How many bits does it take to track an open quantum system?

TL;DR

This paper demonstrates that for any ergodic open quantum system, an adaptive monitoring scheme can confine the system's pure state trajectory to a finite set of states, with a minimal number of bits needed for tracking.

Contribution

It introduces a method to confine system trajectories to a finite set of states using adaptive monitoring, reducing the information needed to track open quantum systems.

Findings

For any ergodic master equation, the system can be confined to at most (D-1)^2+1 states.

A 2-state ensemble can be explicitly constructed for any qubit system, requiring only 1 bit.

Adaptive monitoring schemes can minimize the information required to track quantum jumps.

Abstract

A $D$-dimensional Markovian open quantum system will undergo quantum jumps between pure states, if we can monitor the bath to which it is coupled with sufficient precision. In general these jumps, plus the between-jump evolution, create a trajectory which passes through infinitely many different pure states. Here we show that, for any ergodic master equation, one can expect to find an {\em adaptive} monitoring scheme on the bath that can confine the system state to jumping between only $K$ states, for some $K \geq (D-1)^2+1$. For $D=2$ we explicitly construct a 2-state ensemble for any ergodic master equation, showing that one bit is always sufficient to track a qubit.