Indefinite causal order for quantum metrology with quantum thermal noise

TL;DR

This paper demonstrates that using indefinite causal order in quantum channels enables enhanced phase estimation under thermal noise, surpassing conventional methods by allowing measurements with less interaction and under more noise conditions.

Contribution

It introduces a novel approach utilizing indefinite causal order for quantum metrology in thermal noise environments, revealing capabilities not possible with traditional fixed-order channels.

Findings

Phase estimation achievable by measuring control qubit alone.

Effective phase estimation with depolarized or axis-aligned probes.

Extended analysis from depolarizing to thermal noise environments.

Abstract

A switched quantum channel with indefinite causal order is studied for the fundamental metrological task of phase estimation on a qubit unitary operator affected by quantum thermal noise. Specific capabilities are reported in the switched channel with indefinite order, not accessible with conventional estimation approaches with definite order. Phase estimation can be performed by measuring the control qubit alone, although it does not actively interact with the unitary process -- only the probe qubit doing so. Also, phase estimation becomes possible with a fully depolarized input probe or with an input probe aligned with the rotation axis of the unitary, while this is never possible with conventional approaches. The present study extends to thermal noise, investigations previously carried out with the more symmetric and isotropic qubit depolarizing noise, and it contributes to the timely exploration of properties of quantum channels with indefinite causal order relevant to quantum signal and information processing.