Achieving the Heisenberg limit in quantum metrology using quantum error correction

TL;DR

This paper demonstrates how quantum error correction can enable quantum systems to reach the Heisenberg limit in measurement precision despite noise, by establishing conditions and methods for optimal noise suppression.

Contribution

It provides a necessary and sufficient condition for achieving the Heisenberg limit with noisy quantum probes using quantum error correction, and offers a way to construct optimal codes.

Findings

Heisenberg limit can be achieved with quantum error correction under certain conditions.

A semidefinite program can find the optimal quantum error-correcting code for noise suppression.

The method assumes availability of noiseless ancillas and fast quantum processing.

Abstract

Quantum metrology has many important applications in science and technology, ranging from frequency spectroscopy to gravitational wave detection. Quantum mechanics imposes a fundamental limit on measurement precision, called the Heisenberg limit, which can be achieved for noiseless quantum systems, but is not achievable in general for systems subject to noise. Here we study how measurement precision can be enhanced through quantum error correction, a general method for protecting a quantum system from the damaging effects of noise. We find a necessary and sufficient condition for achieving the Heisenberg limit using quantum probes subject to Markovian noise, assuming that noiseless ancilla systems are available, and that fast, accurate quantum processing can be performed. When the sufficient condition is satisfied, a quantum error-correcting code can be constructed which suppresses the noise without obscuring the signal; the optimal code, achieving the best possible precision, can be found by solving a semidefinite program.