Related papers: Continuous Functions as Quantum Operations: a prob…
This paper shows how the classical finite probability theory (with equiprobable outcomes) can be reinterpreted and recast as the quantum probability calculus of a pedagogical or "toy" model of quantum mechanics over sets (QM/sets). There…
Statistical functions such as the moment-generating function, characteristic function, cumulant-generating function, and second characteristic function are cornerstone tools in classical statistics and probability theory. They provide a…
The concept of time emerges as an ordering structure in a classical statistical ensemble. Probability distributions $p_\tau(t)$ at a given time $t$ obtain by integrating out the past and future. We discuss all-time probability distributions…
We present probability-fidelity tradeoffs for a varying quantum operation with fixed input-output states and for a varying inversion of a fixed quantum operation.
We describe a plausible-speculative form of quantum computation which exploits particle (fermionic, bosonic) statistics, under a generalized, counterfactual interpretation thereof. In the idealized situation of an isolated system, it seems…
This is an introductory chapter of the book in progress on quantum foundations and incompleteness of quantum mechanics. Quantum mechanics is represented as statistical mechanics of classical fields.
This paper presents a new approach to phase space trajectories in quantum mechanics. A Moyal description of quantum theory is used, where observables and states are treated as classical functions on a classical phase space. A quantum…
We introduce another new type of combinations of Bernstein operators in this paper, which can be used to approximate the functions with inner singularities. The direct and inverse results of the weighted approximation of this new type…
In Loop Quantum Gravity, the quantum action of the volume operator is crucial in understanding quantum dynamics. In this work, we implement a generalized numerical algorithm that can compute the quantum action of the volume operator on a…
In this paper we introduce a new family of Bernstein-type exponential polynomials on the hypercube $[0, 1]^d$ and study their approximation properties. Such operators fix a multidimensional version of the exponential function and its…
Quantum signal processing (QSP) represents a real scalar polynomial of degree $d$ using a product of unitary matrices of size $2\times 2$, parameterized by $(d+1)$ real numbers called the phase factors. This innovative representation of…
This paper demonstrates that the space of piecewise smooth functions can be well approximated by the space of functions defined by a set of simple (non-linear) operations on smooth uniform splines. The examples include bivariate functions…
The quotients of a (non-orientable) quantum Seifert manifold by circle actions are described. In this way quantum weighted real projective spaces that include the quantum disc and the quantum real projective space as special cases are…
The term quantum logic has different connotations for different people, having been considered as everything from a metaphysical attack on classical reasoning to an exercise in abstract algebra. Our aim here is to give a uniform…
A certain generalization of the mathematical formalism of quantum mechanics beyond operator algebras is considered. The approach is based on the concept of conditional probability and the interpretation of the Lueders - von Neumann quantum…
An operator space analysis of quantum stochastic cocycles is undertaken. These are cocycles with respect to an ampliated CCR flow, adapted to the associated filtration of subspaces, or subalgebras. They form a noncommutative analogue of…
Functions with singularities are notoriously difficult to approximate with conventional approximation schemes. In computational applications, they are often resolved with low-order piecewise polynomials, multilevel schemes, or other types…
We show that quantum circuits where the initial state and all the following quantum operations can be represented by positive Wigner functions can be classically efficiently simulated. This is true both for continuous-variable as well as…
Quantum mechanics is reformulated using Hartle's definition of the state of an individual physical system and a variant of von Neumann's propositional calculus. An elementary set of quantum postulates lead inductively to the familiar…
We describe a scheme for constructing quantum mechanics in which a quantum system is considered as a collection of open classical subsystems. This allows using the formal classical logic and classical probability theory in quantum…