Related papers: The Quantum Mechanical Potential for the Prime Num…
A version of quantum theory is derived from a set of plausible assumptions related to the following general setting: For a given system there is a set of experiments that can be performed, and for each such experiment an ordinary…
Bounds on quantum probabilities and expectation values are derived for experimental setups associated with Bell-type inequalities. In analogy to the classical bounds, the quantum limits are experimentally testable and therefore serve as…
Quantum computation teaches us that quantum mechanics exhibits exponential complexity. We argue that the standard scientific paradigm of "predict and verify" cannot be applied to testing quantum mechanics in this limit of high complexity.…
Quantum mechanics can emerge from classical statistics. A typical quantum system describes an isolated subsystem of a classical statistical ensemble with infinitely many classical states. The state of this subsystem can be characterized by…
It is shown that quantum mechanics on noncommutative spaces (NQM) can be obtained by the canonical quantization of some underlying second class constrained system formulated in extended configuration space. It leads, in particular, to an…
We consider a probabilistic quantum implementation of a variable of the Pocklington-Lehmer $N-1$ primality test using Shor's algorithm. O($\log^3 N \log\log N \log\log\log N$) elementary q-bit operations are required to determine the…
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…
We derive a standard quantum limit for probing mechanical energy quantization in a class of systems with mechanical modes parametrically coupled to external degrees of freedom. To resolve a single mechanical quantum, it requires a…
Present quantum Monte Carlo codes use statistical techniques adapted to find the amplitude of a quantum system or the associated eigenvalues. Thus, they do not use a true physical random source. It is demonstrated that, in fact, quantum…
Consider a fixed universe of $N=2^n$ elements and the uniform distribution over elements of some subset of size $K$. Given samples from this distribution, the task of complement sampling is to provide a sample from the complementary subset.…
Quantum mechanics may be formulated as {\it Sensible Quantum Mechanics} (SQM) so that it contains nothing probabilistic except conscious perceptions. Sets of these perceptions can be deterministically realized with measures given by…
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…
Recent developments in Quantum Machine Learning have seen the introduction of several models to generalize the classical perceptron to the quantum regime. The capabilities of these quantum models need to be determined precisely in order to…
We show that, in spite of a rather common opinion, quantum mechanics can be represented as an approximation of classical statistical mechanics. The approximation under consideration is based on the ordinary Taylor expansion of physical…
Quantum mechanics is derived from the principle that the universe contain as much variety as possible, in the sense of maximizing the distinctiveness of each subsystem. The quantum state of a microscopic system is defined to correspond to…
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…
According to the statistical interpretation of quantum theory, quantum computers form a distinguished class of probabilistic machines (PMs) by encoding n qubits in 2n pbits (random binary variables). This raises the possibility of a…
To test the limits of quantum mechanics, a proposal for an experiment on protons is suggested. The spin component of proton is measured very rapidly in sequential measurements. The reason for this experiment is derived from the genuine…
A simple methodology is suggested for the efficient calculation of certain central potentials having singularities. The generalized pseudospectral method used in this work facilitates {\em nonuniform} and optimal spatial discretization.…
The quantum mechanical measurement problem does not arise in the quantum real number approach to quantum measurements of the first kind. The attributes of individual microscopic systems in the experimental ensemble always have qr-number…