Related papers: Four Related Combinatorial Problems
We prove a new sum uncertainty relation in quantum theory which states that the uncertainty in the sum of two or more observables is always less than or equal to the sum of the uncertainties in corresponding observables. This shows that the…
A certain generalization of the mathematical formalism of quantum mechanics beyond operator algebras is considered. The approach is based on the concept of conditional probability and the interpretation of the Lueders - von Neumann quantum…
We propose a novel solution to the measurement problem based on quantum field theory and Haag's theorem. According to our proposal in elementary interactions where the particles content is changed, the temporal evolution is non unitary.…
Causality imposes strong restrictions on the type of operators that may be observables in relativistic quantum theories. In fact, causal violations arise when computing conditional probabilities for certain partial causally connected…
The paper reviews and discusses four ideas scattered in previous papers of the author. First, objective properties of quantum systems are not associated with observables but are defined by preparations. Second, measurable results of…
The three-box problem is a gedankenexperiment designed to elucidate some interesting features of quantum measurement and locality. A particle is prepared in a particular superposition of three boxes, and later found in a different (but…
Measurement outcomes of a quantum state can be genuinely random (unpredictable) according to the basic laws of quantum mechanics. The Heisenberg-Robertson uncertainty relation puts constrains on the accuracy of two noncommuting observables.…
The recently established universal uncertainty principle revealed that two nowhere commuting observables can be measured simultaneously in some state, whereas they have no joint probability distribution in any state. Thus, one measuring…
A one-to-one correspondence is established between linearized space-time metrics of general relativity and the wave equations of quantum mechanics. Also, the key role of boundary conditions in distinguishing quantum mechanics from classical…
The geometric form of standard quantum mechanics is compatible with the two postulates: 1) The laws of physics are invariant under the choice of experimental setup and 2) Every quantum observation or event is intrinsically statistical.…
Grade-$d$ measures on a $\sigma$-algebra $\mathcal{A}\subseteq 2^X$ over a set $X$ are generalizations of measures satisfying one of a hierarchy of weak additivity-type conditions initially introduced as interference operators in quantum…
A discussion of the meaning of a physical concept cannot be separated from discussion of the conditions for its ideal measurement. We assert that quantization is no more than the invocation of the quantum of action in the explanation of…
The notorious quantum measurement problem brings out the difficulty to reconcile two quantum postulates: the unitary evolution of closed quantum systems and the wave-function collapse after a measurement. This problematics is particularly…
Three problems stand in the way of deriving classical theories from quantum mechanics: those of realist interpretation, of classical properties and of quantum measurement. Recently, we have identified some tacit assumptions that lie at the…
Incompatible, i.e. non-jointly measurable quantum measurements are a necessary resource for many information processing tasks. It is known that increasing the number of distinct measurements usually enhances the incompatibility of a…
In this paper, we present a general framework to solve a fundamental problem in Random Matrix Theory (RMT), i.e., the problem of describing the joint distribution of eigenvalues of the sum $\bsA+\bsB$ of two independent random Hermitian…
Based on some recent progress on a relation between four dimensional super Yang-Mills gauge theory and quantum integrable system, we study the asymptotic spectrum of the quantum mechanical problems described by the Mathieu equation and the…
The extended Wigner's friend problem deals with two Observers each measuring a sealed laboratory in which a friend is making a quantum measurement. We investigate this problem by relying on the basic rules of quantum mechanics as exposed by…
There exist several different proposals for a measure in Quantum Gravity theories. Although sometimes being labelled as non covariant, the measure derived in [7] for GR has the particularity that, in the extremal, the volume divergences…
This is an introduction to measure theory, integration and function spaces, with all the needed preliminaries included, and with some applications included as well. We first discuss some basic motivations, coming from discrete probability,…