Quantum Capacities of Channels with small Environment

Abstract

We investigate the quantum capacity of noisy quantum channels which can be represented by coupling a system to an effectively small environment. A capacity formula is derived for all cases where both system and environment are two-dimensional--including all extremal qubit channels. Similarly, for channels acting on higher dimensional systems we show that the capacity can be determined if the channel arises from a sufficiently small coupling to a qubit environment. Extensions to instances of channels with larger environment are provided and it is shown that bounds on the capacity with unconstrained environment can be obtained from decompositions into channels with small environment.

References in corpus (9)

• The capacity of the noisy quantum channel
• Quantum Channel Capacity of Very Noisy Channels
• Evidence for Bound Entangled States with Negative Partial Transpose
• Distillability and partial transposition in bipartite systems
• Information-capacity description of spin-chain correlations
• Nonadditivity of Bipartite Distillable Entanglement follows from Conjecture on Bound Entangled Werner States
• Tema Con Variazioni: Quantum Channel Capacity
• Distillability via protocols respecting the positivity of partial transpose
• Activating NPPT distillation with an infinitesimal amount of bound entanglement

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