Related papers: Measurement Models with Separable Interaction Chan…
It is not possible to obtain information about the observable properties of a quantum system without a physical interaction between the system and an external meter. This physical interaction is described by a unitary transformation of the…
Mutually unbiased bases (MUBs) and symmetric informationally complete (SIC) positive operator-valued measurements (POVMs) are two related topics in quantum information theory. They are generalized to mutually unbiased measurements (MUMs)…
The problem of measurement in quantum mechanics is reanalyzed within a general, strictly probabilistic framework (without reduction postulate). Based on a novel comprehensive definition of measurement the natural emergence of objective…
A small quantum scattering system (the microsystem) is studied in interaction with a large quantum system (the macrosystem) described by unknown stochastic variables. The interaction between the two systems is diagonal for the microsystem…
The quantum mechanical measurement problem is the difficulty of dealing with the indefiniteness of the pointer observable at the conclusion of a measurement process governed by unitary quantum dynamics. There has been hope to solve this…
We develop the contextual measurement model (CMM) which is used for clarification of the quantum foundations. This model matches with Bohr's views on the role of experimental contexts. CMM is based on contextual probability theory which is…
In quantum mechanics, we define the measuring system $M$ in a selective measurement by two conditions. Firstly, when we define the measured system $S$ as the system in which the non-selective measurement part acts, $M$ is independent from…
The rapid progress in quantum computing (QC) and machine learning (ML) has attracted growing attention, prompting extensive research into quantum machine learning (QML) algorithms to solve diverse and complex problems. Designing…
Theory of quantum measurements is often classified as decision theory. An event in decision theory corresponds to the measurement of an observable. This analogy looks clear for operationally testable simple events. However, the situation is…
The Heisenberg uncertainty principle imposes a fundamental restriction in quantum mechanics, stipulating that measuring one observable completely erases the information on its conjugate one, thereby preventing simultaneous measurements of…
Until recently, a quantum instrument was defined to be a completely positive operation-valued measure from the set of states on a Hilbert space to itself. In the last few years, this definition has been generalized to such measures between…
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…
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…
The paper gives a systematic review of the basic ideas of (non-relativistic) quantum mechanics including all changes that result from previous work of the authors. This shows that the new theory is self-consistent and (in certain sense)…
Both classical and respectively quantum observables can be modeled as somewhat similar examples of random variables. In such a model the associated measurements preserve the values spectrum of an observable but change the corresponding…
During many years since the birth of quantum mechanics, instrumentalist interpretations prevailed: the meaning of the theory was expressed in terms of measurements results. But in the last decades, several attempts to interpret it from a…
Careful analysis of cluster separability opens a way to a completely new understanding of preparation and registration procedures for microsystems: they are changes of separation status. An important observation is that quantum mechanics…
In Quantum Physics it is not always possible to directly perform the measurement of an obsevable; in some of these cases, however, its value can be {\sl detected}, i.e. it can be inferred by measuring {\sl another} observable characterized…
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…
We consider the problem of determining the state of a quantum system given one or more readings of the expectation value of an observable. The system is assumed to be a finite dimensional quantum control system for which we can influence…