Related papers: Quantum conditional probabilities
The Principle of Complementarity of Probabilities based on of noncommutative probability is introduced.
Considerable effort has been devoted to deriving the Born rule (e.g. that $|\psi(x)|^2 dx$ is the probability of finding a system, described by $\psi$, between $x$ and $x + dx$) in quantum mechanics. Here we show that the Born rule is not…
The notion of probability plays a crucial role in quantum mechanics. It appears in quantum mechanics as the Born rule. In modern mathematics which describes quantum mechanics, however, probability theory means nothing other than measure…
Based on a gambling formulation of quantum mechanics, we derive a Gleason-type theorem that holds for any dimension n of a quantum system, and in particular for n = 2. The theorem states that the only logically consistent probability…
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…
Quantum theory provides a significant example of two intermingling hallmarks of science: the ability to consistently combine physical systems and study them compositely, and the power to extract predictions in the form of correlations. A…
In a recent article entitled "A simple explanation of the quantum violation of a fundamental inequality," Cabello proposes a condition on a class of probabilistic models that, he claims, gives the same bound on contextuality for the KCBS…
Quantum operations are used to describe the observed probability distributions and conditional states of the measured system. In this paper, we address the problem of their joint measurability (coexistence). We derive two equivalent…
One more derivation of the quantum probability rule is presented in order to shed more light on the versatile aspects of this fundamental law. It is shown that the change of state in minimal quantum non-demolition measurement, also known as…
Correlation self-testing of quantum theory involves identifying a task or set of tasks whose optimal performance can be achieved only by theories that can realise the same set of correlations as quantum theory in every causal structure.…
Probabilities enter quantum mechanics via Born's rule, the uniqueness of which was proven by Gleason. Busch subsequently relaxed the assumptions of this proof, expanding its domain of applicability in the process. Extending this work to…
An examination is made of the differing implications from applying the two mainstream interpretations of probability, frequentist and Bayesian, to QM (quantum mechanics) theory for the Bohm-EPR experiment. The joint probability distribution…
In Mod. Phys. Lett. A 9, 3119 (1994), one of us (R.D.S) investigated a formulation of quantum mechanics as a generalized measure theory. Quantum mechanics computes probabilities from the absolute squares of complex amplitudes, and the…
We consider how to define a natural probability distribution over worlds within a simple class of deterministic many-worlds theories. This can help us understand the typical properties of worlds within such states, and hence explain the…
We have studied the possibility of post-quantum theories more nonlocal than the (standard) quantum theory using the modification of the quantum probability rule under the no-signaling condition. For this purpose we have considered the…
We have recently developed a new understanding of probability in quantum gravity. In this paper we provide an overview of this new approach and its implications. Adopting the de Broglie-Bohm pilot-wave formulation of quantum physics, we…
In this work, we show that the quantum mechanical notions of density operator, positive operator-valued measure (POVM), and the Born rule, are all simultaneously encoded in the categorical notion of a natural transformation of functors. In…
Modal interpretations have the ambition to construe quantum mechanics as an objective, man-independent description of physical reality. Their second leading idea is probabilism: quantum mechanics does not completely fix physical reality but…
It has recently been claimed by De Zela that Gleason's theorem, for probability measures on the lattice of projection operators, can be extended to qubits by adding assumptions related to continuity and the existence of 'eigenstates'. This…
Gleason's theorem is a fundamental 60 year old result in the foundations of quantum mechanix, setting up and laying out the surprisingly minimal assumptions required to deduce the existence of quantum density matrices and the Born rule. Now…