Related papers: A substructural logic for quantum measurements
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 subclass of dynamical semigroups induced by the interaction of a quantum system with an environment is introduced. Such semigroups lead to the selection of a stable subalgebra of effective observables. The structure of this subalgebra is…
The best mathematical arguments against a realistic interpretation of quantum mechanics - that gives definite but partially unknown values to all observables - are analysed and shown to be based on reasoning that is not compelling. This…
We consider the standard quantum logic ${\mathcal L}(H)$ associated to a complex Hilbert space $H$, i.e. the lattice of closed subspaces of $H$ together with the orthogonal complementation. The orthogonality and compatibility relations are…
Given a preferred orthonormal basis $B$ in the Hilbert space of a quantum system we define a measure of the coherence generating power of a unitary operation with respect to $B$. This measure is the average coherence generated by the…
Quantum measurement is a physical process. What physical resources and constraints does quantum mechanics require for measurement to produce the classical world we observe? Treating measurement as a fully unitary quantum process, our goal…
For theoretical approach of quantum measurements it is proposed a set of reconsidered conjectures. The proposed approach implies linear functional transformations for probability density and current but preserves the expressions for…
We reconsider the description for property transitions due to perfect measurements, viewing them as a special case of general transitions that are due to an externally imposed change. We propose a corresponding syntax involving operational…
We present a new and feasible test proving quantum contextuality in four-dimensional Hiltbert space. In our scheme, a contradiction between quantum mechanics and noncontextual hidden variables is revealed through the measurement statistics…
This paper investigates quantum logic from the perspective of categorical logic, and starts from minimal assumptions, namely the existence of involutions/daggers and kernels. The resulting structures turn out to (1) encompass many examples…
We introduce and investigate a weighted propositional configuration logic over commutative semirings. Our logic is intended to serve as a specification language for software architectures with quantitative features. We prove an efficient…
Quantum descriptions of many complex systems are formulated most naturally in bases of states that are not mutually orthogonal. We introduce a general and powerful yet simple approach that facilitates solving such models exactly by…
It is shown that Quantum Mechanics is ambiguous when predicting relative frequencies for an entangled system if the measurements of both subsystems are performed in spatially separated events. This ambiguity gives way to unphysical…
Since the pioneering work of Birkhoff and von Neumann, quantum logic has been interpreted as the logic of (closed) subspaces of a Hilbert space. There is a progression from the usual Boolean logic of subsets to the "quantum logic" of…
The measurement process for hidden-configuration formulations of quantum mechanics is analysed. It is shown how a satisfactory description of quantum measurement can be given in this framework. The unified treatment of hidden-configuration…
Units of measure with prefixes and conversion rules are given a formal semantic model in terms of categorial group theory. Basic structures and both natural and contingent semantic operations are defined. Conversion rules are represented as…
A quantum measurement is logically reversible if the premeasurement density operator of the measured system can be calculated from the postmeasurement density operator and from the outcome of the measurement. This paper analyzes why many…
The quantum theory of conductivity of semiconductor objects, to which the quantum wells, wires and dots concern, is constructed. Average values of current and charge densities, induced by a weak electromagnetic field, are calculated. It is…
We introduce a quantitative relational Hoare logic for quantum programs. Assertions of the logic range over a new infinitary extension of positive semidefinite operators. We prove that our logic is sound, and complete for bounded…
It is shown how to endow a hierarchy of sets of binary patterns with the structure of an abstract,normed C*-algebra. In the course we also recover an intermediate connection with the words of a Dyck language and Tempereley-Lieb algebras for…