Quantum Metrology in the Era of Quantum Information*

A comprehensive overview of the most recent advances in theoretical methods of quantum metrology will be presented, that in particular benefit from the quantum information related concepts such as quantum error-correction or matrix product states formalism. The theory developed allows to determine whether the Heisenberg scaling of precision is possible for a quantum sensor subject to a general Markovian noise. The theory takes into account all the possible quantum strategies, including entangling the sensor with ancillary systems, adaptive strategies such as e.g. quantum error correction protocols. Moreover, effective algorithms, based on the matrix product states/matrix product operator formalism, are developed that allow to identify the optimal metrological protocols in presence of noise (also correlated noise) in the limit of large number of probes, inaccessible by the state-of-the-art methods. Finally, by reversing the line of reasoning why may also use the fundamental metrological precission bounds to establish limits on efficiency of quantum error-correcting protocols.

References:
[1] R. Demkowicz-Dobrzanski, J. Czajkowski, P. Sekatski, Adaptive quantum metrology under general Markovian noise, Phys. Rev. X 7, 041009 (2017)
[2] K. Chabuda, J. Dziarmaga, T. Osborne, R. Demkowicz-Dobrzanski, Tensor-Network Approach for Quantum Metrology in Many-Body Quantum Systems, Nature Communications 11, 250 (2020)
[3] A. Kubica, R. Demkowicz-Dobrzanski, Using Quantum Metrological Bounds in Quantum Error Correction: A Simple Proof of the Approximate Eastin-Knill Theorem, arXiv:2004.11893 (2020)