Achieving quantum sensing limits in noisy environment

IQC Colloquium, Sisi Zhou - Perimeter Institute

Quantum metrology studies estimation of unknown parameters in quantum systems. The Heisenberg limit of estimation precision 1/N, with N being the number of probes, is the ultimate sensing limit allowed by quantum mechanics that quadratically outperforms the classically-achievable standard quantum limit 1/√N. The Heisenberg limit is attainable using multi-probe entanglement in the ideal, noiseless case. However, in presence of noise, many quantum systems only allow a constant factor of improvement over the standard quantum limit. To elucidate the noise effect in quantum metrology, we prove a necessary and sufficient condition for achieving the Heisenberg limit using quantum controls. We show that when the condition is satisfied, there exist quantum error correction protocols to achieve the Heisenberg limit; when the condition is violated, no quantum controls can break the standard quantum limit (although quantum error correction can be used to maximize the constant-factor improvement). We will also discuss the modified sensing limits when only restricted types of quantum controls can be applied.