Related papers: History operators in quantum mechanics
Classical mechanics and standard Copenhagen quantum mechanics respect subspace implications. For example, if a particle is confined in a particular region $R$ of space, then in these theories we can deduce that it is confined in regions…
The study of mathematical connections between operator-theoretic formulations of classical dynamics and quantum mechanics began at least as early as the 1930s in work of Koopman and von Neumann and was developed in later decades by many…
We formalize the correspondence between quantum states and quantum operations isometrically, and harness its consequences. This correspondence was already implicit in the various proofs of the operator sum representation of Completely…
We propose a time-of-arrival operator in quantum mechanics by conditioning on a quantum clock. This allows us to bypass some of the problems of previous proposals, and to obtain a Hermitian time of arrival operator whose probability…
We celebrate this year hundred years of quantum mechanics but there is still no consensus regarding its interpretation and limitations. In this article we advocate the statistical contextual interpretation which is free of paradoxes. State…
We introduce quantum history states and their mathematical framework, thereby reinterpreting and extending the consistent histories approach to quantum theory. Through thought experiments, we demonstrate that our formalism allows us to…
A measuring apparatus is described by quantum mechanics while it interacts with the quantum system under observation, and then it must be given a classical description so that the result of the measurement appears as objective reality.…
Without addressing the measurement problem (i.e. what causes the wave function to ``collapse'', or to ``branch'', or a history to become realized, or a property to actualize), I discuss the problem of the timing of the quantum measurement:…
We demonstrate that the time operator that measures the time of arrival of a quantum particle into chosen state can be defined as a self-adjoint quantum-mechanical operator using periodic boundary conditions on applied to wavefuncions in…
I review the decoherent (or consistent) histories approach to quantum mechanics, due to Griffiths, to Gell-Mann and Hartle, and to Omnes. This is an approach to standard quantum theory specifically designed to apply to genuinely closed…
A ring resonator involves a scattering process where a part of the output is fed again into the input. The same formal structure is encountered in the problem of time travel in a neighborhood of a closed timelike curve (CTC). We know how to…
We generalize classical statistical mechanics to describe the kinematics and the dynamics of systems whose variables are constrained by a single quantum postulate (discreteness of the spectrum of values of at least one variable of the…
We attempt to contribute some novel points of view to the "foundations of quantum mechanics", using mathematical tools from "quantum probability theory" (such as the theory of operator algebras). We first introduce an abstract algebraic…
The fundamental dynamics of quantum particles is neutral with respect to the arrow of time. And yet, our experiments are not: we observe quantum systems evolving from the past to the future, but not the other way round. A fundamental…
Quantum measurement and quantum operation theory is developed here by taking the relational properties among quantum systems, instead of the independent properties of a quantum system, as the most fundamental elements. By studying how the…
By building a general dynamical model for quantum measurement process,it is shown that the factorization of reduced evolution operator sufficiently results in the quantum mechanical realization of the wave packet collapse and the state…
In operational quantum mechanics two measurements are called operationally equivalent if they yield the same distribution of outcomes in every quantum state and hence are represented by the same operator. In this paper, I will show that the…
The general formalism of quantum mechanics for the description of statistical experiments is briefly reviewed, introducing in particular position and momentum observables as POVM characterized by their covariance properties with respect to…
This paper is generally concerned with understanding how the uncertainty principle arises in formulations of quantum mechanics, such as the decoherent histories approach, whose central goal is the assignment of probabilities to histories.…
Feynman's sum-over-histories formulation of quantum mechanics is reviewed as an independent statement of quantum theory in spacetime form. It is different from the usual Schr\"odinger-Heisenberg formulation that utilizes states on spacelike…