Related papers: Four Related Combinatorial Problems
Complementarity was originally introduced as a qualitative concept for the discussion of properties of quantum mechanical objects that are classically incompatible. More recently, complementarity has become a \emph{quantitative} relation…
The origin of non-classical correlations is difficult to identify since the uncertainty principle requires that information obtained about one observable invariably results in the disturbance of any other non-commuting observable. Here,…
For an arbitrary preparation, quantum mechanical descriptions refer to the complementary contexts set by incompatible measurements. We argue that an arbitrary preparation, therefore, should be described with respect to such a context by its…
The quantum measurement problems are revisited from a new perspective. One of the main ideas of this work is that the basic entities of our world are various types of particles, elementary or composite. It follows that each elementary…
In this work, we show that very natural, apparently simple problems in quantum measurement theory can be undecidable even if their classical analogues are decidable. Undecidability hence appears as a genuine quantum property here. Formally,…
After a brief review of classical probability theory (measure theory), we present an observation (due to Sorkin) concerning an aspect of probability in quantum mechanics. Following Sorkin, we introduce a generalized measure theory based on…
Unsolved controversies about uncertainty relations and quantum measurements still persists nowadays. They originate around the shortcomings regarding the conventional interpretation of uncertainty relations. Here we show that the respective…
Some of the problems connected with the interpretation of quantum mechanics are enumerated, in particular those related to some well known paradoxes and, above all, to the measurement process. We then show how the so called "Physics…
Measure theory is used in physics, not just to capture classical probability, but also to quantify the number of states. In previous works, we found that state quantification plays a foundational role in classical mechanics, and therefore,…
We introduce quantum correlations measures based on the minimal change in unified entropies induced by local rank-one projective measurements, divided by a factor that depends on the generalized purity of the system in the case of…
We address the extension problem for quantal measures of path-integral type, concentrating on two cases: sequential growth of causal sets, and a particle moving on the finite lattice Z_n. In both cases the dynamics can be coded into a…
The quantum theory of measurement has been a matter of debate for over eighty years. Most of the discussion has focused on theoretical issues with the consequence that operational prescriptions, which are integral to experimental physics,…
Biconformal spaces contain the essential elements of quantum mechanics, making the independent imposition of quantization unnecessary. Based on three postulates characterizing motion and measurement in biconformal geometry, we derive…
Quantum coherence is the most fundamental feature of quantum mechanics. The usual understanding of it depends on the choice of the basis, that is, the coherence of the same quantum state is different within different reference framework. To…
The usual conjectures of quantum measurements approaches, inspired from the traditional interpretation of Heisenberg's ("uncertainty") relations, are proved as being incorrect. A group of reconsidered conjectures and a corresponding new…
A quantum measurement model based upon restricted path-integrals allows us to study measurements of generalized position in various one-dimensional systems of phenomenological interest. After a general overview of the method we discuss the…
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.,…
Deciding which sets of quantum measurements allow a simultaneous readout is a central problem in quantum measurement theory. The problem is relevant not only from the foundational perspective but also has direct applications in quantum…
We prove that the Hilbert space description of all joint von Neumann measurements on a quantum state can be reproduced in terms of a single measure space ({\Omega}, F, {\mu}) with a normalized real-valued measure {\mu}, that is, in terms of…
We propose a class of incompatibility measures for quantum observables based on quantifying the effect of a measurement of one observable on the statistics of the outcomes of another. Specifically, for a pair of observables $A$ and $B$ with…