相关论文: Could a Classical Probability Theory Describe Quan…
Machine Learning classification models learn the relation between input as features and output as a class in order to predict the class for the new given input. Quantum Mechanics (QM) has already shown its effectiveness in many fields and…
Einstein conjectured long ago that much of quantum mechanics might be derived as a statistical formalism describing the dynamics of classical systems. Bell's Theorem experiments have ruled out complete equivalence between quantum field…
Quantum mechanics is essentially a statistical theory. Classical mechanics, however, is usually not viewed as being inherently statistical. Nevertheless, the latter can also be formulated statistically. Furthermore, a statistical…
Quantum Field Theory (QFT) makes predictions by combining two sets of assumptions: (1) quantum dynamics, such as a Schrodinger or Liouville equation; (2) quantum measurement, such as stochastic collapse to an eigenfunction of a measurement…
I propose a general quantum hypothesis testing theory that enables one to test hypotheses about any aspect of a physical system, including its dynamics, based on a series of observations. For example, the hypotheses can be about the…
A rigorous general definition of quantum probability is given, which is valid for elementary events and for composite events, for operationally testable measurements as well as for inconclusive measurements, and also for non-commuting…
One of the crucial differences between mathematical models of classical and quantum mechanics is the use of the tensor product of the state spaces of subsystems as the state space of the corresponding composite system. (To describe an…
The breakdown of Ehrenfest's theorem imposes serious limitations on quaternionic quantum mechanics (QQM). In order to determine the conditions in which the theorem is valid, we examined the conservation of the probability density, the…
The properties which give quantum mechanics its unique character - unitarity, complementarity, non-commutativity, uncertainty, nonlocality - derive from the algebraic structure of Hermitian operators acting on the wavefunction in complex…
By repeated trials, one can determine the fairness of a classical coin with a confidence which grows with the number of trials. A quantum coin can be in a superposition of heads and tails and its state is most generally a density matrix.…
Measurement is a fundamental notion in the usual approximate quantum mechanics of measured subsystems. Probabilities are predicted for the outcomes of measurements. State vectors evolve unitarily in between measurements and by reduction of…
In a fundamental formulation of the quantum mechanics of a closed system such as the universe as a whole, three forms of information are needed to make predictions for the probabilities of alternative time histories of the closed system .…
The implications of the physical theory of quantum mechanics on the question of realism is much a subject of sustaining interest, while the background questions among physicists on how to think about all the theoretical notion and…
Based on a number of experimentally verified physical observations, it is argued that the standard principles of quantum mechanics should be applied to the Universe as a whole. Thus, a paradigm is proposed in which the entire Universe is…
The concept of an injective affine embedding of the quantum states into a set of classical states, i.e., into the set of the probability measures on some measurable space, as well as its relation to statistically complete observables is…
Quantum computing is concerned with computer technology based on the principles of quantum mechanics, with operations performed at the quantum level. Quantum computational models make it possible to analyze the resources required for…
We consider ontological models of a quantum system, assuming that not all probability distributions over the space $\Lambda$ of ontic states are preparable, only those belonging to a certain set C. We assume further that every POVM with a…
Quantum Graphical Models (QGMs) generalize classical graphical models by adopting the formalism for reasoning about uncertainty from quantum mechanics. Unlike classical graphical models, QGMs represent uncertainty with density matrices in…
In previous articles we presented a derivation of Born's rule and unitary transforms in Quantum Mechanics (QM), from a simple set of axioms built upon a physical phenomenology of quantization. Physically, the structure of QM results of an…
By formulating the axioms of quantum mechanics, von Neumann also laid the foundations of a "quantum probability theory". As such, it is regarded a generalization of the "classical probability theory" due to Kolmogorov. Outside of quantum…