New Lower Bounds to the Output Entropy of Multi-Mode Quantum Gaussian Channels

Palma, Giacomo De

doi:10.1109/tit.2019.2914434

Cited by 13 publications

(16 citation statements)

References 39 publications

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“…The main idea of the proof of ( 35) is perturbing the state with the quantum heat semigroup. The same idea has been crucial in the proofs of several quantum versions of the Entropy Power Inequality [43][44][45][46][47][48][49][50][51][52][53][54], of which (35) can be considered a generalization. Let Ḡ achieve the maximum in (35) (if the maximum is not achieved, the result can be obtained with a limiting argument).…”

Section: Generalized Strong Subadditivitymentioning

confidence: 96%

Linear growth of the entanglement entropy for quadratic Hamiltonians and arbitrary initial states

Palma

Hackl

2022

SciPost Phys.

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We prove that the entanglement entropy of any pure initial state of a bipartite bosonic quantum system grows linearly in time with respect to the dynamics induced by any unstable quadratic Hamiltonian. The growth rate does not depend on the initial state and is equal to the sum of certain Lyapunov exponents of the corresponding classical dynamics. This paper generalizes the findings of [Bianchi et al., JHEP 2018, 25 (2018)], which proves the same result in the special case of Gaussian initial states. Our proof is based on a recent generalization of the strong subadditivity of the von Neumann entropy for bosonic quantum systems [De Palma et al., arXiv:2105.05627]. This technique allows us to extend our result to generic mixed initial states, with the squashed entanglement providing the right generalization of the entanglement entropy. We discuss several applications of our results to physical systems with (weakly) interacting Hamiltonians and periodically driven quantum systems, including certain quantum field theory models.

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Section: Generalized Strong Subadditivitymentioning

confidence: 96%

Linear growth of the entanglement entropy for quadratic Hamiltonians and arbitrary initial states

Palma

Hackl

2022

SciPost Phys.

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“…The classical capacity region of a general broadcast channel is still an open problem with or without EA [16,17], except for special cases [16,[18][19][20]. For bosonic optical broadcast channels, although the capacity formula is known in the pure-loss case [19,20], the classical capacity region is still subject to the multi-mode 'entropy photon number inequality' conjecture [21][22][23][24]; for phase-insensitive bosonic Gaussian MACs (BGMACs) that model optical networks, the classical capacity formula with and without EA are known [25][26][27][28][29], whereas the capacity evaluation remains an open question [29,30]. Indeed, unlike the single-sender and single-receiver case, the problem of additivity is complicated by the trade-off between the different senders.…”

Section: Introductionmentioning

confidence: 99%

Computable limits of optical multiple-access communications

Shi,

Zhuang

2021

Preprint

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Communication rates over quantum channels can be boosted by entanglement, via superadditivity phenomena or entanglement assistance. Superadditivity refers to the capacity improvement from entangling inputs across multiple channel uses. Nevertheless, when unlimited entanglement assistance is available, the entanglement between channel uses becomes unnecessary-the entanglementassisted (EA) capacity of a single-sender and single-receiver channel is additive. We generalize the additivity of EA capacity to general multiple-access channels (MACs) for the total communication rate. Furthermore, for optical communication modelled as phase-insensitive bosonic Gaussian MACs, we prove that the optimal total rate is achieved by Gaussian entanglement and therefore can be efficiently evaluated. To benchmark entanglement's advantage, we propose computable outer bounds for the capacity region without entanglement assistance. Finally, we formulate an EA version of minimum entropy conjecture, which leads to the additivity of the capacity region of phaseinsensitive bosonic Gaussian MACs if it is true. The computable limits confirm entanglement's boosts in optical multiple-access communications.

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“…Secrecy in the form of quantum state masking was recently considered in [63]. Quantum broadcast channels were studied in various settings as well, e.g., [64][65][66][67][68][69][70][71][72][73][74]. Yard et al [64] derived the superposition inner bound and determined the capacity region for the degraded classical-quantum broadcast channel.…”

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confidence: 99%

“…The achievability proof is based on rate-splitting, combining the "superposition coding" strategy with the OTP cypher using the shared key. The converse proof relies on the long-standing minimum output-entropy conjecture, which is known to hold in special cases [72]. Without key assistance, confidential transmission is only possible if Bob's channel has a higher transmissivity than Eve's channel, i.e., η > 1 2 .…”

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confidence: 99%

Key Assistance, Key Agreement, and Layered Secrecy for Bosonic Broadcast Channels

Pereg¹,

Ferrara²,

Bloch³

2021

Preprint

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Secret-sharing building blocks based on quantum broadcast communication are studied. The confidential capacity region of the pure-loss bosonic broadcast channel is determined, both with and without key assistance, and an achievable region is established for the lossy bosonic broadcast channel. If the main receiver has a transmissivity of η < 1 2 , then confidentiality solely relies on the key-assisted encryption of the one-time pad. We also address conference key agreement for the distillation of two keys, a public key and a secret key. A regularized formula is derived for the key-agreement capacity region in finite dimensions. In the bosonic case, the key-agreement region is included within the capacity region of the corresponding broadcast channel with confidential messages. We then consider a network with layered secrecy, where three users with different security ranks communicate over the same broadcast network. We derive an achievable layered-secrecy region for a pure-loss bosonic channel that is formed by the concatenation of two beam splitters.

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New Lower Bounds to the Output Entropy of Multi-Mode Quantum Gaussian Channels

Cited by 13 publications

References 39 publications

Linear growth of the entanglement entropy for quadratic Hamiltonians and arbitrary initial states

Linear growth of the entanglement entropy for quadratic Hamiltonians and arbitrary initial states

Computable limits of optical multiple-access communications

Key Assistance, Key Agreement, and Layered Secrecy for Bosonic Broadcast Channels

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