Related papers: Sequential Quantum Measurements and the Instrument…
The observables associated with a quantum system $S$ form a non-commutative algebra ${\mathcal A}_S$. It is assumed that a density matrix $\rho$ can be determined from the expectation values of observables. But $\mathcal A_S$ admits inner…
Recent advancement in fabrication technologies enable the construction of nano-objects with rather rich internal structures such as double or triple quantum dots, which can then be regarded as artificial molecules. The main new ingredient…
Quantum instruments represent the most general type of quantum measurement, as they incorporate processes with both classical and quantum outputs. In many scenarios, it may be desirable to have some "on-demand" device that is capable of…
We present a robust method for quantum process tomography, which yields a set of Lindblad operators that optimally fit the measured density operators at a sequence of time points. The benefits of this method are illustrated using a set of…
In $d$-dimensional de Sitter spacetime, consistency of the perturbative expansion necessitates imposing all second-order gravitational constraints associated with the $SO(1,d)$ isometry group, rather than restricting to the $\R\times…
We study the time evolution of a quantum system without classical counterpart, undergoing a process of entropy increase due to the environment influence. We show that if the environment-induced decoherence is interpreted in terms of…
Quantum Markov Semigroups (QMSs) originally arose in the study of the evolutions of irreversible open quantum systems. Mathematically, they are a generalization of classical Markov semigroups where the underlying function space is replaced…
We adopt a continuous weak measurement tomography protocol to explore the signatures of chaos in the quantum system(s). We generate the measurement record as a series of expectation values of an observable evolving under the desired…
The space of positive operator-valued measures on the Borel sets of a compact (or even locally compact) Hausdorff space with values in the algebra of linear operators acting on a d-dimensional Hilbert space is studied from the perspectives…
In this article, we study a commutative Banach algebra structure on the space $L^1(\mathbb{R}^{2n})\oplus \mathcal{T}^1$, where the $\mathcal{T}^1$ denotes the trace class operators on $L^2(\mathbb{R}^{n})$. The product of this space is…
Small ions are part of the atmospheric aerosol spectrum, and study of ion-aerosol interactions is fundamental in atmospheric physics. Air ion physics and instrumentation are reviewed, including the historical context. A miniaturised Gerdien…
One of the celebrated results of Loop Quantum Gravity (LQG) is the discreteness of the spectrum of geometrical operators such as length, area and volume operators. This is an indication that Planck scale geometry in LQG is discontinuous…
One of the main postulates of quantum mechanics is that measurements destroy quantum coherence (wave function collapse). Recently it was discovered that in a many-body system dilute local measurements still preserve some coherence across…
In this article, part of the author's thesis, we propose a definition for measured quantum groupoid. The aim is the construction of objects with duality including both quantum groups and groupoids. We base ourselves on J. Kustermans and S.…
We discuss symmetric quantum measurements and the associated covariant observables modelled, respectively, as instruments and positive-operator-valued measures. The emphasis of this work are the optimality properties of the measurements,…
The measurement problem in quantum mechanics originates in the inability of the Schr\"odinger equation to predict definite outcomes of measurements. This is due to the lack of objectivity of the eigenstates of the measuring apparatus. Such…
We study the algebra of observables in a time band on the boundary of anti-de Sitter space in a theory of quantum gravity. Strictly speaking this algebra does not have a commutant because products of operators within the time band give rise…
We construct a sheaf-theoretic representation of quantum observables algebras over a base category equipped with a Grothendieck topology, consisting of epimorphic families of commutative observables algebras, playing the role of local…
The Branched Hilbert Subspace Interpretation (BHSI) addresses the quantum measurement problem by preserving unitary quantum evolution within a single world. Its central concept is the Island of Coherence (IOC), an operationally isolated,…
An enlarged group G of nonlinear transformations, modeled on the general linear group GL(2,R), leads to a beautiful, apparently unremarked symmetry between the wave function's phase and the logarithm of its amplitude. Equations Doebner and…