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Nonseparability and squeezing of continuous polarization variables: the complete story

Natalia Korolkova, R. Loudon

Published Mar 21, 2003• 1 citation
OpenAlex

Abstract

The impact of the operator-valued commutator on nonclassical properties of continuous polarization variables is discussed. The definition of polarization squeezing is clarified to exclude those squeezed states which do not contain any new physics beyond quadrature squeezing. We present a consistent derivation of the general nonseparability criterion for the continuous variables with the operator-valued commutator, and apply it to the polarization variables.

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Physical Review A•Aug 5, 2002•15 citations
The impact of the operator-valued commutator on nonclassical properties of continuous polarization variables is discussed. The definition of polarization squeezing is clarified to exclude those squeezed states which do not contain any new physics beyond quadrature squeezing. We present a consistent derivation of the general nonseparability criterion for the continuous variables with the operator-valued commutator, and apply it to the polarization variables.
Quantum information with continuous variables conventionally exploits quantum variables with canonic: commutation relations, like position and momentum, or quadrature field components. In contrast, this contribution is devoted to quantum continuous polarization variables. The relevant observabIes are quantum Stokes operators which obey the SU(2) algebra with a commutator which is not a c-number but an operator. In this paper, we review the concept of polarization squeezing and the new concept of continuous-variable polarization entanglement using quantum Stokes parameters. We discuss the prospects and specific features of such nonclassical polarization states for quantum communication.
A concept of polarization entanglement for continuous variables is introduced. For this purpose the Stokes-parameter operators and the associated Poincar\'e sphere, which describe the quantum-optical polarization properties of light, are defined and their basic properties are reviewed. The general features of the Stokes operators are illustrated by evaluation of their means and variances for a range of simple polarization states. Some of the examples show polarization squeezing, in which the variances of one or more Stokes parameters are smaller than the coherent-state value. The main object of the paper is the application of these concepts to bright squeezed light. It is shown that a light beam formed by interference of two orthogonally polarized quadrature-squeezed beams exhibits squeezing in some of the Stokes parameters. Passage of such a primary polarization-squeezed beam through suitable optical components generates a pair of polarization-entangled light beams with the nature of a two-mode squeezed state. Implementation of these schemes using the double-fiber Sagnac interferometer provides an efficient method for the generation of bright nonclassical polarization states. The important advantage of these nonclassical polarization states for quantum communication is the possibility of experimentally determining all of the relevant conjugate variables of both squeezed and entangled fields using only linear optical elements followed by direct detection.
We investigate nonclassical Stokes-operator variances in continuous-wave polarization-squeezed laser light generated from one and two optical parametric amplifiers. A general expression of how Stokes-operator variances decompose into two-mode quadrature operator variances is given. Stokes parameter variance spectra for four different polarization-squeezed states have been measured and compared with a coherent state. Our measurement results are visualized by three-dimensional Stokes-operator noise volumes mapped on the quantum Poincar\'e sphere. We quantitatively compare the channel capacity of the different continuous-variable polarization states for communication protocols. It is shown that squeezed polarization states provide 33% higher channel capacities than the optimum coherent beam protocol.
When sending a quantum state which originally has nonclassical properties such as various kinds of squeezing and photon antibunching effects according to the protocol for teleportation of continuous variables [S. L. Braunstein and H. J. Kimble, Phys. Rev. Lett. 80, 869 (1998)], we investigate to what extent those nonclassical properties can be preserved in the teleported field. Explicit conditions of the squeezing parameter for the second- and fourth-order quadrature-phase squeezings, the squared amplitude squeezing, and the photon antibunching effect to survive in the teleported field are obtained.