Quantum Metrology with Indefinite Causal Order

TL;DR

This paper demonstrates that indefinite causal order in quantum metrology can significantly surpass traditional limits, achieving super-Heisenberg scaling in estimating displacements, with implications for quantum gravity and fundamental physics.

Contribution

It introduces a novel quantum metrology protocol utilizing indefinite causal order to achieve super-Heisenberg scaling, surpassing fixed-order measurement limits.

Findings

Super-Heisenberg scaling of 1/N^2 in estimation error.

Fixed-order setups cannot surpass the 1/N Heisenberg limit.

Indefinite causal order enables enhanced quantum measurement precision.

Abstract

We address the study of quantum metrology enhanced by indefinite causal order, demonstrating a quadratic advantage in the estimation of the product of two average displacements in a continuous variable system. We prove that no setup where the displacements are probed in a fixed order can have root-mean-square error vanishing faster than the Heisenberg limit 1/N, where N is the number of displacements contributing to the average. In stark contrast, we show that a setup that probes the displacements in a superposition of two alternative orders yields a root-mean-square error vanishing with super-Heisenberg scaling 1/N^2. This result opens up the study of new measurement setups where quantum processes are probed in an indefinite order, and suggests enhanced tests of the canonical commutation relations, with potential applications to quantum gravity.