Applications of position-based coding to classical communication over quantum channels

Abstract

Recently, a coding technique called position-based coding has been used to establish achievability statements for various kinds of classical communication protocols that use quantum channels. In the present paper, we apply this technique in the entanglement-assisted setting in order to establish lower bounds for error exponents, lower bounds on the second-order coding rate, and one-shot lower bounds. We also demonstrate that position-based coding can be a powerful tool for analyzing other communication settings. In particular, we reduce the quantum simultaneous decoding conjecture for entanglement-assisted or unassisted communication over a quantum multiple access channel to open questions in multiple quantum hypothesis testing. We then determine achievable rate regions for entanglement-assisted or unassisted classical communication over a quantum multiple-access channel, when using a particular quantum simultaneous decoder. The achievable rate regions given in this latter case are generally suboptimal, involving differences of Renyi-2 entropies and conditional quantum entropies.

v4: 44 pages, v4 includes a simpler proof for an upper bound on one-shot entanglement-assisted capacity, also found recently and independently in arXiv:1804.09644

References in corpus (7)

• The Quantum Chernoff Bound
• Coding Theorem and Strong Converse for Quantum Channels
• The Chernoff lower bound for symmetric quantum hypothesis testing
• Error Exponent in Asymmetric Quantum Hypothesis Testing and Its Application to Classical-Quantum Channel coding
• Smooth Renyi Entropies and the Quantum Information Spectrum
• Coding Theorem for a Class of Quantum Channels with Long-Term Memory
• Generalized relative entropies and the capacity of classical-quantum channels

Cited by in corpus (27)

• Practical route to entanglement-assisted communication over noisy bosonic channels
• Entanglement-Assisted Communication Surpassing the Ultimate Classical Capacity
• Resource theory of asymmetric distinguishability
• On Composite Quantum Hypothesis Testing
• On converse bounds for classical communication over quantum channels
• Entanglement-assisted capacity regions and protocol designs for quantum multiple-access channels
• Union bound for quantum information processing
• Infinite-fold enhancement in communications capacity using pre-shared entanglement
• On the near-optimality of one-shot classical communication over quantum channels
• One-shot quantum error correction of classical and quantum information
• Simple and Tighter Derivation of Achievability for Classical Communication over Quantum Channels
• Quantum-enabled communication without a phase reference
• Fidelity-Based Smooth Min-Relative Entropy: Properties and Applications
• One-shot Capacity bounds on the Simultaneous Transmission of Classical and Quantum Information
• A Quantum Multiparty Packing Lemma and the Relay Channel
• Transceiver designs to attain the entanglement assisted communications capacity
• Reliable Simulation of Quantum Channels: the Error Exponent
• Lower Bounds on Error Exponents via a New Quantum Decoder
• One-Shot Triple-Resource Trade-Off in Quantum Channel Coding
• Strong Converse Exponent for Entanglement-Assisted Communication
• Postselected communication over quantum channels
• Adversarial quantum channel discrimination
• Quantum channel coding: Approximation algorithms and strong converse exponents
• Towards the ultimate limits of quantum channel discrimination and quantum communication
• On distinguishability distillation and dilution exponents
• Classical capacities of memoryless but not identical quantum channels
• Information storage and transmission under Markovian noise