Decoherence in Quantum Markov Chains

TL;DR

This paper extends the quadratic speedup of hitting times from classical to decoherent quantum Markov chains using a percolation-like model, showing significant advantages in detection problems under certain decoherence conditions.

Contribution

It introduces a decoherent quantum hitting time and identifies a decoherent-intensity range where quantum speedup persists, extending prior results to more realistic decoherent scenarios.

Findings

Decoherent quantum hitting time is quadratically smaller than classical in certain regimes.

Detection problems under decoherence also benefit from quadratic speedup.

The percolation-like model effectively captures decoherence effects in quantum Markov chains.

Abstract

It is known that under some assumptions the hitting time in quantum Markov chains is quadratically smaller than the hitting time in classical Markov chains. This work extends this result for decoherent quantum Markov chains. The decoherence is introduced using a percolation-like graph model, which allows us to define a decoherent quantum hitting time and to establish a decoherent-intensity range for which the decoherent quantum hitting time is quadratically smaller than the the classical hitting time. The detection problem under decoherence is also solved with quadratic speedup in this range.