Superadditivity of private information for any number of uses of the channel

Abstract

The quantum capacity of a quantum channel is always smaller than the capacity of the channel for private communication. However, both quantities are given by the infinite regularization of respectively the coherent and the private information. Here, we construct a family of channels for which the private and coherent information can remain strictly superadditive for unbounded number of uses. We prove this by showing that the coherent information is strictly larger than the private information of a smaller number of uses of the channel. This implies that even though the quantum capacity is upper bounded by the private capacity, the non-regularized quantities can be interleaved. From an operational point of view, the private capacity can be used for gauging the practical value of quantum channels for secure communication and, consequently, for key distribution. We thus show that in order to evaluate the interest a channel for this task it is necessary to optimize the private information over an unlimited number of uses of the channel.

6 pages, 1 figure

References in corpus (7)

• Provably Secure and Practical Quantum Key Distribution over 307 km of Optical Fibre
• Quantum Capacities of Bosonic Channels
• Degenerate Quantum Codes for Pauli Channels
• Unbounded number of channel uses are required to see quantum capacity
• Simplifying additivity problems using direct sum constructions
• Extensive nonadditivity of privacy
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Cited by in corpus (21)

• Converse bounds for private communication over quantum channels
• Principles of Quantum Communication Theory: A Modern Approach
• Approximate Degradable Quantum Channels
• Bounding the energy-constrained quantum and private capacities of phase-insensitive bosonic Gaussian channels
• Semidefinite programming converse bounds for quantum communication
• Potential capacities of quantum channels
• Superadditivity of the Classical Capacity with Limited Entanglement Assistance
• Memory effects can make the transmission capability of a communication channel uncomputable
• Generic nonadditivity of quantum capacity in simple channels
• Entropic singularities give rise to quantum transmission
• Capacity Estimates via comparison with TRO channels
• Geometric Rényi Divergence and its Applications in Quantum Channel Capacities
• Non-convexity of private capacity and classical environment-assisted capacity of a quantum channel
• Allowing leakage can increase quantum transmission
• "Pretty strong" converse for the private capacity of degraded quantum wiretap channels
• Information-theoretic aspects of the generalized amplitude damping channel
• The superadditivity effects of quantum capacity decrease with the dimension for qudit depolarizing channels
• Additivity of quantum capacities in simple non-degradable quantum channels
• Noise is resource-contextual in quantum communication
• Classical State Masking over a Quantum Channel
• Simultaneous superadditivity of the direct and complementary channel capacities