Evading noise in multiparameter quantum metrology with indefinite causal order

TL;DR

This paper demonstrates how indefinite causal order in quantum channels can significantly enhance the simultaneous estimation of multiple parameters, including noise and unitary parameters, surpassing traditional fixed-order methods.

Contribution

It introduces a method leveraging indefinite causal order to improve multiparameter quantum metrology, achieving unbounded advantages over fixed-order schemes.

Findings

Achieves $p^2$ smaller variances in estimation with noise probability $1-p$

Enables simultaneous estimation of unitary and noise parameters in arbitrary dimensions

Provides regimes of unlimited metrological advantage using indefinite causal order

Abstract

Quantum theory allows the traversing of multiple channels in a superposition of different orders. When the order in which the channels are traversed is controlled by an auxiliary quantum system, various unknown parameters of the channels can be estimated by measuring only the control system, even when the state of the probe alone would be insensitive. Moreover, increasing the dimension of the control system increases the number of simultaneously estimable parameters, which has important metrological ramifications. We demonstrate this capability for simultaneously estimating both unitary and noise parameters, including multiple parameters from the same unitary such as rotation angles and axes and from noise channels such as depolarization, dephasing, and amplitude damping in arbitrary dimensions. We identify regimes of unlimited advantages, taking the form of $p^2$ smaller variances in estimation when the noise probability is $1-p$, for both single and multiparameter estimation when using our schemes relative to any comparable scheme whose causal order is definite.