Classical capacities of quantum channels with environment assistance

Abstract

A quantum channel physically is a unitary interaction between the information carrying system and an environment, which is initialized in a pure state before the interaction. Conventionally, this state, as also the parameters of the interaction, is assumed to be fixed and known to the sender and receiver. Here, following the model introduced by us earlier [Karumanchi et al., arXiv[quant-ph]:1407.8160], we consider a benevolent third party, i.e. a helper, controlling the environment state, and how the helper's presence changes the communication game. In particular, we define and study the classical capacity of a unitary interaction with helper, indeed two variants, one where the helper can only prepare separable states across many channel uses, and one without this restriction. Furthermore, the two even more powerful scenarios of pre-shared entanglement between helper and receiver, and of classical communication between sender and helper (making them conferencing encoders) are considered.

28 pages, 9 figures. To appear in "Problems of Information Transmission"

References in corpus (6)

• Aspects of generic entanglement
• Tight uniform continuity bounds for quantum entropies: conditional entropy, relative entropy distance and energy constraints
• Entanglement of assistance and multipartite state distillation
• Continuity of quantum channel capacities
• On some classes of bipartite unitary operators
• Distinguishability, classical information of quantum operations

Cited by in corpus (13)

• Non-Gaussian operations on bosonic modes of light: Photon-added Gaussian channels
• 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
• Finite Block Length Analysis on Quantum Coherence Distillation and Incoherent Randomness Extraction
• Adversarial vs cooperative quantum estimation
• Profitable entanglement for channel discrimination
• How Deep the Theory of Quantum Communications Goes: Superadditivity, Superactivation and Causal Activation
• Quantum reading of quantum information
• Quantum estimation through a bottleneck
• Simultaneous superadditivity of the direct and complementary channel capacities