Robust quantum metrological schemes based on protection of quantum Fisher information

TL;DR

This paper introduces a new approach to quantum metrology that focuses on preserving quantum Fisher information against noise, enabling robust parameter estimation with fewer qubits than traditional error correction methods.

Contribution

The authors develop a theory for quantum metrological schemes that protect quantum Fisher information rather than quantum states, reducing resource requirements for noise immunity.

Findings

Constructed $2t+1$ qubit schemes immune to $t$-qubit errors.

Quantum Fisher information can be preserved even if quantum states are irrecoverably affected.

Fewer qubits are needed compared to standard quantum error correction for error immunity.

Abstract

Fragile quantum features such as entanglement are employed to improve the precision of parameter estimation and as a consequence the quantum gain becomes vulnerable to noise. As an established tool to subdue noise, quantum error correction is unfortunately overprotective because the quantum enhancement can still be achieved even if the states are irrecoverably affected, provided that the quantum Fisher information, which sets the ultimate limit to the precision of metrological schemes, is preserved and attained. Here, we develop a theory of robust metrological schemes that preserve the quantum Fisher information instead of the quantum states themselves against noise. After deriving a minimal set of testable conditions on this kind of robustness, we construct a family of $2t+1$ qubits metrological schemes being immune to $t$-qubit errors after the signal sensing. In comparison at least five qubits are required for correcting arbitrary 1-qubit errors in standard quantum error correction.