# Distinguishing quantum states using time travelling qubits in a presence of thermal environments

## TL;DR

This paper investigates how thermal environments impact quantum circuits with time travel designed to distinguish nonorthogonal quantum states, revealing that dephasing environments preserve some quantum distinguishing power.

## Contribution

It introduces an analysis of thermal noise effects on time-travel quantum circuits and discusses the validity of Deutsch's maximum entropy rule under these conditions.

## Key findings

- Dephasing environments preserve the distinguishing power of time-travel circuits.
- Thermal noise generally degrades quantum state discrimination capabilities.
- The paper provides conditions under which Deutsch's maximum entropy rule remains valid.

## Abstract

We consider quantum circuits with time travel designed for distinguishing specific nonorthogonal quantum states in two most popular models: Deutschs and postselected. We modify them by a presence of weakly coupled thermal environment. Using the Davies approximation we study how the thermal noise affects an ability of the circuits to distinguish nonorthogonal quantum states. We show that for purely dephasing environment a paradoxial power of such circuits remains preserved. We also present a physics based argument for conditions of validity of the maximum entropy rule introduced by David Deutsch for resolving the uniqueness ambiguity in a circuit with time travel.