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Heisenberg scaling precision in multi-mode distributed quantum metrology

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Authors
Gramegna, Giovanni
Triggiani, Danilo
Facchi, Paolo
Narducci, Frank A.
Tamma, Vincenzo
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Date of Issue
2020-03-30
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ArXiv
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Abstract
We propose an NN-photon Gaussian measurement scheme which allows the estimation of a parameter φφ encoded into a multi-port interferometer with a Heisenberg scaling precision (i.e. of order 1/N1/N). In this protocol, no restrictions on the structure of the interferometer are imposed other than linearity and passivity, allowing the parameter φφ to be distributed over several components. In all previous proposals Heisenberg scaling has been obtained provided that both the input state and the measurement at the output are suitably adapted to the unknown parameter φφ. This is a serious drawback which would require in practice the use of iterative procedures with a sequence of trial input states and measurements, which involve an unquantified use of additional resources. Remarkably, we find that only one stage has to be adapted, which leaves the choice of the other stage completely arbitrary. We also show that our scheme is robust against imperfections in the optimized stage. Moreover, we show that the adaptive procedure only requires a preliminary classical knowledge (i.e to a precision 1/N−−√1/N) on the parameter, and no further additional resources. As a consequence, the same adapted stage can be employed to monitor with Heisenberg-limited precision any variation of the parameter of the order of 1/N−−√1/N without any further adaptation.
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Preprint
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Physics
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This work was supported by the Office of Naval Research Global (N62909-18-1-2153). PF and GG are partially supported by Istituto Nazionale di Fisica Nucleare (INFN) through the project “QUANTUM”, and by the Italian National Group of Mathematical Physics (GNFM-INdAM)
Funder
This work was supported by the Office of Naval Research Global (N62909-18-1-2153). PF and GG are partially supported by Istituto Nazionale di Fisica Nucleare (INFN) through the project “QUANTUM”, and by the Italian National Group of Mathematical Physics (GNFM-INdAM)
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5 p.
Citation
Gramegna, Giovanni, et al. "Heisenberg scaling precision in multi-mode distributed quantum metrology." arXiv preprint arXiv:2003.12550 (2020).
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This publication is a work of the U.S. Government as defined in Title 17, United States Code, Section 101. Copyright protection is not available for this work in the United States.
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