Agnostic Parameter Estimation with Large Spins

TL;DR

This paper demonstrates how entanglement with an ancilla enables optimal quantum parameter estimation using large spin probes without prior knowledge of the rotation axis, surpassing limitations of spin-1/2 sensors.

Contribution

It extends entanglement-based quantum metrology techniques from spin-1/2 to large spins, enabling optimal estimation without axis knowledge and analyzing success probabilities.

Findings

Achieves optimal quantum Fisher information with large spins and ancilla.

Utilizes post-selection to overcome limitations of unknown rotation axes.

Shows general entangled states can still attain optimal metrology.

Abstract

The quantum Fisher information of a quantum state with respect to a certain parameter quantifies the sensitivity of the quantum state to changes in that parameter. Maximizing the quantum Fisher information is essential for achieving the optimal estimation precision of quantum sensors. A typical quantum sensor involves a qubit(e.g. a spin-1/2) probe undergoing an unknown rotation, here the unknown rotation angle is the parameter to be estimated. A well known limitation is that if the rotation axis is unknown, the maximal quantum Fisher information is impossible to attain. This limitation has been lifted recently by leveraging entanglement between the probe qubit and an ancilla qubit. Namely, through measurement of the ancilla after the axis is revealed, one can prepare the probe that is optimal for any unknown rotation axis. This proposal, however, works only for a spin-1/2. Considering large spin probes can achieve a larger quantum Fisher information, offering enhanced metrological advantage, we here utilize the entanglement between a large spin probe and an ancilla to achieve optimal quantum Fisher information for estimating the rotation angle, without prior knowledge of the rotation axis. Different from the previous spin-1/2 case, achieving the optimal precision with large spins generally requires post-selection, resulting in a success probability dependent on the dimension of the Hilbert space. Furthermore, we extend the encoding state from the maximally entangled case to general entangled states, showing that optimal metrology can still be achieved with a certain success probability.