Related papers: Empirically Equivalent Distributions in Ontologica…
We review some older and more recent results concerning the energy and particle distribution in ground states of heavy Coulomb systems. The reviewed results are asymptotic in nature: they describe properties of many-particle systems in the…
In this article we derive a useful expectation identity using the language of quantum statistical mechanics, where density matrices represent the state of knowledge about the system. This identity allows to establish relations between…
A distribution of electromagnetic fields presents a statistical assembly of a particular type, which is at scale h a quantum statistical assembly itself and has also been instrumental to concretisation of the basic probability assumption of…
We produce a probabilistic space from logic, both classical and quantum, which is in addition partially ordered in such a way that entropy is monotone. In particular do we establish the following equation: Quantitative Probability = Logic +…
According to a recent no-go theorem (M. Pusey, J. Barrett and T. Rudolph, Nature Physics 8, 475 (2012)), models in which quantum states correspond to probability distributions over the values of some underlying physical variables must have…
It has been shown that the conditional probability distributions obtained by performing measurements on an uncharacterized physical system can be used to infer its underlying dimension in a device-independent way both in the classical and…
Suppose one has access to oracles generating samples from two unknown probability distributions P and Q on some N-element set. How many samples does one need to test whether the two distributions are close or far from each other in the…
A formulation of quantum mechanics, which begins by postulating assertions for individual physical systems, is given. The statistical predictions of quantum mechanics for infinite ensembles are then derived from its assertions for…
We show that probabilities of results of all possible measurements performing on a quantum system depend on the system's state only through its density matrix. Therefore all experimentally available information about the state contains in…
Quantum mechanics fundamentally forbids deterministic discrimination of quantum states and processes. However, the ability to optimally distinguish various classes of quantum data is an important primitive in quantum information science. In…
There is a persistent confusion about determinism and predictability. In spite of the opinions of some eminent philosophers (e.g., Popper), it is possible to understand that the two concepts are completely unrelated. In few words we can say…
Present quantum theory, which is statistical in nature, does not predict joint probability distribution of position and momentum because they are noncommuting. We propose a deterministic quantum theory which predicts a joint probability…
On the basis of our recent model of a one-dimensional (1D) completed scattering we argue that Leggett's principles of macroscopic realism must and can be extended onto the level of single electrons and atoms. These principles need three…
In the Bayesian approach to probability theory, probability quantifies a degree of belief for a single trial, without any a priori connection to limiting frequencies. In this paper we show that, despite being prescribed by a fundamental…
Harrigan and Spekkens (2010) provided a categorization of quantum ontological models classifying them as $\psi$-ontic or $\psi$-epistemic if the quantum state describes respectively either a physical reality or mere observers' knowledge.…
Quantum mechanics may be formulated as Sensible Quantum Mechanics (SQM) so that it contains nothing probabilistic, except, in a certain frequency sense, conscious perceptions. Sets of these perceptions can be deterministically realized with…
We study the computational complexity of certain integrable quantum theories in 1+1 dimensions. We formalize a model of quantum computation based on these theories. In this model, distinguishable particles start out with known momenta and…
Physical interpretations of the time-symmetric formulation of quantum mechanics, due to Aharonov, Bergmann, and Lebowitz are discussed in terms of weak values. The most direct, yet somewhat naive, interpretation uses the time-symmetric…
A test space is the set of outcome-sets associated with a collection of experiments. This notion provides a simple mathematical framework for the study of probabilistic theories -- notably, quantum mechanics -- in which one is faced with…
The most irreducible way to represent information is a sequence of two symbols. In this paper, we construct quantum states using this basic building block. Specifically, we show that the probabilities that arise in quantum theory can be…