# Digital Quantum Estimation

## TL;DR

This paper introduces an information-theoretic approach to quantum metrology, focusing on how many bits of a parameter can be recovered, and redefines fundamental bounds like the Heisenberg limit and standard quantum limit.

## Contribution

It redefines key quantum estimation bounds in an information-theoretic framework and clarifies the conditions for achieving these bounds with different strategies.

## Key findings

- Heisenberg bound achievable only by sequential or entangled parallel strategies.
- Parallel-separable strategies limited by the standard quantum limit.
- Highlights differences between information-theoretic and RMSE-based quantum metrology.

## Abstract

Quantum Metrology calculates the ultimate precision of all estimation strategies, measuring what is their root mean-square error (RMSE) and their Fisher information. Here, instead, we ask how many bits of the parameter we can recover, namely we derive an information-theoretic quantum metrology. In this setting we redefine "Heisenberg bound" and "standard quantum limit" (the usual benchmarks in quantum estimation theory), and show that the former can be attained only by sequential strategies or parallel strategies that employ entanglement among probes, whereas parallel-separable strategies are limited by the latter. We highlight the differences between this setting and the RMSE-based one.