QUROPE Quantum Information Processing and Communication in Europe

Increasing Sensing Resolution with Error Correction
G. Arrad, Y. Vinkler, D. Aharonov, A. Retzker
Phys. Rev. Lett. 112, 150801 (2014);
Quantum Error Correction for Metrology
E.  M. Kessler, I. Lovchinsky, A.  O. Sushkov, M.  D. Lukin
Phys. Rev. Lett. 112, 150802 (2014);
Improved Quantum Metrology Using Quantum Error Correction
W. Dür, M. Skotiniotis, F. Fröwis, B. Kraus
Phys. Rev. Lett. 112, 080801 (2014)

Understanding quantum metrology in noisy environments is crucial for the development of quantum sensing techniques. In particular, it is relevant to know where the effect of noise and decoherence limits the achievable gain in precision by quantum entanglement.
These works consider the use of quantum error correction techniques to improve the sensitivity of quantum metrology in noisy scenarios.

In the first work, Arrad and co-workers utilize quantum error correction to prolonging the coherence time of sensing protocols beyond the fundamental limits of current techniques. They develop an implementable sensing protocol that incorporates error correction, and discuss the characteristics of these protocols in different noise and measurement scenarios. They examine the use of entangled versus separable states, and error correction’s reach of the Heisenberg limit. They show that measurement precision can be enhanced for both one-directional and general noise.

In the second work, Kessler and co-workers also analyze the use of quantum error correction to improve quantum metrology in the presence of noise. They identify the conditions under which these techniques allow one to improve the signal-to-noise ratio in quantum-limited measurements, and demonstrate that it enables, in certain situations, Heisenberg-limited sensitivity. They finally discuss specific applications to nanoscale sensing using nitrogen-vacancy centers in diamond and show improvements on the measurement sensitivity and bandwidth under realistic experimental conditions.

In the third work, Dür and co-workers also show how quantum error correction techniques improve the achievable gain in precision by quantum entanglement in some noisy situations. This is demonstrated in two scenarios, including a many-body Hamiltonian with single-qubit dephasing or depolarizing noise and a single-body Hamiltonian with transversal noise. In both cases, Heisenberg scaling, and hence a quadratic improvement over the classical case, can be retained. For the case of frequency estimation they find that the inclusion of error correction allows, in certain instances, for a finite optimal interrogation time even in the asymptotic limit.