Quantum enhanced precision in a collective measurement

TL;DR

This paper demonstrates that collective quantum measurements on qubits can significantly improve parameter estimation precision, achieving a quadratic enhancement over classical bits by utilizing entangled states.

Contribution

The paper proves a tighter $O(1/N^2)$ precision bound for quantum collective measurements and constructs a protocol that saturates this bound.

Findings

Quantum bits outperform classical bits in collective measurement precision.

The precision bound for qubits is $O(1/N^2)$, tighter than the classical $O(1/N)$.

A measurement protocol is constructed that achieves the optimal bound.

Abstract

We explore the role of $\textit{collective measurements}$ on precision in estimation of a single parameter. Collective measurements are represented by observables which commute with all permutations of the probe particles. We show that with this constraint, quantum bits(qubits) outperform classical bits(non-superposable bits) in optimizing precision. Specifically, we prove that while precision in a collective measurement is loosely bounded by $O\left(\frac{1}{N}\right)$ for $N$ classical bits, using qubits it is tightly bounded by $O\left(\frac{1}{N^2}\right)$. This bound is consistent with quantum metrology protocols with the collective measurement requiring an entangled probe state to saturate. Finally, we construct a canonical measurement protocol that saturates this bound.