Related papers: Uniform approximation for the overlap caustic of a…
A quasi-Gaussian quantum superposition of Ho\v{r}ava-Lifshitz (HL) stationary states is built in order to describe the transition of the quantum cosmological problem to the related classical dynamics. The obtained HL phase-space superposed…
We have studied statistical properties of the values of the Wigner function W(x) of 1D quantum maps on compact 2D phase space of finite area V. For this purpose we have defined a Wigner function probability distribution P(w) = (1/V) int…
In this article we introduce a quasiprobability distribution of work that is based on the Wigner function. This construction rests on the idea that the work done on an isolated system can be coherently measured by coupling the system to a…
Much of the discussion of decoherence has been in terms of a particle moving in one dimension that is placed in an initial superposition state (a Schr\"{o}dinger "cat" state) corresponding to two widely separated wave packets. Decoherence…
A rigorous microscopic theory for the description of quantum-transport phenomena in systems with open boundaries is proposed. We shall show that the application of the conventional Wigner-function formalism to this problem leads to…
We review the problem of state reconstruction in classical and in quantum physics, which is rarely considered at the textbook level. We review a method for retrieving a classical state in phase space, similar to that used in medical imaging…
Using the remarkable mathematical construct of Eugene Wigner to visualize quantum trajectories in phase space, quantum processes can be described in terms of a quasi-probability distribution analogous to the phase space probability…
Quantum non-Gaussian states are crucial for the fundamental understanding of non-linear bosonic systems and simultaneously advanced applications in quantum technologies. In many bosonic experiments the important quantum non-Gaussian feature…
The integral of the Wigner function of a quantum mechanical system over a region or its boundary in the classical phase plane, is called a quasiprobability integral. Unlike a true probability integral, its value may lie outside the interval…
The set of mod $n$ functions associated with primitive roots of unity and discrete Fourier transform is introduced. These functions naturally appear in description of superposition of coherent states related with regular polygon, which we…
For general quantum systems the semiclassical behaviour of eigenfunctions in relation to the ergodic properties of the underlying classical system is quite difficult to understand. The Wignerfunctions of eigenstates converge weakly to…
We study numerically the coordinate wave functions and the Wigner functions of the coherent phase states (CPS), paying the main attention to their differences from the standard (Klauder--Glauber--Sudarshan) coherent states, especially in…
The orthogonality of cat and displaced cat states, underlying Heisenberg limited measurement in quantum metrology, is studied in the limit of large number of states. The asymptotic expression for the corresponding state overlap function,…
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…
A standard method to obtain information on a quantum state is to measure marginal distributions along many different axes in phase space, which forms a basis of quantum state tomography. We theoretically propose and experimentally…
We study Fourier theory on quantum Euclidean space. A modified version of the general definition of the Fourier transform on a quantum space is used and its inverse is constructed. The Fourier transforms can be defined by their Bochner's…
The Lindblad equation governs general markovian evolution of the density operator in an open quantum system. An expression for the rate of change of the Wigner function as a sum of integrals is one of the forms of the Weyl representation…
We express the condition for a phase space Gaussian to be the Wigner distribution of a mixed quantum state in terms of the symplectic capacity of the associated Wigner ellipsoid. Our results are motivated by Hardy's formulation of the…
We establish an exact noise-model-derived characterization of quantum error correction under diagonal local phase noise. Under uniform locality, the maximal logical dimension under t-local phase errors equals Aq(n,2t+1), the classical q-ary…
Over decades, the time evolution of Wigner functions along classical Hamiltonian flows has been used for approximating key signatures of molecular quantum systems. Such approximations are for example the Wigner phase space method, the…