Quantum-error-correction-assisted quantum metrology without entanglement

In this article we study the role that quantum resources play in quantum-error-correction-assisted quantum metrology (QECQM) schemes. We show that there exist classes of such problems where entanglement is not necessary to retrieve noise-free evolution and Heisenberg scaling in the long time limit. Over short timescales, noise-free evolution is also possible even without any form of quantum correlations. In particular, for qubit probes, we show that whenever noise-free quantum metrology is possible via QECQM, entanglement-free schemes over long timescales and correlation-free schemes over short timescales are always possible.

Figure 1

Quantum-error correction in the sequential scheme of quantum metrology. After state preparation, the probe is allowed to evolve for a short period $dt$. This evolution is represented by the quantum map ${\mathcal{E}}_{dt}$ which includes the interaction with some signal Hamiltonian, as well as contributions from noise. The ancillae are assumed to be perfectly shielded and noise free. This is followed by an instantaneous quantum control operation on $\text{probe}+\text{ancillae}$. The process is repeated for a total of $\kappa$ rounds, at the end of which a measurement is performed. The total interrogation time is $t=\kappa dt$.