Quantum-Enhanced Parameter Estimation Without Entanglement

TL;DR

This paper demonstrates that quantum-enhanced parameter estimation beyond the standard quantum limit can be achieved without entanglement by using high-dimensional qudits, reducing resource requirements significantly.

Contribution

It introduces entanglement-free analogues of Dicke and GHZ states on qudits, showing they can reach Heisenberg-limited precision, and links non-classicality to metrological power.

Findings

Achieves Heisenberg-limited precision without entanglement.

Provides exponential resource reduction for quantum metrology.

Establishes a measure of non-classicality based on quantum Fisher information.

Abstract

Entanglement is generally considered necessary for achieving the Heisenberg limit in quantum metrology. We construct analogues of Dicke and GHZ states on a single $N+1$ dimensional qudit that achieve precision equivalent to symmetrically entangled states on $N$ qubits, showing that entanglement is not necessary for going beyond the standard quantum limit. We define a measure of non-classicality based on quantum Fisher information and estimate the achievable precision, suggesting a close relationship between non-classical states and metrological power of qudits. Our work offers an exponential reduction in the physical resources required for quantum-enhanced parameter estimation, making it accessible on any quantum system with a high-dimensional Hilbert space.