Related papers: Factor Graphs for Quantum Probabilities
This paper combines probabilistic and algebraic techniques for computing quantum expectations of operator exponentials (and their products) of quadratic forms of quantum variables in Gaussian states. Such quadratic-exponential functionals…
The hidden-variables premise is shown to be equivalent to the existence of generic filters for algebras of commuting propositions and for certain more general propositional systems. The significance of this equivalence is interpreted in…
Weak measurements of photon position can be used to obtain direct experimental evidence of the wavefunction of a photon between generation and ultimate detection. Significantly, these measurement results can also be understood as complex…
We use the periodicity properties of generalized Gauss sums to factor numbers. Moreover, we derive rules for finding the factors and illustrate this factorization scheme for various examples. This algorithm relies solely on interference and…
The ability to represent complex high dimensional probability distributions in a compact form is one of the key insights in the field of graphical models. Factored representations are ubiquitous in machine learning and lead to major…
The contextuality and noncontextuality notions are considered in framework of probability representation of quantum states. Example of qutrit states and violation of the noncontextuality inequalities are presented by using the spin tomogram…
It is shown that the statistical conception of quantum mechanics is dynamical but not probabilistic, i.e. the statistical description in quantum mechanics is founded on dynamics. A use of the probability theory, when it takes place, is…
An analysis is made of a moving disturbance using a directed cyclic graph. A statistical approach is used to calculate the alternative positions in space and state of the disturbance with a defined observed time. The probability for a…
Quantum theory can be regarded as a non-commutative generalization of classical probability. From this point of view, one expects quantum dynamics to be analogous to classical conditional probabilities. In this paper, a variant of the…
This paper initiates the study of hidden variables from the discrete, abstract perspective of quantum computing. For us, a hidden-variable theory is simply a way to convert a unitary matrix that maps one quantum state to another, into a…
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…
We show that any joint probability mass function (PMF) can be expressed as a product of parity check factors and factors of degree one with the help of some auxiliary variables, if the alphabet size is appropriate for defining a parity…
Quantum computation is a promising emerging technology which, compared to conventional computation, allows for substantial speed-ups e.g. for integer factorization or database search. However, since physical realizations of quantum…
A non-Boolean extension of the classical probability model is proposed. The non-Boolean probabilities reproduce typical quantum phenomena. The proposed model is more general and more abstract, but easier to interpret, than the quantum…
We introduce the probability distributions describing quantum observables in conventional quantum mechanics and clarify their relations to the tomographic probability distributions describing quantum states. We derive the evolution equation…
Today it still remains a challenge whether quantum mechanics has an underlying statistical explanation or not. While there are and were a lot of models trying to explain quantum phenomena with statistical methods these all failed on certain…
The additivity of classical probabilities is only the first in a hierarchy of possible sum-rules, each of which implies its successor. The first and most restrictive sum-rule of the hierarchy yields measure-theory in the Kolmogorov sense,…
We develop an approach where the quantum system states and quantum observables are described as in classical statistical mechanics -- the states are identified with probability distributions and observables, with random variables. An…
The fundamental question of how to best simulate quantum systems using conventional computational resources lies at the forefront of condensed matter and quantum computation. It impacts both our understanding of quantum materials and our…
The tomographic approach to quantum mechanics is revisited as a direct tool to investigate violation of Bell-like inequalities. Since quantum tomograms are well defined probability distributions, the tomographic approach is emphasized to be…