Quantum Capacity Bounds of Gaussian Thermal Loss Channels and Achievable Rates With Gottesman-Kitaev-Preskill Codes

Noh, Kyungjoo; Albert, Victor V.; Jiang, Liang

doi:10.1109/tit.2018.2873764

Cited by 154 publications

(153 citation statements)

References 96 publications

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“…Note that (11.1) is slightly tighter than (5.9) for all parameter regimes. These findings were independently discovered in [NAJ18].…”

Section: Recent Developmentsmentioning

confidence: 71%

“…We then prove that any phase-insensitive channel that is not entanglement breaking [HSR03] can be decomposed as the concatenation of a quantum-limited amplifier channel followed by a pure-loss channel. This theorem was independently proven in [NAJ18,RMG18] (see also [SWAT17]). It has been used to bound the unconstrained quantum capacity of a thermal channel in [RMG18], via a data-processing argument.…”

Section: Summary Of Resultsmentioning

confidence: 95%

“…Also, (5.10) is tighter than (5.11) for certain parameter regimes. We note that the upper bound in (5.11) was independently established in [NAJ18].…”

Section: Data-processing Bound On the Energy-constrained Quantum Capamentioning

confidence: 85%

“…We use this technique to prove an upper bound on the energy-constrained quantum and private capacities of a thermal channel. This technique has also been used most recently in [NAJ18] in similar contexts. In particular, we find that this upper bound is very near to a known lower bound for the case of low thermal noise and both low and high transmissivity.…”

Section: Summary Of Resultsmentioning

confidence: 99%

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Bounding the energy-constrained quantum and private capacities of phase-insensitive bosonic Gaussian channels

et al. 2018

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We establish several upper bounds on the energy-constrained quantum and private capacities of all single-mode phase-insensitive bosonic Gaussian channels. The first upper bound, which we call the 'data-processing bound,' is the simplest and is obtained by decomposing a phase-insensitive channel as a pure-loss channel followed by a quantum-limited amplifier channel. We prove that the dataprocessing bound can be at most 1.45 bits larger than a known lower bound on these capacities of the phase-insensitive Gaussian channel. We discuss another data-processing upper bound as well. Two other upper bounds, which we call the 'ε-degradable bound' and the 'ε-close-degradable bound,' are established using the notion of approximate degradability along with energy constraints. We find a strong limitation on any potential superadditivity of the coherent information of any phase-insensitive Gaussian channel in the low-noise regime, as the data-processing bound is very near to a known lower bound in such cases. We also find improved achievable rates of private communication through bosonic thermal channels, by employing coding schemes that make use of displaced thermal states. We end by proving that an optimal Gaussian input state for the energy-constrained, generalized channel divergence of two particular Gaussian channels is the two-mode squeezed vacuum state that saturates the energy constraint. What remains open for several interesting channel divergences, such as the diamond norm or the Rényi channel divergence, is to determine whether, among all input states, a Gaussian state is optimal.

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“…Note that (11.1) is slightly tighter than (5.9) for all parameter regimes. These findings were independently discovered in [NAJ18].…”

Section: Recent Developmentsmentioning

confidence: 71%

Section: Summary Of Resultsmentioning

confidence: 95%

“…Also, (5.10) is tighter than (5.11) for certain parameter regimes. We note that the upper bound in (5.11) was independently established in [NAJ18].…”

Section: Data-processing Bound On the Energy-constrained Quantum Capamentioning

confidence: 85%

Section: Summary Of Resultsmentioning

confidence: 99%

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Bounding the energy-constrained quantum and private capacities of phase-insensitive bosonic Gaussian channels

et al. 2018

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“…Here ò p , ò q are real Gaussian distributed with standard deviation σ. In fact, it suffices to consider AWGN channels for all Gaussian noise models, due to channel reduction relations [59][60][61][62][63]. As an example, the excitation loss channel h  can be combined with an amplification channel  G in front, described by the mode transform ¢ = -a G a G e 1ˆ † joint on the vacuum environment mode eˆ.…”

Section: Error Correctionmentioning

confidence: 99%

Distributed quantum sensing enhanced by continuous-variable error correction

2020

Self Cite

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A distributed sensing protocol uses a network of local sensing nodes to estimate a global feature of the network, such as a weighted average of locally detectable parameters. In the noiseless case, continuous-variable (CV) multipartite entanglement shared by the nodes can improve the precision of parameter estimation relative to the precision attainable by a network without shared entanglement; for an entangled protocol, the root mean square estimation error scales like 1/M with the number M of sensing nodes, the so-called Heisenberg scaling, while for protocols without entanglement, the error scales like M 1 . However, in the presence of loss and other noise sources, although multipartite entanglement still has some advantages for sensing displacements and phases, the scaling of the precision with M is less favorable. In this paper, we show that using CV error correction codes can enhance the robustness of sensing protocols against imperfections and reinstate Heisenberg scaling up to moderate values of M. Furthermore, while previous distributed sensing protocols could measure only a single quadrature, we construct a protocol in which both quadratures can be sensed simultaneously. Our work demonstrates the value of CV error correction codes in realistic sensing scenarios.Quantum sensing [1-11] uses nonclassical resources to enhance measurement precision. It has many applications, including atomic clocks [12,13], the laser interferometer gravitational-wave observatory [14,15], quantum illumination [16][17][18][19][20][21][22], quantum reading [23] and bio-sensing [24]. When the sensing task involves multiple parties, entanglement can be extremely beneficial. Early works have already shown that when measuring a single physical parameter with M sensor probes, entanglement among the sensors can reduce the root mean square (rms) estimation error to the Heisenberg scaling [4-6, 25-28] of ∝1/M. In contrast, in the absence of entanglement, the rms estimation error always obeys the standard quantum limit (SQL) scaling of µ M 1 , as dictated by the law of large numbers. More recently, this separation between Heisenberg and SQL scaling has been generalized to the scenario of distributed sensing, where an array of sensors aims to sense a global feature, such as a weighted average, of some local parameters detected by different sensor nodes [29][30][31][32][33]. In particular, [31] proposed a protocol to use continuous variable (CV) multi-partite entanglement to enhance the distributed sensing of displacements and phases, which led to the first experimental demonstration [34] of sensing advantage enabled by multi-partite entanglement.Despite being more robust against loss than their discrete variable (DV) cousins, the performance enhancement in CV distributed sensing protocols still decays in the presence of loss and noise [35]. As a consequence, [34] only achieved a ∼20% advantage in the rms estimation error. Therefore, loss mitigation is OPEN ACCESS RECEIVED

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Quantum Computation with Continuous-Variable Systems

Matsuura

2023

Springer Theses

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Quantum Capacity Bounds of Gaussian Thermal Loss Channels and Achievable Rates With Gottesman-Kitaev-Preskill Codes

Cited by 154 publications

References 96 publications

Bounding the energy-constrained quantum and private capacities of phase-insensitive bosonic Gaussian channels

Bounding the energy-constrained quantum and private capacities of phase-insensitive bosonic Gaussian channels

Distributed quantum sensing enhanced by continuous-variable error correction

Quantum Computation with Continuous-Variable Systems

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