Quantum Metrology with Indefinite Causal Order
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 used in a fixed order can have rootmeansquare 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 rootmeansquare error vanishing with superHeisenberg scaling 1 /N^{2}, which we prove to be optimal among all superpositions of setups with definite causal order. Our 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.
 Publication:

Physical Review Letters
 Pub Date:
 May 2020
 DOI:
 10.1103/PhysRevLett.124.190503
 arXiv:
 arXiv:1912.02449
 Bibcode:
 2020PhRvL.124s0503Z
 Keywords:

 Quantum Physics
 EPrint:
 11 pages, 3 figures