Parameter estimation via indefinite causal structures

TL;DR

This paper derives analytical expressions for quantum Fisher information in superpositions of causal orders, revealing how indefinite causal structures can enhance parameter estimation precision in quantum channels.

Contribution

It provides the first analytical formulas for quantum Fisher information with noisy channels in superposed causal orders and identifies optimal causal order combinations for improved estimation.

Findings

Quantum Fisher information increases with the number of causal orders in certain cases.

Certain causal order combinations outperform others in estimation precision.

Optimal causal structures can be used for enhanced quantum probing schemes.

Abstract

Quantum Fisher information is the principal tool used to give the ultimate precision bound on the estimation of parameters for quantum channels. In this work, we present analytical expressions for the quantum Fisher information with three noisy channels for the case where the channels are in superposition of causal orders. We found that the quantum Fisher information increases as the number of causal orders increases for certain combinations. We also show that certain combinations of causal orders attain higher precision on bounds than others for the same number of causal orders. Based on our results, we chose the best combinations of causal orders with three channels for probing schemes using indefinite causal structures