Related papers: Von Neumann-Lueders projection, and its applicabil…
In the normal presentation of the EPR problem a comparison is made between the (weak) Copenhagen interpretation of quantum mechanics which seems to suggest that at times action at a distance may take place, and the hidden parameter…
Bell's theorem applies to the normalizable approximations of the original Einstein-Podolsky-Rosen (EPR) state. The constructions of the proof require measurements difficult to perform, and dichotomic observables. By noticing the fact that…
The impossibility of measuring noncommuting quantum mechanical observables is one of the most fascinating consequences of the quantum mechanical postulates. Hence, to date the investigation of quantum measurement and projection is a…
Measurement Independence is an assumption used in foundational arguments since the EPR thought experiment in 1935, and assumed in a majority of hidden variable models of QM. In this thesis we review the crucial role of this assumption in…
Quantum mechanics under the Copenhagen interpretation is one of the most experimentally well verified formalisms. However, it is known that the interpretation makes explicit reference to external observation or "measurement." One says that…
The application of principles of Quantum Mechanics in areas outside of physics has been getting increasing attention in the scientific community in an emergent discipline called Quantum Cognition. These principles have been applied to…
Born's rule in its conventional textbook form applies to the small class of projective measurements only. It is well-known that a generalization of Born's rule to realistic experiments must be phrased in terms of positive operator valued…
We develop a general formalism, based on the Wigner function representation of continuous-variable quantum states, to describe the action of an arbitrary conditional operation on a multimode Gaussian state. We apply this formalism to…
As has already been pointed out by Birkhoff and von Neumann, quantum logic can be formulated in terms of projective geometry. In three-dimensional Hilbert space, elementary logical propositions are associated with one-dimensional subspaces,…
The quantum principle of relativity (QPR) puts forward an ambitious idea: extend special relativity with a formally superluminal branch of Lorentz-type maps, and treat the resulting consistency constraints as hints about why quantum theory…
According to Bell's theorem, local realism is incompatible with quantum theory. However, it depends on an implied assumption about quantum measurement. We suggest that the assumption might be removed by a detailed quantum analysis of the…
In the quantum mechanical Hilbert space formalism, the probabilistic interpretation is a later ad-hoc add-on, more or less enforced by the experimental evidence, but not motivated by the mathematical model itself. A model involving a clear…
We describe the mathematical underpinnings of the biorthogonal von Neumann method for quantum mechanical simulations (PvB). In particular, we present a detailed discussion of the important issue of non-orthogonal projection onto subspaces…
We review the postulates of quantum mechanics that are needed to discuss the von Neumann's entropy. We introduce it as a generalization of Shannon's entropy and propose a simple game that makes easier understanding its physical meaning.
We provide an overview of standard "projective" quantum measurements with the goal of elucidating connections between theory and experiment. We make use of a unitary "Stinespring" representation of measurements on a dilated Hilbert space…
The Ehrenfest theorem and the Robertson uncertainty relation are well-known basic equations in quantum mechanics. However, there exist problematic cases, where the Ehrenfest theorem and the Robertson uncertainty relation are not correct.…
It is shown that, since an ultrafilter over an operator-algebraically finite (i.e. isomorphic to the lattice of projectors of a finite Von Neumann algebra) quantum logic is not necessarily principal, Arrow's Impossibility Theorem doesn't…
Recently, [arXiv:0810.3134] is accepted and published. We derive an inequality with two settings as tests for the existence of the Bloch sphere in a spin-1/2 system. The probability theory of measurement outcome within the formalism of von…
The term "measurement" in quantum theory (as well as in other physical theories) is ambiguous: It is used to describe both an experience - e.g., an observation in an experiment - and an interaction with the system under scrutiny. If doing…
A notably enhanced comprehension of the underlying meaning of quantum observations is achieved via a novel premise. Assessments, from first principles, are made of unexamined presumptions that lie at the heart of both conventional…