A hypothesis testing approach for communication over entanglement assisted compound quantum channel

Abstract

We study the problem of communication over a compound quantum channel in the presence of entanglement. Classically such channels are modeled as a collection of conditional probability distributions wherein neither the sender nor the receiver is aware of the channel being used for transmission, except for the fact that it belongs to this collection. We provide near optimal achievability and converse bounds for this problem in the one-shot quantum setting in terms of quantum hypothesis testing divergence. We also consider the case of informed sender, showing a one-shot achievability result that converges appropriately in the asymptotic and i.i.d. setting. Our achievability proof is similar in spirit to its classical counterpart. To arrive at our result, we use the technique of position-based decoding along with a new approach for constructing a union of two projectors, which can be of independent interest. We give another application of the union of projectors to the problem of testing composite quantum hypotheses.

arXiv comment21 pages, version 3. Added an application to the composite quantum hypothesis testing. Expanded introduction

References in corpus (16)

• Min- and Max- Relative Entropies and a New Entanglement Monotone
• One-Shot Classical-Quantum Capacity and Hypothesis Testing
• A Hierarchy of Information Quantities for Finite Block Length Analysis of Quantum Tasks
• Error Exponent in Asymmetric Quantum Hypothesis Testing and Its Application to Classical-Quantum Channel coding
• The quantum capacity of channels with arbitrarily correlated noise
• Second-order asymptotics for quantum hypothesis testing
• Finite blocklength converse bounds for quantum channels
• Smooth Max-Information as One-Shot Generalization for Mutual Information
• On the Second-Order Asymptotics for Entanglement-Assisted Communication
• Universal coding for classical-quantum channel
• Quantum union bounds for sequential projective measurements
• Entanglement transmission and generation under channel uncertainty: Universal quantum channel coding
• On Quantum Capacity of Compound Channels
• Sequential decoding of a general classical-quantum channel
• Coding theorems for compound problems via quantum Rényi divergences
• Entanglement-assisted capacities of compound quantum channels

Cited by in corpus (3)

• Universal superposition codes: capacity regions of compound quantum broadcast channel with confidential messages
• Noisy quantum state redistribution with promise and the Alpha-bit
• Intersection and union of subspaces with applications to communication over authenticated classical-quantum channels and composite hypothesis testing