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In a pre-selected Hilbert space of quantum states the unitarity of the evolution is usually guaranteed via a pre-selection of the generator (i.e., of the Hamiltonian operator) in self-adjoint form. In fact, the simultaneous use of both of…
We develop relativistic non-Hermitian quantum theory and its application to neutrino physics in a strong magnetic field. It is well known, that one of the fundamental postulates of quantum theory is the requirement of Hermiticity of…
We demonstrate that quantum instruments can provide a unified operational foundation for quantum theory. Since these instruments directly correspond to laboratory devices, this foundation provides an alternate, more experimentally grounded,…
Thermodynamics is the phenomenological theory of heat and work. Here we analyze to what extent quantum thermodynamic relations are immune to the underlying mathematical formulation of quantum mechanics. As a main result, we show that the…
The approximations of classical mechanics resulting from quantum mechanics are richer than a correspondence of classical dynamical variables with self-adjoint Hilbert space operators. Assertion that classical dynamic variables correspond to…
The rely-guarantee technique allows one to reason compositionally about concurrent programs. To handle interference the technique makes use of rely and guarantee conditions, both of which are binary relations on states. A rely condition is…
In this sequence of papers, noncommutative analysis is used to give a consistent axiomatic approach to a unified conceptual foundation of classical and quantum physics. The present Part I defines the concepts of observables, states and…
A non-commuting measurement transfers, via the apparatus, information encoded in a system's state to the external "observer". Classical measurements determine properties of physical objects. In the quantum realm, the very same notion…
Quantum coherence, the ability of a quantum system to be in a superposition of orthogonal quantum states, is a distinct feature of the quantum mechanics, thus marking a deviation from classical physics. Coherence finds its applications in…
Adjoint functor theorems give necessary and sufficient conditions for a functor to admit an adjoint. In this paper we prove general adjoint functor theorems for functors between $\infty$-categories. One of our main results is an…
It is shown that the formalism of quantum theory naturally incorporates the psychophysical parallelism and thereby interprets itself, if the subjective aspects are taken as equal partners alongside the objective aspects as determinants of…
Assuming the validity of the equivalence principle in the quantum regime, we argue that one of the assumptions of the usual definition of quantum mechanics, namely separation between the ``classical'' detector and the ``quantum'' system,…
During the recent developments of quantum theory it has been clarified that the observable quantities (like energy or position) may be represented by operators (with real spectra) which are manifestly non-Hermitian. The mathematical…
A theory of quantum measurement was introduced some time ago that was based on the notion of the so-called separation status. This separation status had a spatial, local character, so that the theory worked only in special cases.…
Kirkwood-Dirac representations of quantum states are increasingly finding use in many areas within quantum theory. Usually, representations of this sort are only applied to provide a representation of quantum states (as complex functions…
A theorem that is of aid in computing the domain of the adjoint operator is provided. It may serve e.g. as a criterion for selfadjointness of a symmetric operator, for normality of a formally normal operator or for $H$--selfadjointness of…
In this paper, decoherence is studied for quantum systems undergoing adiabatic processes, which are coupled to huge quantum environments. It is shown that decoherence can happen with respect to a preferred basis given by transient…
Here we introduce reflection positive doubles, a general framework for reflection positivity, covering a wide variety of systems in statistical physics and quantum field theory. These systems may be bosonic, fermionic, or parafermionic in…
Quantum theory has the intriguing feature that is inconsistent with noncontextual hidden variable models, for which the outcome of a measurement does not depend on which other compatible measurements are being performed concurrently. While…
Different versions of the notion of a state have been formulated for various so-called quantum structures. In this paper, we investigate the interplay among states on synaptic algebras and on its sub-structures. A synaptic algebra is a…