Related papers: Quantum Bochner's theorem for phase spaces built o…
The nonnegativity of the density operator of a state is faithfully coded in its Wigner distribution, and this places constraints on the moments of the Wigner distribution. These constraints are presented in a canonically invariant form…
The de Finetti representation theorem for continuous variable quantum system is first developed to approximate an N-partite continuous variable quantum state with a convex combination of independent and identical subsystems, which requires…
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…
It is shown that the approximating functions used to define the Bochner integral can be formed using geometrically nice sets, such as balls, from a differentiation basis. Moreover, every appropriate sum of this form will be within a…
We demonstrate a method which allows the stochastic modelling of quantum systems for which the generalised Fokker-Planck equation in the phase space contains derivatives of higher than second order. This generalises quantum stochastics far…
A discussion of discrete Wigner functions in phase space related to mutually unbiased bases is presented. This approach requires mathematical assumptions which limits it to systems with density matrices defined on complex Hilbert spaces of…
The aim of this paper is to give a simple, geometric proof of Wigner's theorem on the realization of symmetries in quantum mechanics that clarifies its relation to projective geometry. Although several proofs exist already, it seems that…
We propose a gate-based quantum algorithm for the prediction step of Bayesian state estimation based on the Fokker-Planck equation on a discretized position-velocity state space. The probability density is encoded in the amplitudes of a…
It has recently been shown that it is possible to represent the complete quantum state of any system as a phase-space quasi-probability distribution (Wigner function) [Phys Rev Lett 117, 180401]. Such functions take the form of expectation…
Polarization quasiprobability distribution defined in the Stokes space shares many important properties with the Wigner function for the position and momentum. Most notably, they both give correct one-dimensional marginal probability…
Lurie's representability theorem gives necessary and sufficient conditions for a functor to be an almost finitely presented derived geometric stack. We establish several variants of Lurie's theorem, making the hypotheses easier to verify…
We provide a mechanism by which, from a background independent model with no quantum mechanics, quantum theory arises in the same limit in which spatial properties appear. Starting with an arbitrary abstract graph as the microscopic model…
Here the probability density of relativistic particles coordinates, satisfying the formal conditions of the quantum mechanics and the special relativity, is determined (under textbooks view, such density does not exist). It is specified for…
The concept of quantum phase space offers a view on quantum mechanics, which is different from the standard Hilbert space approach, but which more closely resembles the classical phase space. Due to the properties of quantum mechanics there…
Quantum dots with conduction electrons or holes originating from several bands are considered. We assume the particles are confined in a harmonic potential and assume the electrons (or holes) belonging to different bands to be different…
In our bouncer-walker model a quantum is a nonequilibrium steady-state maintained by a permanent throughput of energy. Specifically, we consider a "particle" as a bouncer whose oscillations are phase-locked with those of the energy-momentum…
Schwinger's algebra of selective measurements has a natural interpretation in the formalism of groupoids. Its kinematical foundations, as well as the structure of the algebra of observables of the theory, was presented in two previous…
As shown in previous work, number projection can be carried out analytically for states defined in a quasi-particle scheme when the states are expressed in a coherent state representation. The wave functions of number-projected states are…
A gauge-invariant Wigner quantum mechanical theory is obtained by applying the Weyl-Stratonovich transform to the von Neumann equation for the density matrix. The transform reduces to the Weyl transform in the electrostatic limit, when the…
We show that a quantum state may be represented as the sum of a joint probability and a complex quantum modification term. The joint probability and the modification term can both be observed in successive projective measurements. The…