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Properties of Wigner distribution functions applied to quantum mechanics

A V Gorbachev

Вестник Российского университета дружбы народов. Серия: Математика, информатика, физикаJan 1, 20120 citations

HIGHER-ORDER SQUEEZING AND QUASIPROBABILITY DISTRIBUTION FUNCTIONS OF EVEN AND ODD COHERENT STATES

Xia Yun-Jie, LI HONG-ZHEN, Guo Guang-Can +1 more

The higher-order squeezing and quasiprobability distribution function of even and odd coherent states are studied in this paper. The results show that the properties of higher-order squeezing of the two states exclude each other, and characteristic functions and Wigner functions are all not gaussian. Particularly, Wigner functions can not be perseved positive define. Quasiprobability density (QPD) of the two states are neither "elliptic" nor "crescent", but are two-petal-like shape, which shows that squeezing type can not be represented by the QPD figure of a state.The higher-order squeezing and quasiprobability distribution function of even and odd coherent states are studied in this paper. The results show that the properties of higher-order squeezing of the two states exclude each other, and characteristic functions and Wigner functions are all not gaussian. Particularly, Wigner functions can not be perseved positive define. Quasiprobability density (QPD) of the two states are neither "elliptic" nor "crescent", but are two-petal-like shape, which shows that squeezing type can not be represented by the QPD figure of a state.

Acta Physica SinicaJan 1, 19912 citations

Density Matrices and Wigner Functions of Quasiclassical Quantum Systems

V. V. Dodonov, Vladimir I. Man’ko

Moscow Izdatel NaukaJan 1, 19867 citations

Marginal distributions of quasiprobabilities in quantum optics

Arkadiusz Orłowski, Alfred Wünsche

Marginal properties of arbitrary s-ordered quasiprobability distribution fucntions are investigated. The positivity of marginal distributions for all quasiprobabilities, interpolating between the Wigner function and the Q representation of the density operator (s\ensuremath{\le}0), is proven. We also show that, on the contrary, marginal distributions of the remaining quasiprobabilities, interpolating between the Wigner function and the P representation (s>0), can take on negative values. General formulas for the marginal distributions are given, and their relations to the actual quantum-mechanical probability distributions for position and momentum are established. Our results provide an interesting generalization of some recent results concerning marginal properties of the P representation [G. S. Agarwal, Opt. Commun. 95, 109 (1993)].Marginal properties of arbitrary s-ordered quasiprobability distribution fucntions are investigated. The positivity of marginal distributions for all quasiprobabilities, interpolating between the Wigner function and the Q representation of the density operator (s\ensuremath{\le}0), is proven. We also show that, on the contrary, marginal distributions of the remaining quasiprobabilities, interpolating between the Wigner function and the P representation (s>0), can take on negative values. General formulas for the marginal distributions are given, and their relations to the actual quantum-mechanical probability distributions for position and momentum are established. Our results provide an interesting generalization of some recent results concerning marginal properties of the P representation [G. S. Agarwal, Opt. Commun. 95, 109 (1993)].

Physical Review ADec 1, 199310 citations

A Wigner Quasiprobability Distribution of Work

Federico Cerisola, Franco Mayo, Augusto J. Roncaglia

In this article, we introduce a quasiprobability distribution of work that is based on the Wigner function. This proposal rests on the idea that the work conducted on an isolated system can be coherently measured by coupling the system to a quantum measurement apparatus. In this way, a quasiprobability distribution of work can be defined in terms of the Wigner function of the apparatus. This quasidistribution contains the information of the work statistics and also holds a clear operational definition that can be directly measured in a real experiment. Moreover, it is shown that the presence of quantum coherence in the energy eigenbasis is related with the appearance of features related to non-classicality in the Wigner function such as negativity and interference fringes. On the other hand, from this quasiprobability distribution, it is straightforward to obtain the standard two-point measurement probability distribution of work and also the difference in average energy for initial states with coherences.In this article, we introduce a quasiprobability distribution of work that is based on the Wigner function. This proposal rests on the idea that the work conducted on an isolated system can be coherently measured by coupling the system to a quantum measurement apparatus. In this way, a quasiprobability distribution of work can be defined in terms of the Wigner function of the apparatus. This quasidistribution contains the information of the work statistics and also holds a clear operational definition that can be directly measured in a real experiment. Moreover, it is shown that the presence of quantum coherence in the energy eigenbasis is related with the appearance of features related to non-classicality in the Wigner function such as negativity and interference fringes. On the other hand, from this quasiprobability distribution, it is straightforward to obtain the standard two-point measurement probability distribution of work and also the difference in average energy for initial states with coherences.

arXiv:2303.08755EntropyOct 11, 20235 citations

Wigner Distribution Function in Quantum Tunneling

WORLD SCIENTIFIC eBooksJan 1, 20030 citations

Quantum Resonstruction of Wigner Quasiprobability Distribution Function of High Order TEM01Squeezed States

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