Related papers: A Theory of Quantum Instruments
We show that quantum measures and integrals appear naturally in any $L_2$-Hilbert space $H$. We begin by defining a decoherence operator $D(A,B)$ and it's associated $q$-measure operator $\mu (A)=D(A,A)$ on $H$. We show that these operators…
It is proposed a possible new approach of quantum measurements (QMS), disconnected of the traditional interpretation of uncertainty relations and independent of any appeal to the strange idea of collapse (reduction) of wave functions. The…
This article begins with a review of quantum measure spaces. Quantum forms and indefinite inner-product spaces are then discussed. The main part of the paper introduces a quantum integral and derives some of its properties. The quantum…
We introduce a family of operations in quantum mechanics that one can regard as "universal quantum measurements" (UQMs). These measurements are applicable to all finite-dimensional quantum systems and entail the specification of only a…
If $H_1$ and $H_2$ are finite-dimensional Hilbert spaces, a channel from $H_1$ to $H_2$ is a completely positive, linear map $\mathcal{I}$ that takes the set of states $\mathcal{S}(H_1)$ for $H_1$ to the set of states $\mathcal{S}(H_2)$ for…
The purpose of this paper is to show that the mathematics of quantum mechanics (QM) is the mathematics of set partitions (which specify indefiniteness and definiteness) linearized to vector spaces, particularly in Hilbert spaces. That is,…
Studying sequential measurements is of the utmost importance to both the foundational aspects of quantum theory and the practical implementations of quantum technologies, with both of these applications being abstractly described by the…
A new, realist interpretation of the quantum measurement processes is given. In this scenario a quantum measurement is a non-equilibrium phase transition in a ``resonant cavity'' formed by the entire physical universe including all its…
According to the Kolmogorovian Censorship Hypothesis, everything that quantum theory says about the world in the language of the quantum mechanical Hilbert space formalism is actually about relationships between ordinary relative…
We show how quantum mechanics can be understood as a space-time theory provided that its spatial continuum is modelled by a variable real number (qrumber) continuum. Such a continuum can be constructed using only standard Hilbert space…
Measurement models (MMs) stand at the highest structural level of quantum measurement theory. MMs can be employed to construct instruments which stand at the next level. An instrument is thought of as an apparatus that is used to measure…
In quantum physics the term `contextual' can be used in more than one way. One usage, here called `Bell contextual' since the idea goes back to Bell, is that if $A$, $B$ and $C$ are three quantum observables, with $A$ compatible (i.e.,…
In the absence of a satisfactory interpretation of quantum theory, physical law lacks physical basis. This paper reviews the orthodox, or Dirac-von Neumann interpretation, and makes explicit that Hilbert space describes propositions about…
We consider symmetry as a foundational concept in quantum mechanics and rewrite quantum mechanics and measurement axioms in this description. We argue that issues related to measurements and physical reality of states can be better…
A new approach to the problem of measurement in quantum mechanics is proposed. In this approach, the process of measurement is described in the Heisenberg picture and divided into two stages. The first stage is to transduce the measured…
In analogy with conventional quantum mechanics, non-commutative quantum mechanics is formulated as a quantum system on the Hilbert space of Hilbert-Schmidt operators acting on non-commutative configuration space. It is argued that the…
Quantum mechanics started out as a theory to describe the smallest scales of energy in Nature. After a hundred years of development it is now routinely employed to describe, among others, quantum computers with thousands of qubits. This…
By quantum calibration we name an experimental procedure apt to completely characterize an unknown measurement apparatus by comparing it with other calibrated apparatuses. Here we show how to achieve the calibration of an arbitrary…
We present a general formalism for giving a measure space paired with a separable Hilbert space a quantum version based on normalized positive operator-valued measure. The latter are built from families of density operators labelled by…
In the quantum Bayesian (or QBist) conception of quantum theory, "quantum measurement" is understood not as a comparison of something pre-existent with a standard, but instead indicative of the creation of something new in the universe:…