One shot entanglement assisted classical and quantum communication over noisy quantum channels: A hypothesis testing and convex split approach

Abstract

Capacity of a quantum channel characterizes the limits of reliable communication through a noisy quantum channel. This fundamental information theoretic question is very well studied specially in the setting of many independent uses of the channel. An important scenario, both from practical and conceptual point of view, is when the channel can be used only once. This is known as the one-shot channel coding problem. We provide a tight characterization of the one-shot entanglement assisted classical capacity of a quantum channel. We arrive at our result by introducing a simple decoding technique which we refer to as position-based decoding. We also consider two other important quantum network scenarios: quantum channel with a jammer and quantum broadcast channel. For these problems, we use the recently introduced convex split technique [Anshu, Devabathini and Jain 2014] in addition to position based decoding. Our approach exhibits that the simultaneous use of these two techniques provides a uniform and conceptually simple framework for designing communication protocols for quantum networks.

34 pages, 7 figures, version 4: Improvement in the rate of shared entanglement required for the point to point channel in the asymptotic and i.i.d. setting, which matches the corresponding rate obtained in Bennett, Shor, Smolin, Thapliyal [2002]

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Cited by in corpus (42)

• Principles of Quantum Communication Theory: A Modern Approach
• Practical route to entanglement-assisted communication over noisy bosonic channels
• Entanglement-Assisted Communication Surpassing the Ultimate Classical Capacity
• Thermodynamic Capacity of Quantum Processes
• Position-based coding and convex splitting for private communication over quantum channels
• Entanglement-enhanced testing of multiple quantum hypotheses
• Covert Capacity of Bosonic Channels
• Entanglement-assisted private communication over quantum broadcast channels
• A generalized quantum Slepian-Wolf
• Partially smoothed information measures
• Convex-split and hypothesis testing approach to one-shot quantum measurement compression and randomness extraction
• A one-shot achievability result for quantum state redistribution
• Quantum Broadcast Channels with Cooperating Decoders: An Information-Theoretic Perspective on Quantum Repeaters
• 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
• Dynamical Landauer Principle: Quantifying Information Transmission by Thermodynamics
• Thermodynamic Implementations of Quantum Processes
• Inner bounds via simultaneous decoding in quantum network information theory
• Quantum Channel Capacities Per Unit Cost
• Efficient methods for one-shot quantum communication
• Parallelization of Adaptive Quantum Channel Discrimination in the Non-Asymptotic Regime
• A unified approach to source and message compression
• One-shot quantum state redistribution and quantum Markov chains
• Universal superposition codes: capacity regions of compound quantum broadcast channel with confidential messages
• Transceiver designs to attain the entanglement assisted communications capacity
• Reliability Function of Quantum Information Decoupling via the Sandwiched Rényi Divergence
• 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
• Noisy quantum state redistribution with promise and the Alpha-bit
• Optimal one-shot entanglement sharing
• Communication with Quantum Catalysts
• Postselected communication over quantum channels
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• On the compression of messages in the multi-party setting
• Universal tester for multiple independence testing and classical-quantum arbitrarily varying multiple access channel
• Tight relations and equivalences between smooth relative entropies
• Fast suppression of classification error in variational quantum circuits
• Intersection and union of subspaces with applications to communication over authenticated classical-quantum channels and composite hypothesis testing