The probe readout and quantum limited measurements

TL;DR

This paper identifies optimal initial states for quantum probes to achieve quantum-limited measurement precision, analyzing how probe composition and readout restrictions affect measurement uncertainty.

Contribution

It derives the optimal initial states of quantum probes for saturating the quantum Cramer-Rao bound under fixed dynamics and readout, including for multi-qubit systems with different entangling properties.

Findings

Optimal states depend on the probe's dynamics and measurement restrictions.

Entangling and non-entangling probe dynamics are analyzed.

Measurement uncertainty is limited by readout procedures.

Abstract

Assuming that the parameter dependent evolution, as well as the measurements that are done for readout, of a quantum system that acts as the probe in a quantum limited measurement scheme are both fixed, we find the optimal initial states of the probe that will saturate the quantum Cramer-Rao bound. When the probe system is itself made of identical, elementary, two-level subsystems or qubits, we connect the optimal state of the N qubit probe to that of the one qubit probe. This is done for two different classes of dynamics for the probe qubits, one of which is entangling while the other is not. We study the limitations placed on the optimal initial state of the probe and the achievable measurement uncertainty by restrictions on the readout procedure that is applied on the probe qubits at the end of the measurement protocol.