Related papers: Dual Quantum Instruments and Sub-observables
This work discusses quantum states defined in a finite-dimensional Hilbert space. In particular, after the presentation of some of them and their basic properties the work concentrates on the group of the quantum optical models that can be…
We approach wave particle duality, the role of the observer and implications on Retrocausality, by starting with the results of a well verified quantum experiment. We analyze how some current theoretical approaches interpret these results.…
In this paper, subnormal operators, not necessarily bounded, are discussed as generalized observables. In order to describe not only the information about the probability distribution of the output data of their measurement but also a…
We introduce $*$-structures on braided groups and braided matrices. Using this, we show that the quantum double $D(U_q(su_2))$ can be viewed as the quantum algebra of observables of a quantum particle moving on a hyperboloid in q-Minkowski…
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.…
Measuring comodules are defined and shown to provide a useful generalization of the set of maps between modules with a broad range of applications. Three applications are described. Connections on bundles are described in terms of measuring…
The application of the notion of `observable' from gauge theory to diffeomorphism-invariant theories -- most relevantly to general relativity -- has led to numerous conceptual and technical issues when interpreting classical theories with…
We discuss the uniqueness of quantum states compatible with given results for measuring a set of observables. For a given pure state, we consider two different types of uniqueness: (1) no other pure state is compatible with the same…
We consider pairs of quantum observables (POVMs) and analyze the relation between the notions of non-disturbance, joint measurability and commutativity. We specify conditions under which these properties coincide or differ---depending for…
The fact that there are quantum observables without a simultaneous measurement is one of the fundamental characteristics of quantum mechanics. In this work we expand the concept of joint measurability to all kinds of possible measurement…
The use of qubits as sensitive magnetometers has been studied theoretically and recent demonstrated experimentally. In this paper we propose a generalisation of this concept, where a scanning two-state quantum system is used to probe the…
Following earlier applications of weak measurement to new cases (Part I), we proceed to explore its temporal peculiarities. We analyze an idealized experiment in which weak which-path measurements do not prevent consecutive weak…
Abelian duality is realized naturally by combining differential cohomology and locally covariant quantum field theory. This leads to a C$^*$-algebra of observables, which encompasses the simultaneous discretization of both magnetic and…
We deepen the theory of quasiorthogonal and approximately quasiorthogonal operator algebras through an analysis of the commutative algebra case. We give a new approach to calculate the measure of orthogonality between two such subalgebras…
In the Contextuality-by-Default theory random variables representing measurement outcomes are labeled contextually, i.e., not only by what they measure but also under what conditions (in what contexts) the measurements are made, including…
Under the excitation of strings, the wooden structure of string instruments is generally assumed to undergo linear vibrations. As an alternative to the direct measurement of the distortion rate at several vibration levels and frequencies,…
The kinematical foundations of Schwinger's algebra of selective measurements were discussed in a previous paper (arXiv:1905.12274) and, as a consequence of this, a new picture of quantum mechanics based on groupoids was proposed. In this…
To elucidate ideal measurements, one must explain how individual events emerge from quantum theory which deals with statistical ensembles, and how different may end up with different final states. This so-called "measurement problem" is…
We discuss various dualities, relating integrable systems and show that these dualities are explained in the framework of Hamiltonian and Poisson reductions. The dualities we study shed some light on the known integrable systems as well as…
Most of the fundamental characteristics of quantum mechanics, such as non-locality and contextuality, are manifest in discrete, finite-dimensional systems. However, many quantum information tasks that exploit these properties cannot be…