Asymptotically optimal quantum channel reversal for qudit ensembles and multimode Gaussian states

TL;DR

This paper develops an optimal method for reversing quantum channels on large ensembles of qudits and Gaussian states, enhancing quantum communication robustness and providing explicit reversal strategies.

Contribution

It introduces a general approach for optimal reversal of quantum channels on large ensembles, including Gaussian channels, with applications to quantum communication.

Findings

Optimal reversal channel R* maximizes the output ensemble size m/n

Solution maps the problem to Gaussian channel reversal in continuous variables

Application to phase flip channels on multi-qubit registers

Abstract

We investigate the problem of optimally reversing the action of an arbitrary quantum channel C which acts independently on each component of an ensemble of n identically prepared d-dimensional quantum systems. In the limit of large ensembles, we construct the optimal reversing channel R* which has to be applied at the output ensemble state, to retrieve a smaller ensemble of m systems prepared in the input state, with the highest possible rate m/n. The solution is found by mapping the problem into the optimal reversal of Gaussian channels on quantum-classical continuous variable systems, which is here solved as well. Our general results can be readily applied to improve the implementation of robust long-distance quantum communication. As an example, we investigate the optimal reversal rate of phase flip channels acting on a multi-qubit register.