Strong Converse for the Feedback-Assisted Classical Capacity of Entanglement-Breaking Channels

Abstract

Quantum entanglement can be used in a communication scheme to establish a correlation between successive channel inputs that is impossible by classical means. It is known that the classical capacity of quantum channels can be enhanced by such entangled encoding schemes, but this is not always the case. In this paper, we prove that a strong converse theorem holds for the classical capacity of an entanglement-breaking channel even when it is assisted by a classical feedback link from the receiver to the transmitter. In doing so, we identify a bound on the strong converse exponent, which determines the exponentially decaying rate at which the success probability tends to zero, for a sequence of codes with communication rate exceeding capacity. Proving a strong converse, along with an achievability theorem, shows that the classical capacity is a sharp boundary between reliable and unreliable communication regimes. One of the main tools in our proof is the sandwiched Rényi relative entropy. The same method of proof is used to derive an exponential bound on the success probability when communicating over an arbitrary quantum channel assisted by classical feedback, provided that the transmitter does not use entangled encoding schemes.

Quantum Reading Capacity: General Definition and Bounds

“…Proof. A proof follows by combining the bound in (5.14) with the main result of [WWY14] (see also [DW15] for arguments about extending the range of α from (1, 2] to (1, ∞)).…”

Preface to the Second Edition

“…This regime is known as the strong converse regime, and a channel obeys the strong converse property if the error probability tends to one when the communication rate exceeds the capacity. Winter (1999a) and Ogawa and Nagaoka (1999) proved the strong converse for the classical capacity of classical-quantum channels, Koenig and Wehner (2009) for channels with certain symmetry, for entanglement-breaking and Hadamard channels, Bardhan et al (2015) for phase-insensitive quantum Gaussian channels, and Ding and Wilde (2015) for entanglement-breaking channels assisted by a noiseless classical feedback channel.…”

Computable Rényi mutual information: Area laws and correlations

“…Motivated by this, we here explore alternative definitions of the Rényi mutual information, based on the notion of quantum Rényi divergences [16,17]. These are measures of distinguishability of quantum states, which play a pivotal role in information-theoretic tasks, such as single-shot communication protocols [18,19], channel coding [20][21][22][23][24][25] or hypothesis testing [26,27]. In principle, each of the many variants of quantum Rényi divergences [20,[28][29][30][31][32][33] allows us to define a mutual information as we explain in Appendix A.…”