On converse bounds for classical communication over quantum channels

Abstract

We explore several new converse bounds for classical communication over quantum channels in both the one-shot and asymptotic regimes. First, we show that the Matthews-Wehner meta-converse bound for entanglement-assisted classical communication can be achieved by activated, no-signalling assisted codes, suitably generalizing a result for classical channels. Second, we derive a new efficiently computable meta-converse on the amount of classical information unassisted codes can transmit over a single use of a quantum channel. As applications, we provide a finite resource analysis of classical communication over quantum erasure channels, including the second-order and moderate deviation asymptotics. Third, we explore the asymptotic analogue of our new meta-converse, the ${\rm Y}$-information of the channel. We show that its regularization is an upper bound on the classical capacity, which is generally tighter than the entanglement-assisted capacity and other known efficiently computable strong converse bounds. For covariant channels we show that the ${\rm Y}$-information is a strong converse bound.

v3: published version; v2: 18 pages, presentation and results improved

References in corpus (4)

• Transforming quantum operations: quantum supermaps
• One-shot coherence distillation
• The quantum capacity with symmetric side channels
• Generalized relative entropies and the capacity of classical-quantum channels

Cited by in corpus (19)

• Application of the Resource Theory of Channels to Communication Scenarios
• Quantum Channel Simulation and the Channel's Smooth Max-Information
• Physical Implementability of Linear Maps and Its Application in Error Mitigation
• Quantum NETwork: from theory to practice
• No-go theorems for quantum resource purification II: new approach and channel theory
• Defining quantum divergences via convex optimization
• Pursuing the fundamental limits for quantum communication
• The Communication Value of a Quantum Channel
• The Classical Capacity of Additive Quantum Queue-Channels
• Bounding the forward classical capacity of bipartite quantum channels
• Geometric Rényi Divergence and its Applications in Quantum Channel Capacities
• A hierarchy of efficient bounds on quantum capacities exploiting symmetry
• Upper Bounds on the Distillable Randomness of Bipartite Quantum States
• Towards the ultimate limits of quantum channel discrimination and quantum communication
• Adversarial quantum channel discrimination
• Single-shot entanglement manipulation of states and channels revisited
• Quantum channel coding: Approximation algorithms and strong converse exponents
• Classical communication cost of a bipartite quantum channel assisted by non-signalling correlations
• Information storage and transmission under Markovian noise