Related papers: Structure, Positivity and Classical Simulability o…
We discuss the (re-)construction of quasiprobability representations from generic measurements, including noisy ones. Based on the measurement under study, quasiprobabilities and the associated concept of nonclassicality are introduced. A…
In this paper we study stochastic dynamics which leaves quantum gravity equilibrium distribution invariant. We start theoretical study of this dynamics (earlier it was only used for Monte-Carlo simulation). Main new results concern the…
More than 15 years ago, a new approach to quantum mechanics was suggested, in which Hermiticity of the Hamiltonian was to be replaced by invariance under a discrete symmetry, the product of parity and time-reversal symmetry, $\mathcal{PT}$.…
We investigate the relationship between two properties of quantum transformations often studied in popular subtheories of quantum theory: covariance of the Wigner representation of the theory and the existence of a transformation…
We develop a comprehensive analysis of the Kirkwood-Dirac distributions in classical optics, revealing their deep connection with optical coherence as fundamental concept in optics. From their very definition, the Kirkwood-Dirac…
Consumption of magic states promotes the stabilizer model of computation to universal quantum computation. Here, we propose three different classical algorithms for simulating such universal quantum circuits, and characterize them by…
Quasi-probability decompositions (QPDs) have proven essential in many quantum algorithms and protocols -- one replaces a ``difficult'' quantum circuit with an ensemble of ``easier'' circuit variants whose weighted outcomes reproduce any…
In this paper, we study quasi-stationary distributions (QSDs) for one-dimensional diffusions killed at 0, when 0 is a regular boundary and $+\infty$ is a natural boundary. More precisely, we not only give a necessary and sufficient…
In quantum experiments the acquisition and representation of basic experimental information is governed by the multinomial probability distribution. There exist unique random variables, whose standard deviation becomes asymptotically…
The theory of quantum states over time extends the density operator formalism into the temporal domain, providing a unified of treatment of timelike and spacelike separated systems in quantum theory. Although recent results have…
Unitarity cannot be perserved order by order in ordinary perturbation theory because the constraint $UU^\dagger=\1$ is nonlinear. However, the corresponding constraint for $K=\ln U$, being $K=-K^\dagger$, is linear so it can be maintained…
We propose an operational quasiprobability function for qudits, enabling a comparison between quantum and hidden-variable theories. We show that the quasiprobability function becomes positive semidefinite if consecutive measurement results…
Coherent solutions of the classical Liouville equation for the rigid rotator are presented as positive phase-space distributions associated with the Lagrangian submanifolds of Hamilton-Jacobi theory. These solutions become Wigner-type…
In the limit of large quantum excitations, the classical and quantum probability distributions for a Schr\"odinger equation can be compared by using the corresponding WKBJ solutions whose rapid oscillations are averaged. This result is…
Comparing probability distributions is a core challenge across the natural, social, and computational sciences. Existing methods, such as Maximum Mean Discrepancy (MMD), struggle in high-dimensional and non-compact domains. Here we…
We provide an in-depth study of the recently introduced notion of completely incompatible observables and its links to the support uncertainty and to the Kirkwood-Dirac nonclassicality of pure quantum states. The latter notion has recently…
By using an exact analytical non-Hermitian formalism involving the full set of resonance (quasinormal) states and complex energy eigenvalues for quantum tunneling decay, we show that unitarity holds at any instant of time for the…
Many approaches to quantum gravity have resorted to diffusion processes to characterize the spectral properties of the resulting quantum spacetimes. We critically discuss these quantum-improved diffusion equations and point out that a…
We construct minimum-uncertainty states and a non-negative quasi probability distribution for quantum systems on a finite-dimensional space. We reexamine the theorem of Massar and Spindel for the uncertainty relationof the two unitary…
We consider the probabilistic description of nonrelativistic, spinless one-particle classical mechanics, and immerse the particle in a deformed noncommutative phase space in which position coordinates do not commute among themselves and…