Related papers: Quantum Instruments and Conditioned Observables
A finite set of quantum observables (positive operator valued measures) is called compatible if these observables are marginals of a some observable, called a joint observable of them. For a given set of compatible observables, their joint…
The underlying probabilistic theory for quantum mechanics is non-Kolmogorovian. The order in which physical observables will be important if they are incompatible (non-commuting). In particular, the notion of conditioning needs to be…
Recently a problem concerning the equivalence of joint measurability and coexistence of quantum observables was solved [15]. In this paper we generalize two known joint measurability results from sharp observables to the class of extreme…
"Quantum sensing" describes the use of a quantum system, quantum properties or quantum phenomena to perform a measurement of a physical quantity. Historical examples of quantum sensors include magnetometers based on superconducting quantum…
Measurement is a fundamental notion in the usual approximate quantum mechanics of measured subsystems. Probabilities are predicted for the outcomes of measurements. State vectors evolve unitarily in between measurements and by reduction of…
Both classical and respectively quantum observables can be modeled as somewhat similar examples of random variables. In such a model the associated measurements preserve the values spectrum of an observable but change the corresponding…
Two quantum events, represented by positive operators (effects), are coexistent if they can occur as possible outcomes in a single measurement scheme. Equivalently, the corresponding effects are coexistent if and only if they are contained…
Observables in quantum mechanics are represented by self-adjoint operators on Hilbert space. Such ubiquitous, well-known, and very foundational fact, however, is traditionally subtle to be explained in typical first classes in quantum…
The main formal structures of Generalized Quantum Theory are summarized. Recent progress has sharpened some of the concepts, in particular the notion of an observable, the action of an observable on states (putting more emphasis on the role…
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…
We study joint measurability of quantum observables in open systems governed by a master equation of Lindblad form. We briefly review the historical perspective of open systems and conceptual aspects of quantum measurements, focusing…
An analysis of quantum measurement is presented that relies on an information-theoretic description of quantum entanglement. In a consistent quantum information theory of entanglement, entropies (uncertainties) conditional on measurement…
The study of measurements in quantum mechanics exposes many of the ways in which the quantum world is different. For example, one of the hallmarks of quantum mechanics is that observables may be incompatible, implying among other things…
For sharp quantum observables the following facts hold: (i) if we have a collection of sharp observables and each pair of them is jointly measurable, then they are jointly measurable all together; (ii) if two sharp observables are jointly…
We discuss conditional expectations that can be used as generalizations of the partial trace for quantum systems with an infinite-dimensional Hilbert space of states.
We derive essential elements of quantum mechanics from a parametric structure extending that of traditional mathematical statistics. The basic setting is a set $\mathcal{A}$ of incompatible experiments, and a transformation group $G$ on the…
The geometrical description of Quantum Mechanics is reviewed and proposed as an alternative picture to the standard ones. The basic notions of observables, states, evolution and composition of systems are analised from this perspective, the…
In Quantum Physics, a measurement is represented by a projection on some closed subspace of a Hilbert space. We study algebras of operators that abstract from the algebra of projections on closed subspaces of a Hilbert space. The properties…
In the study of quantum process algebras, researchers have introduced different notions of equivalence between quantum processes like bisimulation or barbed congruence. However, there are intuitively equivalent quantum processes that these…
The problem considered is how to map the concepts of Quantum Theory (QT) to elements of a psychological experiment. The QT concepts are "measurement," "state," and "observable". The elements of a psychological experiment are trial,…