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

Pauwels, Jef; Tavakoli, Armin; Woodhead, Erik; Pironio, Stefano

doi:10.48550/arxiv.2108.00442

Cited by 5 publications

(17 citation statements)

References 54 publications

(55 reference statements)

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“…This example was employed to certify quantum correlations allowing to test for nonlocality, steering and quantum state tomography in a single experiment. Based on this nonlocality experiment, entanglement in prepare-and-measure scenarios was further studied in [PTWP21].…”

Section: Discussion and Open Problemsmentioning

confidence: 99%

The Interplay between Quantum Contextuality and Wigner Negativity

Emeriau¹

2022

Preprint

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Q uantum physics has revolutionised our way of conceiving nature and is now bringing about a new technological revolution. The use of quantum information in technology promises to supersede the so-called classical devices used nowadays. Understanding what features are inherently non-classical is crucial for reaching better-than-classical performance.This thesis focuses on two nonclassical behaviours: quantum contextuality and Wigner negativity. The former is a notion superseding nonlocality that can be exhibited by quantum systems. To date, it has mostly been studied in discrete-variable scenarios, where observables take values in discrete and usually finite sets. In those scenarios, contextuality has been shown to be necessary and sufficient for advantages in some cases. On the other hand, negativity of the Wigner function is another unsettling non-classical feature of quantum states that originates from phase-space formulation in continuous-variable quantum optics. Continuous-variable scenarios offer promising candidates for implementing quantum computations and informatic protocols. Wigner negativity is known to be a necessary resource for quantum speedup with continuous variables. However contextuality has been little understood and studied in continuous-variable scenarios.We first set out a robust framework for properly treating contextuality in continuous variables. We also quantify contextuality in such scenarios by using tools from infinite-dimensional optimisation theory. This is achieved by a converging hierarchy of finite-dimensional semidefinite programs that approximates the contextual fraction.Building upon this, we show that Wigner negativity is equivalent to contextuality in continuous variables with respect to Pauli measurements thus establishing a continuous-variable analogue of a celebrated result by Howard et al. in discrete variables.We then introduce experimentally-friendly witnesses for Wigner negativity of single mode and multimode quantum states, based on fidelities with Fock states. They possess a threshold expectation value indicating whether the measured state has a negative Wigner function. We phrase the problem of finding the threshold values as infinite-dimensional linear programs, and we derive two converging hierarchies of semidefinite programs to approximate the threshold values.We further extend the range of previously known discrete-variable results linking contextuality and advantage into a new territory of information retrieval. We introduce a discrete-variable communication game-called the Torpedo Game-where perfect quantum strategies stem from negativity of the discrete Wigner function. Sequential contextuality is shown not only to be necessary and sufficient for quantum advantage, but also to quantify the degree of advantage for information retrieval tasks. i Sa sagesse résonnait jusque dans ses silences. Jamais ses réponses n'étaient précipitées. Jamais mes questions n'étaient sous-estimées. Le roi n'avait pas ri

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Section: Discussion and Open Problemsmentioning

confidence: 99%

The Interplay between Quantum Contextuality and Wigner Negativity

Emeriau¹

2022

Preprint

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“…[1][2][3][4][5][6]) or with a higher success probability (see e.g. [7][8][9][10][11][12][13][14][15]). Underlying these classical communication advantages is the ability of entanglement to produce quantum nonlocality [16][17][18][19][20].…”

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confidence: 99%

“…The option of Bob to adapt to Alice's message naturally also extends to communication scenarios in which the message itself is a quantum state. For general adaptive EA quantum communication [14,15], the correlations p(b|x, y) take the form…”

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Adaptive advantage in entanglement-assisted communications

Pauwels,

Pironio,

Cruzeiro

et al. 2022

Preprint

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Entanglement is known to boost the efficiency of classical communication. In distributed computation, for instance, exploiting entanglement can reduce the number of communicated bits or increase the probability to obtain a correct answer. Entanglement-assisted classical communication protocols usually consist of two successive rounds: first a Bell test round, in which the parties measure their local shares of the entangled state, and then a communication round, where they exchange classical messages. Here, we go beyond this standard approach and investigate adaptive uses of entanglement: we allow the receiver to wait for the arrival of the sender's message before measuring his share of the entangled state. We first show that such adaptive protocols improve the success probability in Random Access Codes. Second, we show that once adaptive measurements are used, an entanglement-assisted bit becomes a strictly stronger resource than a qubit in prepare-and-measure scenarios. We briefly discuss extension of these ideas to scenarios involving quantum communication and identify resource inequalities.

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“…See appendix for details. To obtain a tight bound, we have additionally exploited the symmetries of W [43], which can dramatically boost the efficiency of such computations (examples in [43,[53][54][55]). We have proved tightness by saturating (up to solver precision) the upper bound with a lower bound obtained from an explicit quantum model found via alternating convex search in the communication scenario (see e.g.…”

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confidence: 99%

Certification of a Nonprojective Qudit Measurement using Multiport Beamsplitters

Martı́nez¹,

Gómez²,

Cariñe³

et al. 2022

Preprint

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Generalised quantum measurements go beyond the textbook concept of a projection onto an orthonormal basis in Hilbert space. They are not only of fundamental relevance but have also an important role in quantum information tasks. However, it is highly demanding to certify that a generalised measurement is indeed required to explain the results of a quantum experiment in which only the degrees of freedom are assumed to be known. Here, we use state-of-the-art multicore optical fiber technology to build multiport beamsplitters and faithfully implement a seven-outcome generalised measurement in a four-dimensional Hilbert space with a fidelity of 99.7%. We apply it to perform an elementary quantum communication task and demonstrate a success rate that cannot be simulated in any conceivable quantum protocol based on standard projective measurements on quantum messages of the same dimension. Our approach, which is compatible with modern photonic platforms, showcases an avenue for faithful and high-quality implementation of genuinely nonprojective quantum measurements beyond qubit systems.

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

Cited by 5 publications

References 54 publications

The Interplay between Quantum Contextuality and Wigner Negativity

The Interplay between Quantum Contextuality and Wigner Negativity

Adaptive advantage in entanglement-assisted communications

Certification of a Nonprojective Qudit Measurement using Multiport Beamsplitters

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