Strong Converse for the Classical Capacity of Entanglement-Breaking and Hadamard Channels via a Sandwiched Rényi Relative Entropy

Wilde, Mark M.; Winter, Andreas; Yang, Dong

doi:10.1007/s00220-014-2122-x

Cited by 413 publications

(466 citation statements)

References 82 publications

(158 reference statements)

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“…Generalisations of the relative entropy could also be used to define geometric measures of QCs. Two recently suggested generalisations are the sandwiched relative Rényi entropies [136,137] (see also [138])…”

Section: Hierarchy Of Geometric Measuresmentioning

confidence: 99%

Measures and applications of quantum correlations

Adesso¹,

Bromley²,

Cianciaruso³

2016

J. Phys. A: Math. Theor.

365

402

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Abstract. Quantum information theory is built upon the realisation that quantum resources like coherence and entanglement can be exploited for novel or enhanced ways of transmitting and manipulating information, such as quantum cryptography, teleportation, and quantum computing. We now know that there is potentially much more than entanglement behind the power of quantum information processing. There exist more general forms of non-classical correlations, stemming from fundamental principles such as the necessary disturbance induced by a local measurement, or the persistence of quantum coherence in all possible local bases. These signatures can be identified and are resilient in almost all quantum states, and have been linked to the enhanced performance of certain quantum protocols over classical ones in noisy conditions. Their presence represents, among other things, one of the most essential manifestations of quantumness in cooperative systems, from the subatomic to the macroscopic domain. In this work we give an overview of the current quest for a proper understanding and characterisation of the frontier between classical and quantum correlations in composite states. We focus on various approaches to define and quantify general quantum correlations, based on different yet interlinked physical perspectives, and comment on the operational significance of the ensuing measures for quantum technology tasks such as information encoding, distribution, discrimination and metrology. We then provide a broader outlook of a few applications in which quantumness beyond entanglement looks fit to play a key role.

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Section: Hierarchy Of Geometric Measuresmentioning

confidence: 99%

Measures and applications of quantum correlations

Adesso¹,

Bromley²,

Cianciaruso³

2016

J. Phys. A: Math. Theor.

365

402

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“…Rényi entropies share many mathematical properties with the Shannon entropy and are powerful tools in many information-theoretic arguments. A significant part of this book is thus devoted to exploring quantum generalizations of Rényi entropies, for example the ones proposed by Petz [132] and a more recent specimen [122,175] that has already found many applications.…”

Section: Rényi and Smooth Entropiesmentioning

confidence: 99%

“…The minimal quantum Rényi divergence is also called 'quantum Rényi divergence' [122] and 'sandwiched quantum Rényi relative entropy' [175] in the literature, but we propose here to call it minimal quantum Rényi divergence since it is the smallest quantum Rényi divergence that still satisfies the crucial data-processing inequality as seen in (4.31). Thus, it is the minimal quantum Rényi divergence for which we can expect operational significance.…”

Section: Minimal Quantum Rényi Divergencementioning

confidence: 99%

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Quantum Information Processing with Finite Resources

Tomamichel¹

2016

SpringerBriefs in Mathematical Physics

253

397

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“…Despite their significance in understanding the ultimate information-carrying capacity of noisy communication channels, strong converse theorems are known to hold only for a handful of quantum channels: for those with classical inputs and quantum outputs [3], [4] (see earlier results for all classical channels [5], [6]), for all covariant channels with additive minimum output Rényi entropy [7], for all entanglementbreaking and Hadamard channels [8], as well as for pure-loss bosonic channels [9].…”

Section: Introductionmentioning

confidence: 99%

Strong Converse for the Classical Capacity of Optical Quantum Communication Channels

Bardhan

García−Patrón

Wilde

et al. 2015

IEEE Trans. Inform. Theory

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We establish the classical capacity of optical quantum channels as a sharp transition between two regimes-one which is an error-free regime for communication rates below the capacity, and the other in which the probability of correctly decoding a classical message converges exponentially fast to zero if the communication rate exceeds the classical capacity. This result is obtained by proving a strong converse theorem for the classical capacity of all phase-insensitive bosonic Gaussian channels, a well-established model of optical quantum communication channels, such as lossy optical fibers, amplifier and free-space communication. The theorem holds under a particular photonnumber occupation constraint, which we describe in detail in the paper. Our result bolsters the understanding of the classical capacity of these channels and opens the path to applications, such as proving the security of noisy quantum storage models of cryptography with optical links. Index Termschannel capacity, Gaussian quantum channels, optical communication channels, photon number constraint, strong converse theorem I. INTRODUCTION One of the most fundamental tasks in quantum information theory is to determine the ultimate limits on achievable data transmission rates for a noisy communication channel. The classical capacity is defined as the maximum rate at which it is possible to send classical data over a quantum channel such that the error probability decreases to zero in the limit of many independent uses of the channel [1], [2]. As such, the classical capacity serves as a distinctive bound on our ability to faithfully recover classical information sent over the channel.The above definition of the classical capacity states that (a) for any rate below capacity, one can communicate with vanishing error probability in the limit of many channel uses and (b) there cannot exist such a communication scheme in the limit of many channel uses whenever the rate exceeds the capacity. However, strictly speaking, for any rate R above capacity, the above definition leaves open the possibility for one to increase the communication rate R by allowing for some error ε > 0. Leaving room for the possibility of such a trade-off between the rate R and the error ε is the characteristic of a "weak converse,"

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Strong Converse for the Classical Capacity of Entanglement-Breaking and Hadamard Channels via a Sandwiched Rényi Relative Entropy

Cited by 413 publications

References 82 publications

Measures and applications of quantum correlations

Measures and applications of quantum correlations

Quantum Information Processing with Finite Resources

Strong Converse for the Classical Capacity of Optical Quantum Communication Channels

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