Related papers: Classicality in discrete Wigner functions
In the realm of fault-tolerant quantum computing, stabilizer operations play a pivotal role, characterized by their remarkable efficiency in classical simulation. This efficiency sets them apart from non-stabilizer operations within the…
The domain of application of quantization methods is traditionally restricted to smooth classical observables. We show that the coherent states or "anti-Wick" quantization enables us to construct fairly reasonable quantum versions of…
Given a choice of an ordered, orthonormal basis for a $D$-dimensional Hilbert space, one can define a discrete version of the Wigner function -- a quasi-probability distribution which represents any quantum state as a real, normalized…
The Hilbert spaces for stable scattering states and particles are determined by the representations of the characterizing Euclidean and Poincar\'e group and given, respectively, by the square integrable functions on the momentum 2-spheres…
We show that qubit stabilizer states can be represented by non-negative quasi-probability distributions associated with a Wigner-Weyl-Moyal formalism where Clifford gates are positive state-independent maps. This is accomplished by…
We present further progress, in the form of analytical results, on the Wigner entropy conjecture set forth in https://link.aps.org/doi/10.1103/PhysRevA.104.042211 and https://iopscience.iop.org/article/10.1088/1751-8121/aa852f/meta. Said…
We investigate the classical aspects of Quantum theory and under which description Quantum theory does appear Classical. Although such descriptions or variables are known as "ontological" or "hidden", they are not hidden at all, but are…
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…
A function of positive type can be defined as a positive functional on a convolution algebra of a locally compact group. In the case where the group is abelian, by Bochner's theorem a function of positive type is, up to normalization, the…
We define a new quantifier of classicality for a quantum state, the Roughness, which is given by the $\mathcal{L}^2 (\R^2)$ distance between Wigner and Husimi functions. We show that the Roughness is bounded and therefore it is a useful…
It is standard to assume that the Wigner distribution of a mixed quantum state consisting of square-integrable functions is a quasi-probability distribution, that is that its integral is one and that the marginal properties are satisfied.…
The recently proposed Wigner function for a particle in an infinite lattice [NJP 14, 103009 (2012)] is extended here to include an internal degree of freedom, as spin. The formalism is developed to account for dynamical processes, with or…
The use of quantum information in technology promises to supersede the so-called classical devices used nowadays. Understanding what features are inherently non-classical is crucial for reaching better-than-classical performance. This…
We propose the assumption of quantum mechanics on a discrete space and time, which implies the modification of mathematical expressions for some postulates of quantum mechanics. In particular we have a Hilbert space where the vectors are…
We introduce a construction that turns a category of pure state spaces and operators into a category of observable algebras and superoperators. For example, it turns the category of finite-dimensional Hilbert spaces into the category of…
Transition from quantum to semiclassical behaviour and loss of quantum coherence for inhomogeneous perturbations generated from a non-vacuum initial state in the early Universe is considered in the Heisenberg and the Schr\"odinger…
In this note, we consider the question of classicality for the theory which is known to be the effective description of two-dimensional black holes - the Morse quantum mechanics. We calculate the Wigner function and the Fisher information…
Wigner functions help visualise quantum states and dynamics while supporting quantitative analysis in quantum information. In the discrete setting, many inequivalent constructions coexist for each Hilbert-space dimension. This fragmentation…
A new non-perturbative approach to quantum theory in curved spacetime and to quantum gravity, based on a generalisation of the Wigner equation, is proposed. Our definition for a Wigner equation differs from what have otherwise been…
We briefly review some results concerning the problem of classical singularities in general relativity, obtained with the help of the theory of differential spaces. In this theory one studies a given space in terms of functional algebras…