Related papers: Kirkwood-Dirac representations beyond quantum stat…
Statistical functions such as the moment-generating function, characteristic function, cumulant-generating function, and second characteristic function are cornerstone tools in classical statistics and probability theory. They provide a…
The scientific methodology based on two descriptive levels, ontic (reality as it is ) and epistemic (observational), is briefly presented. Following Schr\"odinger, we point to the possible gap between these two descriptions. Our main aim is…
Conditions under which a quantum particle is described using classical quantities are studied. The one-dimensional (1D) and three-dimensional (3D) problems are considered. It is shown that the sum of the contributions from all quantum…
This paper represents one approach to making explicit some of the assumptions and conditions implied in the widespread representation of numbers by composite quantum systems. Any nonempty set and associated operations is a set of natural…
We define the Kirkwood-Dirac quasiprobability representation of quantum mechanics associated with the Fourier transform over second countable locally compact abelian groups. We discuss its link with the Kohn-Nirenberg quantization of the…
The geometric form of standard quantum mechanics is compatible with the two postulates: 1) The laws of physics are invariant under the choice of experimental setup and 2) Every quantum observation or event is intrinsically statistical.…
Recently, a self-contained trajectory-based formulation of non-relativistic quantum mechanics was developed [Ann. Phys. 315, 505 (2005); Chem. Phys. 370, 4 (2010); J. Chem. Phys. 136, 031102 (2012)], that makes no use of wavefunctions or…
A classical state-preparation device cannot generate states in relative superposition. We introduce classical models in which devices that are individually unable to generate states with relative superposition can be stochastically…
A new representation for canonical gravity and supergravity is presented, which combines advantages of Ashtekar's and the Wheeler~DeWitt representation: it has a nice geometric structure and the singular metric problem is absent. A formal…
The nonclassicality of quantum states is a fundamental resource for quantum technologies and quantum information tasks in general. In particular, a pivotal aspect of quantum states lies in their coherence properties, encoded in the…
This is mainly a lecture note taken by myself following Weinberg's book, but also contains some corrections to the abuse of mathematical treatment. This article discusses projective unitary representations of Poincare group on the single…
In a recent work, arXiv:2503.05884, we proposed a unified notion of nonclassicality that applies to arbitrary processes in quantum theory, including individual quantum states, measurements, channels, set of these, etc. This notion is…
The standard presentation of the principles of quantum mechanics is critically reviewed both from the experimental/operational point and with respect to the request of mathematical consistency and logical economy. A simpler and more…
Exploring quantum phenomena beyond predictions of any classical model has fundamental importance to understand the boundary of classical and quantum descriptions of nature. As a typical property that a quantum system behaves distinctively…
We introduce an equivariant version of contextuality with respect to a symmetry group, which comes with natural applications to quantum theory. In the equivariant setting, we construct cohomology classes that can detect contextuality. This…
Quasiprobability representations, such as the Wigner function, play an important role in various research areas. The inevitable appearance of negativity in such representations is often regarded as a signature of nonclassicality, which has…
Using arbitrary symplectic structures and parametrization invariant actions, we develop a formalism, based on Dirac's quantization procedure, that allows us to consider theories with both space-space as well as space-time noncommutativity.…
Basic quantum effects are often illustrated using single particle interferences in two-path interferometers. A wider range of non-classical phenomena can be illustrated using three-path interferometers, but the increased complexity of…
We study a formal extension of the Dirac equation in the framework of a non-commutative two-sheeted space-time. It is shown that this approach naturally extends the classical Dirac theory by doubling the number of fermionic states, which…
I propose a new and direct connection between classical mechanics and quantum mechanics where I derive the quantum mechanical propagator from a variational principle. This variational principle is Hamilton's modified principle generalized…