Challenges
Datasets
Workspaces
Papers
Discussions
Leaderboard
Log inSign up
Challenges
Datasets
Workspaces
Papers
Discussions
Leaderboard
Blog
Job Board
Q3AS

© 2026 Aqora Quantum S.A.S.

TermsPrivacyLegal Notice

Physical Review A

Degree of polarization in quantum optics

Alfredo Luis

Published Jul 15, 2002• 122 citations
Publisher

Abstract

Quantum optics entails polarization properties that cannot be fully described by the classical Stokes parameters. In this work, we characterize the polarization of classical as well as quantum fields by means of a probability distribution on the Poincar\'e sphere. This serves to define the degree of polarization of a field state as the distance between the corresponding polarization distribution and the uniform distribution representing unpolarized light. We apply this definition to relevant quantum field states such as SU(2) coherent, squeezed, number, and phase states.

DOI
10.1103/physreva.66.013806

Related papers

Quantum concepts in optical polarization

Aaron Z. Goldberg, Pablo de la Hoz, Gunnar G. Bjork +4 more

We comprehensively review the quantum theory of the polarization properties of light. In classical optics, these traits are characterized by the Stokes parameters, which can be geometrically interpreted using the Poincaré sphere. Remarkably, these Stokes parameters can also be applied to the quantum world, but then important differences emerge: now, because fluctuations in the number of photons are unavoidable, one is forced to work in the three-dimensional Poincaré space that can be regarded as a set of nested spheres. Additionally, higher-order moments of the Stokes variables might play a substantial role for quantum states, which is not the case for most classical Gaussian states. This brings about important differences between these two worlds that we review in detail. In particular, the classical degree of polarization produces unsatisfactory results in the quantum domain. We compare alternative quantum degrees and put forth that they order various states differently. Finally, intrinsically nonclassical states are explored, and their potential applications in quantum technologies are discussed.

arXiv:2011.03979•Advances in Optics and Photonics•Nov 17, 2020•98 citations

Distance-based degrees of polarization for a quantum field

A. B. Klimov, Luis Lorenzo Sánchez-Soto, E. C. Yustas +2 more

It is well established that unpolarized light is invariant with respect to any SU(2) polarization transformation. This requirement fully characterizes the set of density matrices representing unpolarized states. We introduce the degree of polarization of a quantum state as its distance to the set of unpolarized states. We use two different candidates of distance, namely the Hilbert-Schmidt and the Bures metric, showing that they induce fundamentally different degrees of polarization. We apply these notions to relevant field states and we demonstrate that they avoid some of the problems arising with the classical definition.

arXiv:quant-ph/0504226•Physical Review A•Sep 16, 2005•58 citations

Polarization distribution and degree of polarization for three-dimensional quantum light fields

Alfredo Luis

We introduce a probability distribution for polarization of three-dimensional quantum light fields as a marginal of the quadrature $Q$ function for a three-mode field by removing the variables irrelevant for polarization (total intensity and global phase). The probability distribution turns out to be determined by projection on SU(3) coherent states. We introduce a degree of polarization as the distance between the polarization distribution and the uniform distribution associated with completely unpolarized light. We study the relation between two- and three-dimensional polarization by considering field states with a component in the vacuum state. We apply this formalism to some relevant field states.

Physical Review A•Jun 22, 2005•32 citations

Degree of polarization in quantum optics through the second generalization of intensity

Ravi Shankar Singh, Hari Prakash

The classical definition of degree of polarization (DOP) is expressed in the quantum domain by replacing intensities through quantum mechanical average values of relevant number operators and is viewed as the first generalization of intensity. This definition assigns inaccurately the unpolarized status to some typical optical fields, e.g., amplitude-coherent phase-randomized and hidden-polarized light, which are not truly unpolarized light. The apparent paradoxical trait is circumvented by proposing a new definition of DOP in quantum optics through the second generalization of intensity. The correspondence of a new DOP to the usual DOP in quantum optics is established. It is seen that the two definitions disagree significantly for intense optical fields but coincide for weak light (thermal light) or for optical fields in which occupancy of photons in the orthogonal mode is very feeble. Our proposed definition of DOP, similar to other proposals in literature, reveals an interesting feature that states of polarization of optical quantum fields depend upon the average photons (intensity) present therein.

arXiv:1301.3616•Physical Review A•Feb 7, 2013•7 citations

Quantum phase measurements and non-classical polarization states of light

A. P. Alodjants, Sergei M Arakelyan

In our paper we consider the non-classical behaviour of both the Hermitian (observable) Stokes parameters of light and the phase difference of two modes that describe the quantum polarization states of optical field. To characterize the degree of polarization of light we introduce a new quantity taking into account the quantum properties of different quantum states of two orthogonally polarized modes. The problem of determination of the phase difference in two modes of optical field for the quantum polarization states of light is discussed. To describe in general such a quantum field we introduce two pairs of the phase operators: the phase angles for the Stokes parameters of light in a three-dimensional picture of the Poincaré sphere. We also consider a special type of the eight-port polarization interferometer (polarimeter) for simultaneous homodyne detection of both the Stokes parameters of light and the polarization phase operators and their fluctuations as well. Using an anisotropic (spatioperiodic) Kerr-like nonlinear medium associated with the polarization interferometer we could generate and also observe the polarization-squeezed phase states of light. The fluctuations in the phase difference between two orthogonally polarized modes for these non-classical states are less than the fluctuations for light in coherent state.

Journal of Modern Optics•Mar 1, 1999•44 citations

Optical field-strength polarization of two-mode single-photon states

Jesús Liñares, María C. Nistal, David Barral +1 more

We present a quantum analysis of two-mode single-photon states based on the probability distributions of the optical field strength (or position quadrature) in order to describe their quantum polarization characteristics, where polarization is understood as a significative confinement of the optical field-strength values on determined regions of the two-mode optical field-strength plane. We will show that the mentioned probability distributions along with the values of quantum Stokes parameters allow us to characterize the polarization of a two-mode single-photon state, in an analogous way to the classical case, and to distinguish conceptually between mixture and partially polarized quantum states; in this way, we propose a simple definition of the quantum polarization degree based on the recent concept of distance measure to an unpolarized distribution, which gives rise to a depolarization degree equivalent to an overlapping between the probability distribution of the quantum state and a non-polarized two-mode Gaussian distribution. The work is particularly intended to university physics teachers and graduate students as well as to physicists and specialists concerned with the issue of optical polarization.

European Journal of Physics•Jul 9, 2010•10 citations
Quantum optics entails polarization properties that cannot be fully described by the classical Stokes parameters. In this work, we characterize the polarization of classical as well as quantum fields by means of a probability distribution on the Poincar'e sphere. This serves to define the degree of polarization of a field state as the distance between the corresponding polarization distribution and the uniform distribution representing unpolarized light. We apply this definition to relevant quantum field states such as SU(2) coherent, squeezed, number, and phase states.
We comprehensively review the quantum theory of the polarization properties of light. In classical optics, these traits are characterized by the Stokes parameters, which can be geometrically interpreted using the Poincaré sphere. Remarkably, these Stokes parameters can also be applied to the quantum world, but then important differences emerge: now, because fluctuations in the number of photons are unavoidable, one is forced to work in the three-dimensional Poincaré space that can be regarded as a set of nested spheres. Additionally, higher-order moments of the Stokes variables might play a substantial role for quantum states, which is not the case for most classical Gaussian states. This brings about important differences between these two worlds that we review in detail. In particular, the classical degree of polarization produces unsatisfactory results in the quantum domain. We compare alternative quantum degrees and put forth that they order various states differently. Finally, intrinsically nonclassical states are explored, and their potential applications in quantum technologies are discussed.
It is well established that unpolarized light is invariant with respect to any SU(2) polarization transformation. This requirement fully characterizes the set of density matrices representing unpolarized states. We introduce the degree of polarization of a quantum state as its distance to the set of unpolarized states. We use two different candidates of distance, namely the Hilbert-Schmidt and the Bures metric, showing that they induce fundamentally different degrees of polarization. We apply these notions to relevant field states and we demonstrate that they avoid some of the problems arising with the classical definition.
We introduce a probability distribution for polarization of three-dimensional quantum light fields as a marginal of the quadrature QQQ function for a three-mode field by removing the variables irrelevant for polarization (total intensity and global phase). The probability distribution turns out to be determined by projection on SU(3) coherent states. We introduce a degree of polarization as the distance between the polarization distribution and the uniform distribution associated with completely unpolarized light. We study the relation between two- and three-dimensional polarization by considering field states with a component in the vacuum state. We apply this formalism to some relevant field states.
The classical definition of degree of polarization (DOP) is expressed in the quantum domain by replacing intensities through quantum mechanical average values of relevant number operators and is viewed as the first generalization of intensity. This definition assigns inaccurately the unpolarized status to some typical optical fields, e.g., amplitude-coherent phase-randomized and hidden-polarized light, which are not truly unpolarized light. The apparent paradoxical trait is circumvented by proposing a new definition of DOP in quantum optics through the second generalization of intensity. The correspondence of a new DOP to the usual DOP in quantum optics is established. It is seen that the two definitions disagree significantly for intense optical fields but coincide for weak light (thermal light) or for optical fields in which occupancy of photons in the orthogonal mode is very feeble. Our proposed definition of DOP, similar to other proposals in literature, reveals an interesting feature that states of polarization of optical quantum fields depend upon the average photons (intensity) present therein.
In our paper we consider the non-classical behaviour of both the Hermitian (observable) Stokes parameters of light and the phase difference of two modes that describe the quantum polarization states of optical field. To characterize the degree of polarization of light we introduce a new quantity taking into account the quantum properties of different quantum states of two orthogonally polarized modes. The problem of determination of the phase difference in two modes of optical field for the quantum polarization states of light is discussed. To describe in general such a quantum field we introduce two pairs of the phase operators: the phase angles for the Stokes parameters of light in a three-dimensional picture of the Poincaré sphere. We also consider a special type of the eight-port polarization interferometer (polarimeter) for simultaneous homodyne detection of both the Stokes parameters of light and the polarization phase operators and their fluctuations as well. Using an anisotropic (spatioperiodic) Kerr-like nonlinear medium associated with the polarization interferometer we could generate and also observe the polarization-squeezed phase states of light. The fluctuations in the phase difference between two orthogonally polarized modes for these non-classical states are less than the fluctuations for light in coherent state.
We present a quantum analysis of two-mode single-photon states based on the probability distributions of the optical field strength (or position quadrature) in order to describe their quantum polarization characteristics, where polarization is understood as a significative confinement of the optical field-strength values on determined regions of the two-mode optical field-strength plane. We will show that the mentioned probability distributions along with the values of quantum Stokes parameters allow us to characterize the polarization of a two-mode single-photon state, in an analogous way to the classical case, and to distinguish conceptually between mixture and partially polarized quantum states; in this way, we propose a simple definition of the quantum polarization degree based on the recent concept of distance measure to an unpolarized distribution, which gives rise to a depolarization degree equivalent to an overlapping between the probability distribution of the quantum state and a non-polarized two-mode Gaussian distribution. The work is particularly intended to university physics teachers and graduate students as well as to physicists and specialists concerned with the issue of optical polarization.