Higher (2nd)-order Wigner distribution function in quantum phase space for entangled bi-modal coherent states, a representative of higher (2nd)-order optical-polarization, is introduced by generalizing kernel (transiting) operator in Cahill-Glauber C(s)-correspondence rule. The nature is analyzed which reveals the occurrence of oscillating three peaks: 'two' for individual bi-modes and third for interference between modes. Also, the graphics of 2nd-order polarization-Wigner distribution function, incisively, demonstrates that it is of non-Gaussian nature attaining non-negative values in quantum phase space.
We derive quantum polarization distributions on the Poincar\'e sphere for two-mode fields as suitable marginals of the standard
s-ordered quadrature distributions that include the Wigner function. We compare them with previously introduced distributions directly defined on the sphere from first principles. We apply this approach to some relevant field states such as coherent and number states.
Various phase-space distributions, from the celebrated Wigner function, to the Husimi
Q function and the Glauber–Sudarshan
P distribution, have played an interesting and important role in the phase-space formulation of quantum mechanics in general, and quantum optics in particular. A unified approach to all these distributions based on the notion of the
s -ordered phase-space distribution was introduced by Cahill and Glauber. With the intention of illuminating the physical meaning of the parameter
s , we interpret the
s -ordered phase-space distribution as the Wigner function of a state under the Gaussian noise channel, and thus reveal an intrinsic connection between the
s -ordered phase-space distribution and the Gaussian noise channel, which yields a physical insight into the
s -ordered phase-space distribution. In this connection, the parameter
−s/2 (rather than the original
s ) acquires the role of the noise occurring in the Gaussian noise channel. An alternative representation of the Gaussian noise channel as the scaling-measurement preparation in a coherent states is illuminated. Furthermore, by exploiting the freedom in the parameter
s , we introduce a computable and experimentally testable quantifier for optical nonclassicality, reveal its basic properties, and illustrate it by typical examples. A simple and convenient criterion for optical nonclassicality in terms of the
s -ordered phase-space distribution is derived.
The probability distribution for finding a quantum state of the light field with a particular phase can be described by a number of theoretical methods. One of the most frequently used in quantum optics is the Pegg–Barnett phase distribution which identifies the phase distribution as the (necessarily positive) modulus square of the overlap of the quantum state with the relevant phase state. Other phase distributions have been proposed which employ the phase-sensitivity of various quantum quasi-probabilities such as the Wigner function. In this paper we discuss the connections between these approaches and illustrate their similarities and important differences for a number of pertinent quantum states of light. For some of these states, quantum interference can generate significant regions of phase space for which the Wigner quasi-probability is negative, and as we show, this may render the quasi-probability phase distribution negative. We discuss the general significance of this phenomenon.
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.