Quantum Channel Capacities with Passive Environment Assistance

Abstract

We initiate the study of passive environment-assisted communication via a quantum channel, modeled as a unitary interaction between the information carrying system and an environment. In this model, the environment is controlled by a benevolent helper who can set its initial state such as to assist sender and receiver of the communication link. (The case of a malicious environment, also known as jammer, or arbitrarily varying channel, is essentially well-understood and comprehensively reviewed.) Here, after setting out precise definitions, focussing on the problem of quantum communication, we show that entanglement plays a crucial role in this problem: indeed, the assisted capacity where the helper is restricted to product states between channel uses is different from the one with unrestricted helper. Furthermore, prior shared entanglement between the helper and the receiver makes a difference, too.

14 pages, 13 figures, IEEE format, Theorem 9 (statement and proof) changed, updated References and Example 11 added. Comments are welcome!

References in corpus (15)

• Post-selection technique for quantum channels with applications to quantum cryptography
• Quantum Communication With Zero-Capacity Channels
• Entanglement of assistance and multipartite state distillation
• Unbounded number of channel uses are required to see quantum capacity
• Quantum Capacity of a dephasing channel with memory
• Quantum Capacities of Channels with small Environment
• Continuity of quantum channel capacities
• Inverting quantum decoherence by classical feedback from the environment
• Superadditivity of private information for any number of uses of the channel
• Additive Extensions of a Quantum Channel
• Classical capacities of quantum channels with environment assistance
• Spectrum conditions for symmetric extendible states
• Capacities of lossy bosonic channel with correlated noise
• Quantum information reclaiming after amplitude damping
• Optimal transfer of an unknown state via a bipartite operation

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• Bosonic quantum communication across arbitrarily high loss channels
• Fully Quantum Arbitrarily Varying Channels: Random Coding Capacity and Capacity Dichotomy
• On some classes of bipartite unitary operators
• Dense Coding with Locality Restriction for Decoder: Quantum Encoders vs. Super-Quantum Encoders
• Capacities of Gaussian Quantum Channels with Passive Environment Assistance
• Simultaneous transmission of classical and quantum information under channel uncertainty and jamming attacks
• Adversarial vs cooperative quantum estimation
• Non-convexity of private capacity and classical environment-assisted capacity of a quantum channel
• How Deep the Theory of Quantum Communications Goes: Superadditivity, Superactivation and Causal Activation
• Estimation of two-qubit interactions through channels with environment assistance
• Quantum reading of quantum information