An extended phase space x – p – X – P is introduced for one-mode systems, where x – p is the position–momentum plane and X – P is the quantum correlations plane. The Wigner functions W ( x , p ) and the Weyl functions ( X , P ) for arbitrary operators are studied in this space. Creation and annihilation operators for Wigner and Weyl functions are introduced and are used to perform displacements and squeezing in the x – p – X – P extended phase space. The formalism can be used for the construction of quantum states with desirable correlation properties.An extended phase space x – p – X – P is introduced for one-mode systems, where x – p is the position–momentum plane and X – P is the quantum correlations plane. The Wigner functions W ( x , p ) and the Weyl functions ( X , P ) for arbitrary operators are studied in this space. Creation and annihilation operators for Wigner and Weyl functions are introduced and are used to perform displacements and squeezing in the x – p – X – P extended phase space. The formalism can be used for the construction of quantum states with desirable correlation properties.

Journal of Physics A Mathematical and GeneralNov 13, 20016 citations

Correlation Functions of One-dimensional Quantum Systems

Akihiko Matsuyama

Feb 26, 19991 citation

Phase-Space Analysis of Time-Correlation Functions

G. S. Agarwal

Using the recently developed phase-space techniques for the treatment of quantum-mechanical problems, we set up a procedure for calculating multitime-correlation functions in terms of the joint distribution functions. The correlation functions are then expressed simply as integrals over the associated phase space. Explicit expressions are given for these joint distribution functions, in terms of Green's functions of the $c$ -number equations of motion for the phase-space equivalent of the density operator. Using these joint distribution functions, an exact regression theorem is rederived, and the connection with the multitime correspondence between classical and quantum stochastic processes is discussed.Using the recently developed phase-space techniques for the treatment of quantum-mechanical problems, we set up a procedure for calculating multitime-correlation functions in terms of the joint distribution functions. The correlation functions are then expressed simply as integrals over the associated phase space. Explicit expressions are given for these joint distribution functions, in terms of Green's functions of the $c$-number equations of motion for the phase-space equivalent of the density operator. Using these joint distribution functions, an exact regression theorem is rederived, and the connection with the multitime correspondence between classical and quantum stochastic processes is discussed.

Physical ReviewJan 5, 196916 citations

On the evaluation of the correlation functions in quantum statistical physics

D. N. Zubarev, Yu. G. Rudoi

Uspekhi Fizicheskih NaukJan 1, 19935 citations

On the evaluation of the correlation functions in quantum statistical physics

D. N. Zubarev, Yu. G. Rudoi

Physics-UspekhiMar 31, 19936 citations

Probing nonclassicality with matrices of phase-space distributions

Martin Bohmann, Elizabeth Agudelo, Jan Sperling

We devise a method to certify nonclassical features via correlations of phase-space distributions by unifying the notions of quasiprobabilities and matrices of correlation functions. Our approach complements and extends recent results that were based on Chebyshev's integral inequality \cite{BA19}. The method developed here correlates arbitrary phase-space functions at arbitrary points in phase space, including multimode scenarios and higher-order correlations. Furthermore, our approach provides necessary and sufficient nonclassicality criteria, applies to phase-space functions beyond s -parametrized ones, and is accessible in experiments. To demonstrate the power of our technique, the quantum characteristics of discrete- and continuous-variable, single- and multimode, as well as pure and mixed states are certified only employing second-order correlations and Husimi functions, which always resemble a classical probability distribution. Moreover, nonlinear generalizations of our approach are studied. Therefore, a versatile and broadly applicable framework is devised to uncover quantum properties in terms of matrices of phase-space distributions.We devise a method to certify nonclassical features via correlations of phase-space distributions by unifying the notions of quasiprobabilities and matrices of correlation functions. Our approach complements and extends recent results that were based on Chebyshev's integral inequality \cite{BA19}. The method developed here correlates arbitrary phase-space functions at arbitrary points in phase space, including multimode scenarios and higher-order correlations. Furthermore, our approach provides necessary and sufficient nonclassicality criteria, applies to phase-space functions beyond s -parametrized ones, and is accessible in experiments. To demonstrate the power of our technique, the quantum characteristics of discrete- and continuous-variable, single- and multimode, as well as pure and mixed states are certified only employing second-order correlations and Husimi functions, which always resemble a classical probability distribution. Moreover, nonlinear generalizations of our approach are studied. Therefore, a versatile and broadly applicable framework is devised to uncover quantum properties in terms of matrices of phase-space distributions.

arXiv:2003.11031QuantumOct 15, 202031 citations

c

-number equations of motion for the phase-space equivalent of the density operator. Using these joint distribution functions, an exact regression theorem is rederived, and the connection with the multitime correspondence between classical and quantum stochastic processes is discussed.