Related papers: Non-classical conditional probability and the quan…
This work discusses simple examples how quantum systems are obtained as subsystems of classical statistical systems. For a single qubit with arbitrary Hamiltonian and for the quantum particle in a harmonic potential we provide explicitly…
It is known that the stronger no-cloning theorem and the no-deleting theorem taken together provide the permanence property of quantum information. Also, it is known that the violation of the no-deletion theorem would imply signalling.…
Quantum Mechanics (QM) is a quantum probability theory based on the density matrix. The possibility of applying classical probability theory, which is based on the probability distribution function(PDF), to describe quantum systems is…
The dramatic increase in the efficiency of a quantum computer over a classical computer, raises a natural question asking, how much of this success could be attributed to its quantum nature and how much to its probabilistic content. To…
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 show the following: a randomly chosen pure state as a resource for measurement-based quantum computation, is - with overwhelming probability - of no greater help to a polynomially bounded classical control computer, than a string of…
A type of mechanics will be presented that possesses some distinctive properties. On the one hand, its physical description & rules of operation are readily comprehensible & intuitively clear. On the other, it fully satisfies all observable…
It is argued that although quantum theory isn't an absolutely deterministic theory, it is partially deterministic. The approach followed here is in the framework of the standard (Copenhagen interpretation of) quantum mechanics without any…
The no-communication theorem states that the observation of a subsystem of an entangled state does not affect another subsystem. Nevertheless, this theorem is based on the assumption that all quantum processes are unitary. We examine a…
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…
A simple and unifying method to show the perfect error-correcting condition is provided based on the quantum mutual information. The one-to-one parameterization of quantum operations and the properties of the quantum relative entropy are…
The predictions of quantum mechanics are probabilistic. Quantum probabilities are extracted using a postulate of the theory called the Born rule, the status of which is central to the "measurement problem" of quantum mechanics. Efforts to…
I show that probabilities in quantum mechanics are a measure of belief in the presence of human ignorance, just like all other probabilities. The Born interpretation of the square of modulus of the wave function arises from the interaction…
We introduce a class of probabilistic theories, termed Minimal Strongly Causal Operational Probabilistic Theories, where system dynamics are constrained to the minimal set of operations consistent with the set of states and permitting…
We construct the most general form of our previously proposed nonlinear extension of quantum mechanics that possesses three basic properties. Unlike the simpler model, the new version is not completely integrable, but it has an underlying…
The collapse of a quantum state can be understood as a mathematical way to construct a joint probability density even for operators that do not commute. We can formalize that construction as a non-commutative, non-associative collapse…
Perfect Quantum Cloning Machines (QCM) would allow to use quantum nonlocality for arbitrary fast signaling. However perfect QCM cannot exist. We derive a bound on the fidelity of QCM compatible with the no-signaling constraint. This bound…
Quantum computation has suggested new forms of quantum logic, called quantum computational logics. The basic semantic idea is the following: the meaning of a sentence is identified with a quregister, a system of qubits, representing a…
A quantum probability model is introduced and used to explain human probability judgment errors including the conjunction, disjunction, inverse, and conditional fallacies, as well as unpacking effects and partitioning effects. Quantum…
We show that the linearity of an evolution of Quantum Mechanics follows from the definition of kinematics. The same result is obtained for an arbitrary theory with the state space that includes mixtures of different preparations. Next, we…