A decoupling approach to the quantum capacity
Patrick Hayden, Michal Horodecki, Andreas Winter, Jon Yard
TL;DR
The paper addresses the quantum capacity of noisy quantum channels and proves that the coherent information I_c(phi^{A'}, N) is an achievable rate for entanglement generation. It introduces a decoupling-based coding scheme that uses random codes generated by a unitarily covariant measurement on a typical subspace and shows that decoupling from the environment suffices to enable reliable entanglement transmission. A key contribution is a one-shot decoupling theorem bounding the average distance between the transmitted state and a product state, which is then extended to memoryless channels via typical subspace technology and the method of types. The work offers a simpler, decoder-free proof of the quantum channel coding theorem, discusses practical code families via unitary 2-designs and stabilizer constructions, and highlights open questions on additivity and capacity computation for general channels.
Abstract
We give a short proof that the coherent information is an achievable rate for the transmission of quantum information through a noisy quantum channel. Our method is to produce random codes by performing a unitarily covariant projective measurement on a typical subspace of a tensor power state. We show that, provided the rank of each measurement operator is sufficiently small, the transmitted data will with high probability be decoupled from the channel's environment. We also show that our construction leads to random codes whose average input is close to a product state and outline a modification yielding unitarily invariant ensembles of maximally entangled codes.