Achieving the Heisenberg limit in quantum metrology using quantum error correction. (arXiv:1706.02445v2 [quant-ph] UPDATED)

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.

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