Bosonic quantum communication across arbitrarily high loss channels

Lami, Ludovico; Plenio, Martin B.; Giovannetti, Vittorio; Holevo, Alexander S.

doi:10.48550/arxiv.2003.08895

Cited by 2 publications

(2 citation statements)

References 59 publications

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“…Nevertheless there is an increasing pressure to go beyond the Gaussian channels paradigm [7,8]. Heading in this direction we investigate here the quantum capacity of one of the most physically relevant non-Gaussian channel, namely the dephasing channel (see e.g.…”

Section: Introductionmentioning

confidence: 99%

Quantum capacity of a bosonic dephasing channel

2020

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We study the LOCC-assisted quantum capacity of bosonic dephasing channel with energy constraint on input states. We start our analysis by focusing on the energy-constrained squashed entanglement of the channel, which is an upper bound for the energy-constrained LOCC-assisted quantum capacity. As computing energy-constrained squashed entanglement of the channel is challenging due to a double optimization (over the set of density matrices and over the isometric extensions of a squashing channel), we first derive an upper bound for it, and then we discuss how tight that bound is for energy-constrained LOCC-assisted quantum capacity of bosonic dephasing channel. We prove that the optimal input state is diagonal in the Fock basis. Furthermore, we prove that the optimal squashing channel in the set of weakly-degradable and anti-degradable channels is a weakly-self-complementary channel. Restricting the search for optimal squashing channel to the set of weakly-self-complementary one-mode Gaussian quantum channels, we derive explicit upper and lower bounds for the energy-constrained LOCC-assisted quantum capacity of the bosonic dephasing channel in terms of its quantum capacity with different noise parameters. Thanks to the tightness of these bounds we provide a very good estimation of the LOCC-assisted quantum capacity of bosonic dephasing channel. We also study weakly-self-complementary qubit squashing channels which gives tighter upper bound to the energy-constrained LOCC-assisted quantum capacity of bosonic dephasing channel.

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Section: Introductionmentioning

confidence: 99%

Quantum capacity of a bosonic dephasing channel

2020

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“…The proof of this theorem, which we give in Appendix A, is obtained by assuming the existence of a quantum channel Γ satisfying the degradability condition (63) and then showing that this leads to a contradiction. In particular, for q ≤ 1/2 the claim follows from the fact that the channel is Gaussian universally anti-degradable, but has positive coherent information, and hence cannot be anti-degradable, for some non-Gaussian environment states [19].…”

Section: Universal (Anti-)degradability Propertiesmentioning

confidence: 99%

Capacities of Gaussian Quantum Channels with Passive Environment Assistance

Oskouei,

Mancini,

Winter

2021

Preprint

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Passive environment assisted communication takes place via a quantum channel modeled as a unitary interaction between the information carrying system and an environment, where the latter is controlled by a passive helper, who can set its initial state such as to assist sender and receiver, but not help actively by adjusting her behaviour depending on the message. Here we investigate the information transmission capabilities in this framework by considering Gaussian unitaries acting on Bosonic systems.We consider both quantum communication and classical communication with helper, as well as classical communication with free classical coordination between sender and helper (conferencing encoders).Concerning quantum communication, we prove general coding theorems with and without energy constraints, yielding multi-letter (regularized) expressions.In the search for cases where the capacity formula is computable, we look for Gaussian unitaries that are universally degradable or anti-degradable. However, we show that no Gaussian unitary yields either a degradable or anti-degradable channel for all environment states. On the other hand, restricting to Gaussian environment states, results in universally degradable unitaries, for which we thus can give single-letter quantum capacity formulas.Concerning classical communication, we prove a general coding theorem for the classical capacity under and energy constraint, given by a multi-letter expression. Furthermore, we derive an uncertainty-type relation between the classical capacities of the sender and the helper, helped respectively by the other party, showing a lower bound on the sum of the two capacities. Then, this is used to lower bound the classical information transmission rate in the scenario of classical communication between sender and helper.

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Bosonic quantum communication across arbitrarily high loss channels

Cited by 2 publications

References 59 publications

Quantum capacity of a bosonic dephasing channel

Quantum capacity of a bosonic dephasing channel

Capacities of Gaussian Quantum Channels with Passive Environment Assistance

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