arXiv:1111.1005 · Journal of Physics A Mathematical and Theoretical

On detection of quasiclassical states

Michał Oszmaniec, Marek Kuś

Published May 30, 2012• 15 citations

Abstract

We give a criterion of classicality for mixed states in terms of expectation values of a quantum observable. Using group representation theory, we identify all cases when the criterion can be computed exactly in terms of the spectrum of a single operator. This article is part of a special issue of Journal of Physics A: Mathematical and Theoretical devoted to 'Coherent states: mathematical and physical aspects'.

DOI: 10.1088/1751-8113/45/24/244034

Related papers

2 On detection of quasiclassical states

Micha L Oszmaniec

We give a criterion of classicality for mixed states in terms of expectation values of a quantum observable. Using group representation theory we identify all cases when the criterion can be computed exactly in terms of the spectrum of a single operator.

Aug 14, 201614 citations

Multicopy observables for the detection of optically nonclassical states

Matthieu Arnhem, Célia Griffet, Nicolas J. Cerf

Distinguishing quantum states that admit a classical counterpart from those that exhibit nonclassicality has long been a central issue in quantum optics. Finding an implementable criterion certifying optical nonclassicality (i.e., the incompatibility with a statistical mixture of coherent states) is of major importance as it often is a prerequisite to quantum information processes. A hierarchy of conditions for detecting whether a quantum state exhibits optical nonclassicality can be written based on matrices of moments of the optical field [E. V. Shchukin and W. Vogel, Phys. Rev. A 72, 043808 (2005)]. Here, we design optical nonclassicality observables that act on several replicas of a quantum state and whose expectation value coincides with the determinant of these matrices, hence providing witnesses of optical nonclassicality that overcome the need for state tomography. These multicopy observables are used to construct a family of physically implementable schemes involving linear optical operations and photon number detectors.

arXiv:2205.12040Physical Review AOct 7, 20227 citations

Coherent states

J. C. Garrison, R. Y. Chiao

The elementary quantum theory of quasi-classical states for mechanical harmonic oscillators is applied to the radiation oscillators describing light, and thus used to define quasi-classical states of light. These states are called “coherent”, because the expectation value of any normally ordered product of creation and annihilation operators factorizes for them. A theoretical discussion of possible sources for coherent states is followed by experimental evidence for their existence. The mathematical properties of coherent states, e.g., nonorthogonality and overcompleteness, are explained in order to use them to represent states and operators. These representations provide a suitable replacement for the classical phase space description of light, which is forbidden by the uncertainty principle. The quantum phase space approach leads to the definition of the Wigner distribution, the Q-function, the P-function, and Gaussian mixed states.

Oxford University Press eBooksJun 5, 20080 citations

MINIMUM-ERROR DISCRIMINATION AMONG MIXED QUANTUM STATES

Chih‐Lung Chou

We review the problem of discriminating with minimum error among mixed quantum states, with emphasize on the analytically solved quantum ensembles.

International Journal of Quantum InformationNov 1, 20050 citations

Generalized coherent states and extremal positive operator valued measures

Teiko Heinosaari, Juha-Pekka Pellonpää

We present a correspondence between positive operator valued measures (POVMs) and sets of generalized coherent states. POVMs describe quantum observables and, similar to quantum states, quantum observables can also be mixed. We show how the formalism of generalized coherent states leads to a useful characterization of extremal POVMs. We prove that covariant phase-space observables related to squeezed states are extremal, while those related to number states are not extremal. This article is part of a special issue of Journal of Physics A: Mathematical and Theoretical devoted to 'Coherent states: mathematical and physical aspects'.

arXiv:1112.4280Journal of Physics A Mathematical and TheoreticalMay 30, 20129 citations

Quantum detection of coherent-state signals in the presence of noise

Victor A. Vilnrotter, Chi-Wung Lau

A general method for solving an important class of quantum detection problems will be presented and evaluated. The quantum theory for detecting pure states for communications purposes has been developed over two decades ago, however the mixed state problem representing signal plus noise states has received little attention due to its great complexity. Here we develop a practical model for solving the mixed-state problem using a discrete approximation to the coherent-state representation of signal plus noise density operators.

Jan 21, 20030 citations