Generalized Limits for Parameter Sensitivity via Quantum Ziv-Zakai Bound

TL;DR

This paper establishes fundamental limits on quantum parameter sensitivity using the quantum Ziv-Zakai bound, demonstrating that known states cannot surpass the Heisenberg limit even with adaptive measurements.

Contribution

It derives new lower bounds for quantum parameter sensitivity considering unbounded Hamiltonians and adaptive measurements, connecting sensitivity limits to the minimum detectable parameter.

Findings

Known quantum states cannot outperform the Heisenberg limit.

Derived bounds apply to unbounded Hamiltonians and adaptive measurement schemes.

Parameter sensitivity is limited by the minimum detectable parameter.

Abstract

We study the generalized limit for parameter sensitivity in quantum estimation theory considering the effects of repeated and adaptive measurements. Based on the quantum Ziv-Zakai bound, we derive some lower bounds for parameter sensitivity when the Hamiltonian of system is unbounded and when the adaptive measurements are implemented on the system. We also prove that the parameter sensitivity is bounded by the limit of the minimum detectable parameter. In particular, we examine several known states in quantum phase estimation with non-interacting photons, and show that they can not perform better than Heisenberg limit in a much simpler way with our result.