Entanglement-assisted communication of classical and quantum information

Abstract

We consider the problem of transmitting classical and quantum information reliably over an entanglement-assisted quantum channel. Our main result is a capacity theorem that gives a three-dimensional achievable rate region. Points in the region are rate triples, consisting of the classical communication rate, the quantum communication rate, and the entanglement consumption rate of a particular coding scheme. The crucial protocol in achieving the boundary points of the capacity region is a protocol that we name the classically-enhanced father protocol. The classically-enhanced father protocol is more general than other protocols in the family tree of quantum Shannon theoretic protocols, in the sense that several previously known quantum protocols are now child protocols of it. The classically-enhanced father protocol also shows an improvement over a time-sharing strategy for the case of a qubit dephasing channel--this result justifies the need for simultaneous coding of classical and quantum information over an entanglement-assisted quantum channel. Our capacity theorem is of a multi-letter nature (requiring a limit over many uses of the channel), but it reduces to a single-letter characterization for at least three channels: the completely depolarizing channel, the quantum erasure channel, and the qubit dephasing channel.

23 pages, 5 figures, 1 table, simplification of capacity region--it now has the simple interpretation as the unit resource capacity region translated along the classically-enhanced father trade-off curve

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Cited by in corpus (47)

• Quantum channels and memory effects
• Catalytic quantum error correction
• Approaches for approximate additivity of the Holevo information of quantum channels
• Entanglement-assisted quantum turbo codes
• Trade-off capacities of the quantum Hadamard channels
• Entropic proofs of Singleton bounds for quantum error-correcting codes
• Trading classical communication, quantum communication, and entanglement in quantum Shannon theory
• Resource convertibility and ordered commutative monoids
• Quantum rate distortion, reverse Shannon theorems, and source-channel separation
• The apex of the family tree of protocols: Optimal rates and resource inequalities
• One-shot entanglement-assisted quantum and classical communication
• Quantum trade-off coding for bosonic communication
• The quantum dynamic capacity formula of a quantum channel
• Information trade-offs for optical quantum communication
• Classical communication over a quantum interference channel
• Measuring Quantum Entropy
• Public and private resource trade-offs for a quantum channel
• Superadditivity of the Classical Capacity with Limited Entanglement Assistance
• Fundamental limitations to information transfer in accelerated frames
• Capacities of Quantum Amplifier Channels
• Codes for Simultaneous Transmission of Quantum and Classical Information
• One-shot quantum error correction of classical and quantum information
• Entanglement-assisted concatenated quantum codes
• Quantum-enabled communication without a phase reference
• Asymmetric Quantum Concatenated and Tensor Product Codes with Large Z-Distances
• Capacities of Grassmann channels
• Sequential, successive, and simultaneous decoders for entanglement-assisted classical communication
• New lower bounds to the output entropy of multi-mode quantum Gaussian channels
• Hybrid Codes
• Trade-off coding for universal qudit cloners motivated by the Unruh effect
• Simultaneous transmission of classical and quantum information under channel uncertainty and jamming attacks
• Stabilizer Formalism for Operator Algebra Quantum Error Correction
• Error correction schemes for fully correlated quantum channels protecting both quantum and classical information
• Universal random codes: Capacity regions of the compound quantum multiple-access channel with one classical and one quantum sender
• Singleton Bounds for Entanglement-Assisted Classical and Quantum Error Correcting Codes
• Encoding Classical Information in Gauge Subsystems of Quantum Codes
• Noisy quantum state redistribution with promise and the Alpha-bit
• One-Shot Triple-Resource Trade-Off in Quantum Channel Coding
• Codes for entanglement-assisted classical communication
• A unification of the coding theory and OAQEC perspective on hybrid codes
• The Learnability of Unknown Quantum Measurements
• CB-norm estimates for maps between noncommutative $L_p$-spaces and quantum channel theory
• Quantum Complementarity and Operator Structures
• Classical State Masking over a Quantum Channel
• Explicit decoders using fixed-point amplitude amplification based on QSVT
• Higher Rank Matricial Ranges and Hybrid Quantum Error Correction
• Relativistic Quantum Communication