Gaussian systems for quantum-enhanced multiple phase estimation

Abstract

Original citation:Gagatsos, Christos N., Branford, Dominic and Datta, Animesh. (2016) Gaussian systems for quantum-enhanced multiple phase estimation. Physical Review A, 94 (4). 042342. Permanent WRAP URL: http://wrap.warwick.ac.uk/83269 Copyright and reuse:The Warwick Research Archive Portal (WRAP) makes this work by researchers of the University of Warwick available open access under the following conditions. Copyright © and all moral rights to the version of the paper presented here belong to the individual author(s) and/or other copyright owners. To the extent reasonable and practicable the material made available in WRAP has been checked for eligibility before being made available.Copies of full items can be used for personal research or study, educational, or not-for-profit purposes without prior permission or charge. Provided that the authors, title and full bibliographic details are credited, a hyperlink and/or URL is given for the original metadata page and the content is not changed in any way. Publisher statement: © 2016 American Physical Society A note on versions:The version presented here may differ from the published version or, version of record, if you wish to cite this item you are advised to consult the publisher's version. Please see the 'permanent WRAP URL' above for details on accessing the published version and note that access may require a subscription. For a fixed average energy, the simultaneous estimation of multiple phases can provide a better total precision than estimating them individually. We show this for a multimode interferometer with a phase in each mode, using Gaussian inputs and passive elements, by calculating the covariance matrix. The quantum Cramér-Rao bound provides a lower bound to the covariance matrix via the quantum Fisher information matrix, whose elements we derive to be the covariances of the photon numbers across the modes. We prove that this bound can be saturated. In spite of the Gaussian nature of the problem, the calculation of non-Gaussian integrals is required, which we accomplish analytically. We find our simultaneous strategy to yield no more than a factor-of-2 improvement in total precision, possibly because of a fundamental performance limitation of Gaussian states. Our work shows that no modal entanglement is necessary for simultaneous quantum-enhanced estimation of multiple phases.

Subdiffraction incoherent optical imaging via spatial-mode demultiplexing

“…The quantum optimality of SPADE for general imaging is in particular an interesting question. These daunting problems may be attacked by more advanced methods in quantum metrology [43][44][45][46][75][76][77][78], quantum state tomography [79][80][81], compressed sensing [55][56][57]81], and photonics design [52][53][54]. For the TEM scheme, this implies that each qth channel contains information about not only q q 2 but also the higher-order moments.…”

Optimal Gaussian metrology for generic multimode interferometric circuit

“…There are works in the literature which discuss the unnecessity of mode entanglement [5,39,40,50,53,55,96,97]. Note, however, that in those works the probe states are not restricted to Gaussian states and in addition just the achievability of the Heisenberg scaling (quadratic in N ) is discussed.…”

Experimental multiphase estimation on a chip

“…Such scenario is provided by the multiphase problem, where the parameters to be estimated are a set of optical phases. Several theoretical works have been reported in this direction [6,20,31,39,[45][46][47][48][49][50][51][52][53][54]. Very recent results reported necessary and sufficient conditions to define the optimal projective measurements for pure states [31], with a subsequent extension to general probe states [53].…”