Intrinsic metrological resolution as a distance measure and nonclassical light

TL;DR

This paper introduces a Hilbert-Schmidt distance-based measure for quantum metrological accuracy, revealing nonclassical states with resolution surpassing coherent states and analyzing the properties of this measure.

Contribution

It develops a symmetric probe-transformation measure for quantum signals, extending variance concepts, and explores its implications for nonclassical states and quantum metrology.

Findings

States with resolution better than coherent states are nonclassical

The measure $ extLambda$ generalizes variance but lacks an uncertainty relation for complementary generators

The formalism applies to feasible quantum probes and transformations

Abstract

We elaborate on a Hilbert-Schmidt distance measure assessing the intrinsic metrological accuracy in the detection of signals imprinted on quantum probe states by signal-dependent transformations. For small signals this leads to a probe-transformation measure $\Lambda$ fully symmetric on the probe $\rho$ and the generator $G$ of the transformation $\Lambda (\rho, G) = \Lambda (G, \rho)$. Although $\Lambda$ can be regarded as a generalization of variance we show that no uncertainty relation holds for the product of measures corresponding to complementary generators. We show that all states with resolution larger than coherent states are nonclassical. We apply this formalism to feasible probes and transformations.