Quantum enhanced precision in a collective measurement

Abstract

We explore the role of $\text{collective measurements}$ 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.

16 Pages, 1 Figure, 2 Tables

References in corpus (5)

• Generalized Limits for Single-Parameter Quantum Estimation
• Entanglement-enhanced measurement of a completely unknown phase
• Quantum Metrology: Dynamics vs. Entanglement
• Comparison between the Cramer-Rao and the mini-max approaches in quantum channel estimation
• Quantum measurement bounds beyond the uncertainty relations