Related papers: Cylindrical Wigner measures
Quantum mechanics has been formulated in phase space, with the Wigner function as the representative of the quantum density operator, and classical mechanics has been formulated in Hilbert space, with the Groenewold operator as the…
Since the very early days of quantum theory there have been numerous attempts to interpret quantum mechanics as a statistical theory. This is equivalent to describing quantum states and ensembles together with their dynamics entirely in…
We show that quantum circuits where the initial state and all the following quantum operations can be represented by positive Wigner functions can be classically efficiently simulated. This is true both for continuous-variable as well as…
We prove a theorem, using the density functional approach and relying on a classical result by Lieb and Simon on Thomas-Fermi model, showing that in the thermodynamic limit bulk matter is at most semiclassical and coherence preserving. The…
The Wigner function of a finite-dimensional system can be constructed via dual pairing of a density matrix with the Stratonovich-Weyl kernel. Following Kenfack and $\dot{\text{Z}}$yczkowski, we consider the indicator of nonclassicality of a…
We introduce a quantum phase space representation for the orientation state of extended quantum objects, using the Euler angles and their conjugate momenta as phase space coordinates. It exhibits the same properties as the standard Wigner…
Matrix configurations coming from matrix models comprise many important aspects of modern physics. They represent special quantum spaces and are thus strongly related to noncommutative geometry. In order to establish a semiclassical limit…
The convenience of coherent state representation is discussed from the viewpoint of what is in a broad sense called the measurement problem in quantum mechanics. Standard quantum theory in coherent state representation is intrinsically…
The quantum nature of the state of a bosonic quantum field manifests itself in its entanglement, coherence, or optical nonclassicality which are each known to be resources for quantum computing or metrology. We provide quantitative and…
In a numerical study, we investigate the steady-state generation of nonclassical states of light from a coherently driven two-level atom in a one-dimensional waveguide. Specifically, we look for states with a negative Wigner function, since…
Just as a coherent state may be considered as a quantum point, its restriction to a factor space of the full Hilbert space can be interpreted as a quantum plane. The overlap of such a factor coherent state with a full pure state is akin to…
Parallel to the quantization of the complex plane, using the canonical coherent states of a right quaternionic Hilbert space, quaternion field of quaternionic quantum mechanics is quantized. Associated upper symbols, lower symbols and…
We show that classicality emerges during quantum phase transitions due to parametric interactions without coupling to environments. The Wigner functions are explicitly calculated for the Gaussian vacuum, number, and thermal states of a free…
We demonstrate the possibility of controlling the border between the quantum and the classical world by performing nonselective measurements on quantum systems. We consider a quantum harmonic oscillator initially prepared in a Schroedinger…
We construct normalizable, semi-classical states for the previously proposed model of quantum gravity which is formulated as a spectral triple over holonomy loops. The semi-classical limit of the spectral triple gives the Dirac Hamiltonian…
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 investigate within the formalism of Symplectic Quantum Mechanics a two-dimensional non-relativistic strong interacting system that represents the bound heavy quark-antiquark state, where it was considered a linear potential in the…
We present a treatment of many-body Fermionic systems that facilitates an expression of the well-known quantities in a series expansion of the Planck's constant. The ensuing semiclassical result contains to a leading order of the response…
The manner in which unpredictable chaotic dynamics manifests itself in quantum mechanics is a key question in the field of quantum chaos. Indeed, very distinct quantum features can appear due to underlying classical nonlinear dynamics. Here…
We prove that Wigner functions contain a symplectic connection. The latter covariantises the symplectic exterior derivative on phase space. We analyse the role played by this connection and introduce the notion of local symplectic…