Related papers: Quantum information aspects of noncommutative quan…
How much of the uncertainty in predicting measurement outcomes for non-commuting quantum observables is genuinely quantum mechanical? We provide a natural decomposition of the total entropic uncertainty of two non-commuting observables into…
In this paper and a companion paper, we attempt to systematically investigate the possibility that the concept of information may enable a derivation of the quantum formalism from a set of physically comprehensible postulates. To do so, we…
The engine that powers quantum cryptography is the principle that there are no physical means for gathering information about the identity of a quantum system's state (when it is known to be prepared in one of a set of nonorthogonal states)…
We explore the notion of spatial extent and structure, already alluded to in earlier literature, within the formulation of quantum mechanics on the noncommutative plane. Introducing the notion of average position and its measurement, we…
A variety of physical unknowables are discussed. Provable lack of physical omniscience, omnipredictability and omnipotence is derived by reduction to problems which are known to be recursively unsolvable. "Chaotic" symbolic dynamical…
We attempt to contribute some novel points of view to the "foundations of quantum mechanics", using mathematical tools from "quantum probability theory" (such as the theory of operator algebras). We first introduce an abstract algebraic…
Robertson and Hadamard-Robertson theorems on non-negative definite hermitian forms are generalized to an arbitrary ordered field. These results are then applied to the case of formal power series fields, and the Heisenberg-Robertson,…
The operator and the functional formulations of the dynamics of constrained systems are explored for determining unambiguously the quantum Hamiltonian of a nonrelativistic particle in a curved space.
An analysis of quantum measurement is presented that relies on an information-theoretic description of quantum entanglement. In a consistent quantum information theory of entanglement, entropies (uncertainties) conditional on measurement…
Trying to connect a fundamentally non-commutative spacetime with the conservative perturbative approach to quantum gravity, we are led to the natural question: are non-commutative geometrical effects already present in the regime where…
Quantum information processing is the emerging field that defines and realizes computing devices that make use of quantum mechanical principles, like the superposition principle, entanglement, and interference. In this review we study the…
Quantum coherence constitutes a foundational characteristic of quantum mechanics and is integral to emerging quantum resource theories. However, quantum coherence is severely restricted by environmental noise in general quantum processing,…
It is shown that polymer quantization leads to a modified uncertainty principle similar to that obtained from string theory and non-commutative geometry. When applied to quantum field theory on general background spacetimes, corrections to…
The uncertainty principle bounds the uncertainties about incompatible measurements, clearly setting quantum theory apart from the classical world. Its mathematical formulation via uncertainty relations, plays an irreplaceable role in…
The quantum mechanical formalism for position and momentum of a particle in a one dimensional cyclic lattice is constructively developed. Some mathematical features characteristic of the finite dimensional Hilbert space are compared with…
We consider the status of quantum information in the quantum theory and based on the correspondence principle, we propose an interpretation of the wave function as a mathematical representation of quantum information. We consider Clauser's…
These are expanded lecture notes of a mini-course whose objectives were to introduce the basic concepts, constructions and techniques of noncommutative geometry, as well as their uses as a framework for modelling quantum spacetime. Key…
We consider a twisted version of quantum groups corepresentations. This generalization amounts to include in the theory the case where quantum space coordinates and its endomorphism matrix entries belong to a non-commutative quadratic…
Resource theories play an important role in quantum information theory, as they identify resourceful states and channels that are potentially useful for the accomplishment of tasks that would be otherwise unreachable. The elementary…
In the last years noncommutative quantum mechanics has been investigated intensively. We consider the influence of magnetic field on decoherence of a system in the noncommutative quantum plane. Particularly, we point out a model in which…