Semidefinite Programming Converse Bounds for Quantum Communication

Wang, Xin; Fang, Kun; Duan, Runyao

doi:10.1109/tit.2018.2874031

Cited by 56 publications

(72 citation statements)

References 61 publications

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“…In the following, we eliminate Ω for the case of unassisted codes. We write Ω = NS and Ω = PPT for NS-assisted and PPT-assisted codes, respectively [28][29][30][31][32]. In particular,…”

Section: Channel Simulation and Codesmentioning

confidence: 99%

Quantum Channel Simulation and the Channel’s Smooth Max-Information

Fang

Wang

Tomamichel

et al. 2020

IEEE Trans. Inform. Theory

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We study the general framework of quantum channel simulation, that is, the ability of a quantum channel to simulate another one using different classes of codes. First, we show that the minimum error of simulation and the one-shot quantum simulation cost under no-signalling assisted codes are given by semidefinite programs. Second, we introduce the channel's smooth max-information, which can be seen as a one-shot generalization of the mutual information of a quantum channel. We provide an exact operational interpretation of the channel's smooth max-information as the oneshot quantum simulation cost under no-signalling assisted codes. Third, we derive the asymptotic equipartition property of the channel's smooth max-information, i.e., it converges to the quantum mutual information of the channel in the independent and identically distributed asymptotic limit. This implies the quantum reverse Shannon theorem in the presence of no-signalling correlations. Finally, we explore the simulation cost of various quantum channels. * Electronic address: kun.fang-1@student.uts.edu.au arXiv:1807.05354v1 [quant-ph]

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Section: Channel Simulation and Codesmentioning

confidence: 99%

Quantum Channel Simulation and the Channel’s Smooth Max-Information

Fang

Wang

Tomamichel

et al. 2020

IEEE Trans. Inform. Theory

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“…The SDP is a generalization of the SDP formulation of the max-Rains information of a point-to-point channel [29]. Whereas R 2→2 max is sufficient to bound entanglement distillation rates, the existence of positive-partial-transpose (PPT) entanglement useful for quantum key distribution [14,15] motivates the introduction of a second measure of entanglement, the bidirectional max-relative entropy of entanglement:…”

mentioning

confidence: 99%

“…Summary and Outlook-We have provided strong converse upper bounds on the PPT-assisted quantum capacity and the LOCC-assisted private capacity of a bidirectional quantum channel. The bound on the quantum capacity is related to the Rains bound [31,32], as well as that in [29], and can be efficiently computed by SDP solvers. We have provided examples that demonstrate the applicability of our bound.…”

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confidence: 99%

Fundamental Limits on the Capacities of Bipartite Quantum Interactions

2018

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Bipartite quantum interactions have applications in a number of different areas of quantum physics, reaching from fundamental areas such as quantum thermodynamics and the theory of quantum measurements to other applications such as quantum computers, quantum key distribution, and other information processing protocols. A particular aspect of the study of bipartite interactions is concerned with the entanglement that can be created from such interactions. In this paper, we present our work on two basic building blocks of bipartite quantum protocols, namely, the generation of maximally entangled states and secret key via bipartite quantum interactions. In particular, we provide a non-trivial, efficiently computable upper bound on the positive-partial-transposeassisted (PPT-assisted) quantum capacity of a bipartite quantum interaction. In addition, we provide an upper bound on the secret-key-agreement capacity of a bipartite quantum interaction assisted by local operations and classical communication (LOCC). As an application, we introduce a cryptographic protocol for the read-out of a digital memory device that is secure against a passive eavesdropper.

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“…For the method to apply to such cases, it suffices to embed the system into a 2 k dimensional Hilbert space of qubits and restrict the channel to act only on a subspace of this space. It is also interesting to note the apparent resemblance between the causality bound and the max-Rains information bound [12] which is also expressible through properties of the Choi state. Indeed, in the Supplemental Material, we show that the max-Rains bound for a channel N is upper bounded by the causality bound for the conjugate channel N * .…”

Section: Figmentioning

confidence: 98%

Causal Limit on Quantum Communication

et al. 2019

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The capacity of a channel is known to be equivalent to the highest rate at which it can generate entanglement. Analogous to entanglement, the notion of a causality measure characterises the temporal aspect of quantum correlations. Despite holding an equally fundamental role in physics, temporal quantum correlations have yet to find their operational significance in quantum communication. Here we uncover a connection between quantum causality and channel capacity. We show the amount of temporal correlations between two ends of the noisy quantum channel, as quantified by a causality measure, implies a general upper bound on its channel capacity. The expression of this new bound is simpler to evaluate than most previously known bounds. We demonstrate the utility of this bound by applying it to a class of shifted depolarizing channels, which results in improvement over previously calculated bounds for this class of channels.

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Semidefinite Programming Converse Bounds for Quantum Communication

Cited by 56 publications

References 61 publications

Quantum Channel Simulation and the Channel’s Smooth Max-Information

Quantum Channel Simulation and the Channel’s Smooth Max-Information

Fundamental Limits on the Capacities of Bipartite Quantum Interactions

Causal Limit on Quantum Communication

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