Gaussian States Minimize the Output Entropy of One-Mode Quantum Gaussian Channels

Palma, Giacomo De; Trevisan, Dario; Giovannetti, Vittorio

doi:10.1103/physrevlett.118.160503

Cited by 32 publications

(44 citation statements)

References 42 publications

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“…Entanglement production has been extensively studied in physical systems ranging from quantum fields and gravity [1][2][3][4][5][6][7][8] to condensed matter [9][10][11][12][13][14] and quantum information [15][16][17]. It has been recently probed experimentally in systems of ultracold bosonic atoms in optical lattices [18,19].…”

Section: Introductionmentioning

confidence: 99%

Entanglement production in bosonic systems: Linear and logarithmic growth

et al. 2018

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We study the time evolution of the entanglement entropy in bosonic systems with timeindependent, or time-periodic, Hamiltonians. In the first part, we focus on quadratic Hamiltonians and Gaussian initial states. We show that all quadratic Hamiltonians can be decomposed into three parts: (a) unstable, (b) stable, and (c) metastable. If present, each part contributes in a characteristic way to the time-dependence of the entanglement entropy: (a) linear production, (b) bounded oscillations, and (c) logarithmic production. In the second part, we use numerical calculations to go beyond Gaussian states and quadratic Hamiltonians. We provide numerical evidence for the conjecture that entanglement production through quadratic Hamiltonians has the same asymptotic behavior for non-Gaussian initial states as for Gaussian ones. Moreover, even for non-quadratic Hamiltonians, we find a similar behavior at intermediate times. Our results are of relevance to understanding entanglement production for quantum fields in dynamical backgrounds and ultracold atoms in optical lattices. arXiv:1710.04279v2 [hep-th]

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Section: Introductionmentioning

confidence: 99%

Entanglement production in bosonic systems: Linear and logarithmic growth

et al. 2018

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“…Such an EA scenario is widely applicable to radiofrequency communication, deep space communication [21], and covert communication [22,23].Despite the large advantage of EA capacity, a practical EA encoding and decoding scheme that achieves any advantage over the classical capacity is unknown in the high noise regime. Previous experiments [24,25] focused on ideal scenarios with qubits; Although the EA capac- * zhuangquntao@email.arizona.edu ity formula for bosonic Gaussian channel is well established [26,27], the achievability proof in Ref.[1] relies on approximating an infinite dimensional channel as a channel with finite but large dimension; thus a structured encoding scheme is not given for bosonic channels. In fact, simple schemes like continuous-variable (CV) superdense coding [28][29][30] do not beat the classical capacity in the noisy and weak signal regime [31], making experimental demonstrations of the EA capacity advantage elusive [32][33][34].…”

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confidence: 99%

Practical Route to Entanglement-Assisted Communication Over Noisy Bosonic Channels

2020

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Entanglement can offer substantial advantages in quantum information processing, but loss and noise hinder its applications in practical scenarios. Although it has been well known for decades that the classical communication capacity over lossy and noisy bosonic channels can be significantly enhanced by entanglement, no practical encoding and decoding schemes are available to realize any entanglement-enabled advantage. Here, we report structured encoding and decoding schemes for such an entanglement-assisted communication scenario. Specifically, we show that phase encoding on the entangled two-mode squeezed vacuum state saturates the entanglement-assisted classical communication capacity and overcomes the fundamental limit of covert communication without entanglement assistance. We then construct receivers for optimum hypothesis testing protocols under discrete phase modulation and for optimum noisy phase estimation protocols under continuous phase modulation. Our results pave the way for entanglement-assisted communication and sensing in the radiofrequency and microwave spectral ranges. I. INTRODUCTIONEntanglement's benefit for quantum information processing has been revealed by pioneer works in communication [1], sensing [2-4], and computation [5]. Notably, the entanglement-enabled advantages even survive loss and noise in certain scenarios, as predicted [6][7][8] and experimentally demonstrated [9][10][11] in the entanglementenhanced sensing protocol called quantum illumination.It is also known, in theory, that pre-shared entanglement increases the classical communication capacity, i.e., the maximum rate of reliable communication of classical bits (cbits), over a quantum channel Φ. In an ideal case, the superdense-coding [12] protocol allows for sending two cbits on a single qubit, with the assistance of one entanglement bit (ebit). Formally, one characterizes the rate limit of such EA communication by the classical capacity with unlimited entanglement-assistance [1,[13][14][15], C E (Φ) [16]. Compared with the classical capacity without entanglement-assistance, i.e., the Holevo-Schumacher-Westmoreland capacity, C (Φ) [17][18][19], the improvement enabled by entanglement can be drastic even over a noisy channel Φ. In particular, it is known [1] that the ratio of C E (Φ) /C (Φ) can diverge logarithmically with the inverse of signal power over a noisy and lossy bosonic channel [20]. Such an EA scenario is widely applicable to radiofrequency communication, deep space communication [21], and covert communication [22,23].Despite the large advantage of EA capacity, a practical EA encoding and decoding scheme that achieves any advantage over the classical capacity is unknown in the high noise regime. Previous experiments [24,25] focused on ideal scenarios with qubits; Although the EA capac- * zhuangquntao@email.arizona.edu ity formula for bosonic Gaussian channel is well established [26,27], the achievability proof in Ref.[1] relies on approximating an infinite dimensional channel as a channel with finite but large d...

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“…Now, we need to consider proper lower bounds on the quantum capacity for our general attenuators and amplifiers in order to compare with the upper bounds. We can obtain lower bounds on those channels by means of Gaussian optimizer with fixed input entropy [30], in which the thermal state reaches the minimum output entropy of the given channel. We can express a lower bound of the quantum capacity for the general attenuator as…”

Section: Lower Bounds On the Quantum Capacitymentioning

confidence: 99%

Upper bounds on the quantum capacity for a general attenuator and amplifier

et al. 2019

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There have been several upper bounds on the quantum capacity of the single-mode Gaussian channels with thermal noise, such as thermal attenuator and amplifier. We consider a class of attenuator and amplifier with more general noises, including squeezing or even non-Gaussian one. We derive new upper bounds on the energy-constrained quantum capacity of those channels by using the quantum conditional entropy power inequality. Also, we obtain lower bounds for the same channels by means of Gaussian optimizer with fixed input entropy. They give narrow bounds when the transmissivity is near unity and the energy of input state is low.

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Gaussian States Minimize the Output Entropy of One-Mode Quantum Gaussian Channels

Cited by 32 publications

References 42 publications

Entanglement production in bosonic systems: Linear and logarithmic growth

Entanglement production in bosonic systems: Linear and logarithmic growth

Practical Route to Entanglement-Assisted Communication Over Noisy Bosonic Channels

Upper bounds on the quantum capacity for a general attenuator and amplifier

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