相关论文: A Subjective Approach to Quantum Probability

State representations summarize our knowledge about a system. When unobservable quantities are introduced the state representation is typically no longer unique. However, this non-uniqueness does not affect subsequent inferences based on…

Researchers have long been aiming to understand how the characteristics of Quantum Theory and General Relativity combine to account for regimes in their interface. One reason why this is a hard task is how differently the theories approach…

We consider a finite universe U (more exactly - a family U of them) and second order quantifiers Q_K, where for each U this means quantifying over a family of n(K)-place relations closed under permuting U. We define some natural orders and…

We first prove that ontological models of the quantum state which are capable of reproducing the Born probability rule and fall in the class of $\psi$-epistemic models are inconsistent with the Sch{\"o}dinger time evolution. We then model…

Measurement uncertainty relations are lower bounds on the errors of any approximate joint measurement of two or more quantum observables. The aim of this paper is to provide methods to compute optimal bounds of this type. The basic method…

We develop a kind of quantum formalism (Hilbert space probabilistic calculus) for measurements performed over cognitive (in particular, conscious) systems. By using this formalism we could predict averages of cognitive observables.…

We discuss how to reconstruct quantum theory from operational postulates. In particular, the following postulates are consistent only with for classical probability theory and quantum theory. Logical Sharpness: There is a one-to-one map…

In the first part of this two-part article, we have introduced and analyzed a multidimensional model, called the 'general tension-reduction' (GTR) model, able to describe general quantum-like measurements with an arbitrary number of…

Quantum theory is formulated as the only consistent way to manipulate probability amplitudes. The crucial ingredient is a consistency constraint: if there are two different ways to compute an amplitude the two answers must agree. This…

A scenario is outlined for quantum measurement, assuming that self-sustaining classicality is the consequence of an attractive gravitational self-interaction acting on massive bodies, and randomness arises already in the classical domain. A…

We consider successive measurements of position and momentum of a single particle. Let P be the conditional probability to measure the momentum k with precision dk, given a previously successful position measurement q with precision dq.…

Following the B. Hiley belief that unresolved problems of conventional quantum mechanics could be the result of a wrong mathematical structure, an alternative basic structure is suggested. Critical part of the structure is modification of…

Quantization for a probability distribution refers to the idea of estimating a given probability by a discrete probability supported by a finite number of points. In this paper, firstly a general approach to this process is outlined using…

This survey gives a comprehensive account of quantum correlations understood as a phenomenon stemming from the rules of quantization. Centered on quantum probability it describes the physical concepts related to correlations (both classical…

If one assumes there is probability of perception in quantum mechanics, then unitarity dictates that it must have the coefficient squared form, in agreement with experiment.

We develop a systematic approach to quantum probability as a theory of rational betting in quantum gambles. In these games of chance the agent is betting in advance on the outcomes of several (finitely many) incompatible measurements. One…

We find that a class of entanglement measures for bipartite pure state can be expressed by the average values of quantum operators, which are related to any complete basis of one partite operator space. Two specific examples are given based…

A geometric approach to formulate the uncertainty principle between quantum observables acting on an $N$-dimensional Hilbert space is proposed. We consider the fidelity between a density operator associated with a quantum system and a…

Probabilities for observations in cosmology are conditioned both on the universe's quantum state and on local data specifying the observational situation. We show the quantum state defines a measure for prediction through such conditional…

Entropic arguments are shown to play a central role in the foundations of quantum theory. We prove that probabilities are given by the modulus squared of wave functions, and that the time evolution of states is linear and also unitary.