Memory effects in repeated uses of quantum channels

TL;DR

This paper investigates how continuous use of quantum channels without resetting introduces memory effects that significantly impair quantum state transfer fidelity, especially under timing errors.

Contribution

It derives an analytical expression for the average QST fidelity in $U(1)$-symmetric channels and analyzes the impact of timing errors on memory effects.

Findings

Memory effects arise from timing errors in continuous quantum channel use.

Timing errors significantly reduce quantum state transfer fidelity.

Analytical expression for $n$-th use average fidelity derived for $U(1)$-symmetric channels.

Abstract

Quantum Information Processing (QIP) tasks can be efficiently formulated in terms of quantum dynamical maps, whose formalism is able to provide the appropriate mathematical representation of the evolution of open quantum systems. A key QIP task is quantum state transfer (QST) aimed at sharing quantum information between distant nodes of a quantum network, enabling, e.g. quantum key distribution and distributed quantum computing. QST has primarily been addressed insofar by resetting the quantum channel after each use, thus giving rise to memoryless channels. Here we consider the case where the quantum channel is continuously used, without implementing time- and resource- consuming resetting operations. We derive a general, analytical expression for the $n^{\mathrm{th}}$-use average QST fidelity for $U(1)$-symmetric channels and apply our formalism to a perfect QST channel in the presence of imperfect readout timing. We show that even relatively small readout timing errors give rise to memory effects which have a highly detrimental impact on subsequent QST tasks.