Memory effects in repeated uses of quantum channels and their impact on quantum state transfer and entanglement distribution

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, for example, quantum key distribution and distributed quantum computing. QST has thus far primarily been addressed by resetting the quantum channel after each use, thereby giving rise to memoryless channels. Here we consider the case where the quantum channel, embodied by a spin- 1 2 chain, is continuously used, that is, without implementing time- and resource-consuming resetting operations. We derive a general, analytical expression for the n 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.