# Quantum metrology with generalized cat states

## TL;DR

This paper establishes a broad connection between superpositions of macroscopically distinct states, called generalized cat states, and enhanced sensitivity in quantum metrology, achieving Heisenberg-limited and beyond-quantum-limit precision.

## Contribution

It introduces a new criterion for generalized cat states, demonstrating their metrological usefulness and potential to surpass standard quantum limits even under noise.

## Key findings

- Generalized cat states achieve Heisenberg-limited sensitivity without noise.
- They surpass the standard quantum limit under dephasing.
- A specific example shows orders of magnitude improvement over previous sensors.

## Abstract

We show a general relationship between a superposition of macroscopically distinct states and sensitivity in quantum metrology. Generalized cat states are defined by using an index which extracts the coherence between macroscopically distinct states, and a wide variety of states, including a classical mixture of an exponentially large number of states, has been identified as the generalized cat state with this criterion. We find that, if we use the generalized cat states for magnetic field sensing without noise, we achieve the Heisenberg limited sensitivity. Moreover, we even show that sensitivity of generalized cat states achieves the ultimate scaling sensitivity beyond the standard quantum limit under the effect of dephasing. As an example, we investigate the sensitivity of a generalized cat state that is attainable through a single global manipulation on a thermal equilibrium state and find an improvement of a few orders of magnitude from the previous sensors. Clarifying a wide class that includes such a peculiar state as metrologically useful, our results significantly broaden the potential of quantum metrology.