TY - JOUR

T1 - Informationally complete sets of Gaussian measurements

AU - Kiukas, Jukka

AU - Schultz, Jussi

N1 - Copyright:
Copyright 2013 Elsevier B.V., All rights reserved.

PY - 2013/11/12

Y1 - 2013/11/12

N2 - We prove the necessary and sufficient conditions for the informational completeness of an arbitrary set of Gaussian observables on continuous variable systems with a finite number of degrees of freedom. In particular, we show that an informationally complete set either contains a single informationally complete observable, or includes infinitely many observables. We show that for a single informationally complete observable, the minimal outcome space is the phase space, and the corresponding probability distribution can always be obtained from the quantum optical Q-function by linear postprocessing and Gaussian convolution, in a suitable symplectic coordinatization of the phase space. In the case of projection valued Gaussian observables, e.g., generalized field quadratures, we show that an informationally complete set of observables is necessarily infinite. Finally, we generalize the treatment to the case where the measurement coupling is given by a general linear bosonic channel, and characterize informational completeness for an arbitrary set of the associated observables.

AB - We prove the necessary and sufficient conditions for the informational completeness of an arbitrary set of Gaussian observables on continuous variable systems with a finite number of degrees of freedom. In particular, we show that an informationally complete set either contains a single informationally complete observable, or includes infinitely many observables. We show that for a single informationally complete observable, the minimal outcome space is the phase space, and the corresponding probability distribution can always be obtained from the quantum optical Q-function by linear postprocessing and Gaussian convolution, in a suitable symplectic coordinatization of the phase space. In the case of projection valued Gaussian observables, e.g., generalized field quadratures, we show that an informationally complete set of observables is necessarily infinite. Finally, we generalize the treatment to the case where the measurement coupling is given by a general linear bosonic channel, and characterize informational completeness for an arbitrary set of the associated observables.

UR - http://www.scopus.com/inward/record.url?scp=84888634270&partnerID=8YFLogxK

U2 - 10.1088/1751-8113/46/48/485303

DO - 10.1088/1751-8113/46/48/485303

M3 - Article

AN - SCOPUS:84888634270

SN - 1751-8113

VL - 46

JO - Journal of Physics A: Mathematical and Theoretical

JF - Journal of Physics A: Mathematical and Theoretical

IS - 48

M1 - 485303

ER -