Extensive nonadditivity of privacy

Abstract

Quantum information theory establishes the ultimate limits on communication and cryptography in terms of channel capacities for various types of information. The private capacity is particularly important because it quantifies achievable rates of quantum key distribution. We study the power of quantum channels with limited private capacity, focusing on channels that dephase in random bases. These display extensive nonadditivity of private capacity: a channel with 2 log d input qubits has a private capacity less than 2, but when used together with a second channel with zero private capacity the joint capacity jumps to (1/2)log d. In contrast to earlier work which found nonadditivity vanishing as a fraction of input size or conditional on unproven mathematical assumptions, this provides a natural setting manifesting nonadditivity of privacy of the strongest possible sort.

4 pages, two figures. Final version

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Cited by in corpus (41)

• A Survey on Quantum Channel Capacities
• Quantum Reverse Shannon Theorem
• Gaussian bosonic synergy: quantum communication via realistic channels of zero quantum capacity
• Nonadditivity of quantum and classical capacities for entanglement breaking multiple-access channels and butterfly network
• Dephrasure channel and superadditivity of coherent information
• Superactivation of the Asymptotic Zero-Error Classical Capacity of a Quantum Channel
• Quantum and private capacities of low-noise channels
• Potential capacities of quantum channels
• Superadditivity of private information for any number of uses of the channel
• When does noise increase the quantum capacity?
• Quantum enigma machines and the locking capacity of a quantum channel
• Generic nonadditivity of quantum capacity in simple channels
• Random tensor theory: extending random matrix theory to random product states
• Game-theoretic characterization of antidegradable channels
• Entropic singularities give rise to quantum transmission
• Distributed Private Randomness Distillation
• Maximal Privacy Without Coherence
• Strong converse exponents for the feedback-assisted classical capacity of entanglement-breaking channels
• Uniform Additivity in Classical and Quantum Information
• Bounding the forward classical capacity of bipartite quantum channels
• Exploring super-additivity of coherent information of noisy quantum channels through Genetic algorithms
• Bounding quantum capacities via partial orders and complementarity
• Random and free positive maps with applications to entanglement detection
• Public Quantum Communication and Superactivation
• Quantum superadditivity in linear optics networks: sending bits via multiple access Gaussian channels
• Non-convexity of private capacity and classical environment-assisted capacity of a quantum channel
• Black hole microstates vs. the additivity conjectures
• Quantum Communications Made Easy: Deterministic Models of Bosonic Channels
• Entanglement can completely defeat quantum noise
• Quantum enhancement of randomness distribution
• What exactly does Bekenstein bound?
• Information Geometric Superactivation of Asymptotic Quantum Capacity and Classical Zero-Error Capacity of Zero-Capacity Quantum Channels
• Allowing leakage can increase quantum transmission
• How Deep the Theory of Quantum Communications Goes: Superadditivity, Superactivation and Causal Activation
• "Pretty strong" converse for the private capacity of degraded quantum wiretap channels
• Parrondo's paradox and superactivation of classical and quantum capacity of communication channels with memory
• Schemes of transmission of classical information via quantum channels with many senders: discrete and continuous variables cases
• Entropy Bound for the Classical Capacity of a Quantum Channel Assisted by Classical Feedback
• Noise is resource-contextual in quantum communication
• Simultaneous superadditivity of the direct and complementary channel capacities
• Information storage and transmission under Markovian noise