Quantum Finite-Depth Memory Channels: Case Study

TL;DR

This paper investigates the memory depth of quantum channels with a qubit memory, showing that memory effects are either infinite or vanish after two uses, and explores control via reset sequences.

Contribution

It explicitly characterizes all interactions with finite memory depth in qubit channels and demonstrates how reset sequences can control memory effects.

Findings

Memory effects are either infinite or vanish after two uses.

Reset sequences can control and manipulate finite memory channels.

Actions separated by reset sequences are memoryless.

Abstract

We analyze the depth of the memory of quantum memory channels generated by a fixed unitary transformation describing the interaction between the principal system and internal degrees of freedom of the process device. We investigate the simplest case of a qubit memory channel with a two-level memory system. In particular, we explicitly characterize all interactions for which the memory depth is finite. We show that the memory effects are either infinite, or they disappear after at most two uses of the channel. Memory channels of finite depth can be to some extent controlled and manipulated by so-called reset sequences. We show that actions separated by the sequences of inputs of the length of the memory depth are independent and constitute memoryless channels.