Related papers: Excluding joint probabilities from quantum theory
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 compare the classical Kolmogorov and quantum probability models. We show that the gap between these model is not so huge as it was commonly believed. The main structures of quantum theory (interference of probabilities, Born's rule,…
In this paper we discuss the existence of joint probability distributions for quantum-like response computations in the brain. We do so by focusing on a contextual neural-oscillator model shown to reproduce the main features of behavioral…
Uncertainty principle is one of the cornerstones of quantum theory. In the literature, there are two types of uncertainty relations, the operator form concerning the variances of physical observables and the entropy form related to entropic…
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…
With basis on (i) the physical principle of local causality and (ii) a certain notion of elements of reality, Einstein, Podolsky, and Rosen (EPR) put forward an argument showing that physical instances may exist in which two non-commuting…
Given two or more non-commuting observables, it is generally not possible to simultaneously assign precise values to each. This quantum mechanical uncertainty principle is widely understood to be encapsulated by some form of uncertainty…
The Born rule provides a probability vector (distribution) with a quantum state for a measurement setting. For two settings, we have a pair of vectors from the same quantum state. Each pair forms a combined-probability vector that obeys…
Quantum theory has the intriguing feature that is inconsistent with noncontextual hidden variable models, for which the outcome of a measurement does not depend on which other compatible measurements are being performed concurrently. While…
We extend Einstein's hole argument into the quantum domain, and argue that quantum observables for quasiclassical superpositional states of gravitational fields require additional information to be well-defined, namely, relative positions…
The Jordan structure of finite-dimensional quantum theory is derived, in a conspicuously easy way, from a few simple postulates concerning abstract probabilistic models (each defined by a set of basic measurements and a convex set of…
By invoking quantum estimation theory we formulate bounds of errors in quantum measurement for arbitrary quantum states and observables in a finite-dimensional Hilbert space. We prove that the measurement errors of two observables satisfy…
The nondistributivity of compound quantum mechanical propositions leads to a theorem that rules out the possibility of microscopic deterministic hidden variables, the Logical No-Go Theorem. We observe that there appear in fact two distinct…
Quantum theory demands that, in contrast to classical physics, not all properties can be simultaneously well defined. The Heisenberg Uncertainty Principle is a manifestation of this fact. Another important corollary arises that there can be…
Quantum bits can be isolated to perform useful information-theoretic tasks, even though physical systems are fundamentally described by very high-dimensional operator algebras. This is because qubits can be consistently embedded into…
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.…
It is usually assumed that the quantum state is sufficient for deducing all probabilities for a system. This may be true when there is a single observer, but it is not true in a universe large enough that there are many copies of an…
Joint measurements of qubit observables have recently been studied in conjunction with quantum information processing tasks such as cloning. Considerations of such joint measurements have until now been restricted to a certain class of…
Three notions of complementarity - operational, probabilistic, and value complementarity - are reanalysed with respect to the question of joint measurements and compared with reference to some examples of canonically conjugate observables.…
We study the quantum measurement problem in the context of an infinite, statistically uniform space, as could be generated by eternal inflation. It has recently been argued that when identical copies of a quantum measurement system exist,…