A triangle of dualities: reversibly decomposable quantum channels, source-channel duality, and time reversal

Abstract

Two quantum information processing protocols are said to be dual under resource reversal if the resources consumed (generated) in one protocol are generated (consumed) in the other. Previously known examples include the duality between entanglement concentration and dilution, and the duality between coherent versions of teleportation and super-dense coding. A quantum feedback channel is an isometry from a system belonging to Alice to a system shared between Alice and Bob. We show that such a resource may be reversibly decomposed into a perfect quantum channel and pure entanglement, generalizing both of the above examples. The dual protocols responsible for this decomposition are the ``feedback father'' (FF) protocol and the ``fully quantum reverse Shannon'' (FQRS) protocol. Moreover, the ``fully quantum Slepian-Wolf'' protocol (FQSW), a generalization of the recently discovered ``quantum state merging'', is related to FF by source-channel duality, and to FQRS by time reversal duality, thus forming a triangle of dualities. The source-channel duality is identified as the origin of the previously poorly understood ``mother-father'' duality. Due to a symmetry breaking, the dualities extend only partially to classical information theory.

5 pages, 5 figures

References in corpus (1)

• Quantum information can be negative

Cited by in corpus (28)

• The mother of all protocols: Restructuring quantum information's family tree
• Quantum Reverse Shannon Theorem
• The exact cost of redistributing multipartite quantum states
• Capacity Theorems for Quantum Multiple Access Channels: Classical-Quantum and Quantum-Quantum Capacity Regions
• Optimal quantum source coding with quantum information at the encoder and decoder
• The information-theoretic costs of simulating quantum measurements
• A father protocol for quantum broadcast channels
• Dualities and non-Abelian mechanics
• Trading classical communication, quantum communication, and entanglement in quantum Shannon theory
• Quantum rate distortion, reverse Shannon theorems, and source-channel separation
• One-shot lossy quantum data compression
• Strong converse theorems using Rényi entropies
• Quantum state redistribution based on a generalized decoupling
• Convexity and Operational Interpretation of the Quantum Information Bottleneck Function
• Coherent Communication with Continuous Quantum Variables
• Quantum Rate-Distortion Coding of Relevant Information
• Public and private communication with a quantum channel and a secret key
• Quantum Predictive Filtering
• Decoupling by local random unitaries without simultaneous smoothing, and applications to multi-user quantum information tasks
• Reliable Simulation of Quantum Channels: the Error Exponent
• Quantum state rotation: Circularly transferring quantum states of multiple users
• Time reversal and exchange symmetries of unitary gate capacities
• Asymptotic Compressibility of Entanglement and Classical Communication in Distributed Quantum Computation
• Distributed Compression and Squashed Entanglement
• State transfer with quantum side information
• Channel simulation with quantum side information
• Random coding exponents galore via decoupling
• On the Entanglement Cost of One-Shot Compression