Conjugate Degradability and the Quantum Capacity of Cloning Channels

Abstract

A quantum channel is conjugate degradable if the channel's environment can be simulated up to complex conjugation using the channel's output. For all such channels, the quantum capacity can be evaluated using a single-letter formula. In this article we introduce conjugate degradability and establish a number of its basic properties. We then use it to calculate the quantum capacity of N to N+1 and 1 to M universal quantum cloning machines as well as the quantum capacity of a channel that arises naturally when data is being transmitted to an accelerating receiver. All the channels considered turn out to have strictly positive quantum capacity, meaning they could be used as part of a communication system to send quantum states reliably.

18 pages

References in corpus (14)

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Cited by in corpus (32)

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• Quantum broadcast channels
• Quantum fisher information in noninertial frames
• Trade-off capacities of the quantum Hadamard channels
• Quantum trade-off coding for bosonic communication
• Useful states and entanglement distillation
• Private and Quantum Capacities of More Capable and Less Noisy Quantum Channels
• Quantum Communication in Rindler Spacetime
• An Infinite Sequence of Additive Channels: the Classical Capacity of Cloning Channels
• Public and private resource trade-offs for a quantum channel
• "Pretty strong" converse for the quantum capacity of degradable channels
• The capacity of black holes to transmit quantum information
• Black holes as bosonic Gaussian channels
• Detecting positive quantum capacities of quantum channels
• The Structure and Quantum Capacity of a Partially Degradable Quantum Channel
• Resonant Multilevel Amplitude Damping Channels
• Quantum Information Transmission over a Partially Degradable Channel
• Quantum Fisher and Skew information for Unruh accelerated Dirac qubit
• Capacities of Grassmann channels
• The Private Classical Capacity of a Partially Degradable Quantum Channel
• Partially Coherent Direct Sum Channels
• Quasi-Superactivation of Classical Capacity of Zero-Capacity Quantum Channels
• Degradability of Fermionic Gaussian Channels
• Degradable Quantum Channels Using Pure to Product of Pure States Isometries
• Relating compatibility and divisibility of quantum channels
• The pitfalls of deciding whether a quantum channel is (conjugate) degradable and how to avoid them
• Allowing leakage can increase quantum transmission
• The superadditivity effects of quantum capacity decrease with the dimension for qudit depolarizing channels
• Stimulated Emission of Radiation and the Black Hole Information Problem
• Additivity of quantum capacities in simple non-degradable quantum channels
• Conjugate degradable channels: A new class of quantum channels with a tractable quantum capacity formula