both entanglement and quantum communication has also started to be considered [32][33][34] . Remarkably, it has been proven that quantum advantages in CCPs can be mapped to the violation of Bell inequalities 19,35,36 , thus establishing an important link between two key concepts of computer science and quantum theory.…”

Section: Introductionmentioning

confidence: 99%

Entanglement-based quantum communication complexity beyond Bell nonlocality

Moreno

Brito

et al. 2022

npj Quantum Inf

Self Cite

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Efficient distributed computing offers a scalable strategy for solving resource-demanding tasks, such as parallel computation and circuit optimisation. Crucially, the communication overhead introduced by the allotment process should be minimised—a key motivation behind the communication complexity problem (CCP). Quantum resources are well-suited to this task, offering clear strategies that can outperform classical counterparts. Furthermore, the connection between quantum CCPs and non-locality provides an information-theoretic insight into fundamental quantum mechanics. Here we connect quantum CCPs with a generalised non-locality framework—beyond Bell’s paradigmatic theorem—by incorporating the underlying causal structure, which governs the distributed task, into a so-called non-local hidden-variable model. We prove that a new class of communication complexity tasks can be associated with Bell-like inequalities, whose violation is both necessary and sufficient for a quantum gain. We experimentally implement a multipartite CCP akin to the guess-your-neighbour-input scenario, and demonstrate a quantum advantage when multipartite Greenberger-Horne-Zeilinger (GHZ) states are shared among three users.

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Semi-device-independent certification of entanglement in superdense coding

Cited by 14 publications

References 52 publications

Entanglement in prepare-and-measure scenarios: many questions, a few answers

Entanglement in prepare-and-measure scenarios: many questions, a few answers

Correlations in entanglement-assisted prepare-and-measure scenarios

Entanglement-based quantum communication complexity beyond Bell nonlocality

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