Quantum phase measurements and a general method for the simulation of random processes

    Authors

    S. R. Shepard

    Comments

    Authors: contact us about adding a copy of your work at STARS@ucf.edu

    Abbreviated Journal Title

    Nonlinear Anal.-Theory Methods Appl.

    Keywords

    SU(2); STATE; Mathematics, Applied; Mathematics

    Abstract

    Quantum interferences offer the potential for improving the effective resolution wavelength of many measurements by a factor of N. Coincidence detection methods to date have been limited to N = 4 due to an increase in complexity of the apparatus with N. We offer an alternative method of extracting this higher-order phase information from a standard (first-order) interferometer. This "phase function fitting'' algorithm also eliminates the need to null the interferometer. We compare the interferometer's statistics to those of the quantum phase measurement, which we also utilize to derive Heisenberg limits for the quantum noon states. States which surpass this noon state limit are then demonstrated; and we discuss how state optimization for various signal environments might proceed. The phase representation is also shown to yield computationally efficient and conceptually revealing forms for calculating the statistics of the interferometer itself. We define a static limit in which the signal varies slowly enough that we can make the integration time long enough to approach perfect measurement of the interferometer statistics. We discuss the sense in which the phase function fitting algorithm can approach zero error in this limit, while still at finite N-satisfying the power constraint (but approaching infinite energy as we collect over longer times). To incorporate the signal dynamics we present a general method in which we can approximately prescribe the autocorrelation, as well as the probability distribution, of a random process; and illustrate how probabilistic effects can mitigate the spectral distortions of an onlinear mapping. Mathematical challenges in applying these techniques to the simulation of the quantum phase measurement are circumvented-enabling the simulation of a variety of quantum algorithms for the estimation and tracking of various signal models in this exciting application. (C) 2009 Published by Elsevier Ltd

    Journal Title

    Nonlinear Analysis-Theory Methods & Applications

    Volume

    71

    Issue/Number

    12

    Publication Date

    1-1-2009

    Document Type

    Article

    Language

    English

    First Page

    E1160

    Last Page

    E1168

    WOS Identifier

    WOS:000277952800017

    ISSN

    0362-546X

    Share

    COinS