Achieving the Heisenberg limit in quantum metrology using quantum error correction

• Published in: Nature communications Vol. 9; no. 1; pp. 78 - 11
• Main Authors: Zhou, Sisi, Zhang, Mengzhen, Preskill, John, Jiang, Liang
• Format: Journal Article
• Language: English
• Published: London Nature Publishing Group UK 08.01.2018; Nature Publishing Group; Nature Portfolio
• Subjects: 639/766/483/1139; 639/766/483/1255; 639/766/483/481; Error correcting codes; Error correction; Error correction & detection; Gravitational waves; Gravity; Humanities and Social Sciences; Markov processes; Metrology; multidisciplinary; Noise; Quantum mechanics; Quantum theory; Science; Science (multidisciplinary); Spectroscopy
• ISSN: 2041-1723; 2041-1723
• DOI: 10.1038/s41467-017-02510-3

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 that suppresses the noise without obscuring the signal; the optimal code, achieving the best possible precision, can be found by solving a semidefinite program. The possibility to reach Heisenberg-limited quantum measurements in the presence of noise is a long-standing problem. Here, the authors derive a necessary and sufficient condition on the noise acting on any finite-dimensional probe to establish whether the Heisenberg limit is reachable using quantum error correction.