Related papers: A Theory of Quantum Instruments
This article considers quantum systems described by a finite-dimensional complex Hilbert space $H$. We first define the concept of a finite observable on $H$. We then discuss ways of combining observables in terms of convex combinations,…
In this paper, we present a general theory of finite quantum measurements, for which we assume that the state space of the measured system is a finite dimensional Hilbert space and that the possible outcomes of a measurement is a finite set…
Quantum instruments are mathematical devices introduced to describe the conditional state change during a quantum process. They are completely positive map valued measures on measurable spaces. We may also view them as non-commutative…
Observables and instruments have played significant roles in recent studies on the foundations of quantum mechanics. Sequential products of effects and conditioned observables have also been introduced. After an introduction in Section~1,…
This article points out that observables and instruments can be combined in many ways that have natural and physical interpretations. We shall mainly concentrate on the mathematical properties of these combinations. Section~1 reviews the…
We demonstrate that quantum instruments can provide a unified operational foundation for quantum theory. Since these instruments directly correspond to laboratory devices, this foundation provides an alternate, more experimentally grounded,…
General quantum measurements are represented by instruments. In this paper the mathematical formalization is given of the idea that an instrument is a channel which accepts a quantum state as input and produces a probability and an a…
While a positive operator valued measure gives the probabilities in a quantum measurement, an instrument gives both the probabilities and the a posteriori states. By interpreting the instrument as a quantum channel and by using the typical…
In this paper, we extend the standard formalism of quantum mechanics to a quantum theory for a total system including one internal measuring apparatus. The internality of the measuring apparatus implies that different decomposition of a…
A concept of the generalized quantum measurement is introduced as the transformation, which establishes a correspondence between the initial states of the object system and final states of the object--measuring device (meter) system with…
Quantum instruments describe both the classical outcome and the updated state associated with a quantum measurement. We ask whether these processes can be simulated using only a natural subset of resources, namely projective measurements on…
Our basic structure is a finite-dimensional complex Hilbert space $H$. We point out that the set of effects on $H$ form a convex effect algebra. Although the set of operators on $H$ also form a convex effect algebra, they have a more…
In this paper, we attempt to establish quantum measurement theory in the Heisenberg picture. First, we review foundations of quantum measurement theory, that is usually based on the Schr\"{o}dinger picture. The concept of instrument is…
In the present paper we consider the problem of description of an arbitrary generalized quantum measurement with outcomes in a measurable space. Analyzing the unitary invariants of a measuring process, we present the most general form of a…
Generalized quantum instruments correspond to measurements where the input and output are either states or more generally quantum circuits. These measurements describe any quantum protocol including games, communications, and algorithms.…
We consider three types of entities for quantum measurements. In order of generality, these types are: observables, instruments and measurement models. If $\alpha$ and $\beta$ are entities, we define what it means for $\alpha$ to be a part…
We introduce the concepts of dual instruments and sub-observables. We show that although a dual instruments measures a unique observable, it determines many sub-observables. We define a unique minimal extension of a sub-observable to an…
Transition probabilities are an important and useful tool in quantum mechanics. However, in their present form, they are limited in scope and only apply to pure quantum states. In this article we extend their applicability to mixed states…
Quantum instruments describe outcome probability as well as state change induced by measurement of a quantum system. Incompatibility of two instruments, i. e. the impossibility to realize them simultaneously on a given quantum system,…
The structure of covariant instruments is studied and a general structure theorem is derived. A detailed characterization is given to covariant instruments in the case of an irreducible representation of a locally compact group.