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Dynamical phase transitions as a resource for quantum enhanced metrology

Macieszczak, Katarzyna; Guţă, Mădălin; Lesanovsky, Igor; Garrahan, Juan P.

Authors

Katarzyna Macieszczak

Mădălin Guţă

Igor Lesanovsky

Juan P. Garrahan



Abstract

We consider the general problem of estimating an unknown control parameter of an open quantum system. We establish a direct relation between the evolution of both system and environment and the precision with which the parameter can be estimated. We show that when the open quantum system undergoes a first-order dynamical phase transition the quantum Fisher information (QFI), which gives the upper bound on the achievable precision of any measurement of the system and environment, becomes quadratic in observation time (cf. “Heisenberg scaling”). In fact, the QFI is identical to the variance of the dynamical observable that characterizes the phases that coexist at the transition, and enhanced scaling is a consequence of the divergence of the variance of this observable at the transition point. This identification makes it possible to establish the finite time scaling of the QFI. Near the transition the QFI is quadratic in time for times shorter than the correlation time of the dynamics. In the regime of enhanced scaling the optimal measurement whose precision is given by the QFI involves measuring both system and output. As a particular realization of these ideas, we describe a theoretical scheme for quantum enhanced estimation of an optical phase shift using the photons being emitted from a quantum system near the coexistence of dynamical phases with distinct photon emission rates.

Journal Article Type Article
Publication Date Feb 3, 2016
Journal Physical Review A
Print ISSN 2469-9926
Electronic ISSN 2469-9934
Publisher American Physical Society
Peer Reviewed Peer Reviewed
Volume 93
Issue 2
Article Number 022103
APA6 Citation Macieszczak, K., Guţă, M., Lesanovsky, I., & Garrahan, J. P. (2016). Dynamical phase transitions as a resource for quantum enhanced metrology. Physical Review A, 93(2), https://doi.org/10.1103/PhysRevA.93.022103
DOI https://doi.org/10.1103/PhysRevA.93.022103
Publisher URL http://journals.aps.org/pra/abstract/10.1103/PhysRevA.93.022103
Copyright Statement Copyright information regarding this work can be found at the following address: http://eprints.nottingh.../end_user_agreement.pdf

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Copyright Statement
Copyright information regarding this work can be found at the following address: http://eprints.nottingham.ac.uk/end_user_agreement.pdf





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