Qubit-assisted quantum metrology under a time-reversal strategy

TL;DR

This paper introduces a quantum metrology protocol utilizing a two-step joint evolution with an ancillary qubit, achieving Heisenberg-limited precision even with non-resource initial states and showing robustness against imperfections.

Contribution

It presents a novel time-reversal quantum metrology protocol that attains Heisenberg scaling without requiring entanglement or squeezing, and is resilient to various system imperfections.

Findings

QFI approaches Heisenberg scaling $N^2$ with probe size $N$.

Protocol is robust against initial state imperfections and decoherence.

CFI saturates quantum Fisher information using a single-shot measurement.

Abstract

We propose a quantum metrology protocol based on a two-step joint evolution of the probe system and an ancillary qubit and quantum measurement. With a proper initial state of the ancillary qubit and an optimized evolution time, the quantum Fisher information (QFI) about the phase parameter encoded in the probe system is found to be determined by the expectation value of the square of a phase generator, irrespective of the probe initial state. Consequently, even if the probe is prepared as a finite-temperature state, faraway from the so-called resource state, e.g., the squeezed spin state or the Greenberger-Horne-Zeilinger state in atomic systems, the QFI in our protocol can approach the Heisenberg scaling $N^2$ with respect to the probe size $N$. This quadratic scaling behavior shows robustness against the imperfections about the initial state of the ancillary qubit and the optimized evolution time of the whole system. Also it is not sensitive to the deviation in system parameters and the qubit decoherence. Using the time-reversal strategy and a single-shot projective measurement, the classical Fisher information (CFI) in our metrology protocol is saturated with its quantum counterpart. Our work thus provides an economical method to reach the Heisenberg limit in metrology precision with no input of entanglement or squeezing.