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This work discusses simple examples how quantum systems are obtained as subsystems of classical statistical systems. For a single qubit with arbitrary Hamiltonian and for the quantum particle in a harmonic potential we provide explicitly…
Given two orthonormal bases in a d-dimensional Hilbert space, one associates to each state its Kirkwood-Dirac (KD) quasi-probability distribution. KD-nonclassical states - for which the KD-distribution takes on negative and/or nonreal…
A number of recent studies have proposed that linear representations are appropriate for solving nonlinear dynamical systems with quantum computers, which fundamentally act linearly on a wave function in a Hilbert space. Linear…
We describe a cohomological framework for measurement based quantum computation, in which symmetry plays a central role. Therein, the essential information about the computational output is contained in topological invariants, namely…
In Part I of this series we presented the general ideas of applying group-algebraic methods for describing quantum systems. The treatment was there very "ascetic" in that only the structure of a locally compact topological group was used.…
We describe new constructions of the infinite-dimensional representations of $U(\mathfrak{g})$ and $U_q(\mathfrak{g})$ for $\mathfrak{g}$ being $\mathfrak{gl}(N)$ and $\mathfrak{sl}(N)$. The application of these constructions to the quantum…
We prove a far-reaching generalization of Rickman's Picard theorem for a surprisingly large class of mappings, based on the recently developed theory of quasiregular values. Our results are new even in the planar case.
We explain why, in a configuration space that is multiply connected, i.e., whose fundamental group is nontrivial, there are several quantum theories, corresponding to different choices of topological factors. We do this in the context of…
Recently, it has been argued that quantum mechanics is a complete theory, and that different quantum states do necessarily correspond to different elements of reality, under the assumptions that quantum mechanics is correct and that…
Recent works have shown that defining a behavioural equivalence that matches the observational properties of a quantum-capable, concurrent, non-deterministic system is a surprisingly difficult task. We explore coalgebras over distributions…
Quasisymmetric functions have recently been used in time series analysis as polynomial features that are invariant under, so-called, dynamic time warping. We extend this notion to data indexed by two parameters and thus provide warping…
We propose a method for directly measuring the quantum mechanical pseudo-distribution of observable properties via its characteristic function. Vandermonde matrices of the eigenvalues play a central role in the theory. This proposal…
Classical random walk formalism shows a significant role across a wide range of applications. As its quantum counterpart, the quantum walk is proposed as an important theoretical model for quantum computing. By exploiting the quantum…
Continuing a previous analysis originally motivated by physics, we consider representable states on quasi-local quasi *-algebras, starting with examining the possibility for a {\em compatible} family of {\em local} states to give rise to a…
Treating neural network inputs and outputs as random variables, we characterize the structure of neural networks that can be used to model data that are invariant or equivariant under the action of a compact group. Much recent research has…
We present a framework to treat quantum networks and all possible transformations thereof, including as special cases all possible manipulations of quantum states, measurements, and channels, such as, e.g., cloning, discrimination,…
Presented is a novel methodology for determining representational structure, which builds upon the existing Spotlight Resonance method. This new tool is used to gain insight into how discrete representations can emerge and organise in…
This paper proposes an interpretation of quantum mechanics, relying on the time-symmetric stochastic dynamics of quantum particles and on non-classical probability theory. Our main purpose is to demonstrate that the wave function and its…
Quantum bits can be isolated to perform useful information-theoretic tasks, even though physical systems are fundamentally described by very high-dimensional operator algebras. This is because qubits can be consistently embedded into…
We present a new measure of non-Markovianity based on the property of nonincreasing quantum coherence via Kirkwood-Dirac (KD) quasiprobability under incoherent completely positive trace-preserving maps. Quantum coherence via the KD…