Related papers: Probabilistic foundations of quantum mechanics and…
The success of the abstract model of computation, in terms of bits, logical operations, programming language constructs, and the like, makes it easy to forget that computation is a physical process. Our cherished notions of computation and…
Quantum information is an emerging field which has attracted a lot of attention in the last fifteen years or so. It is a broad subject which covers from the most applied questions (e.g., how to build quantum computers or secure…
A principle of information conservation is shown in abstract terms to rule out probabilistic physical laws, necessitating the existence of state trajectories. It furthermore provides a geometric-thermodynamic mechanism for the appearance of…
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…
Interpretations of key concepts, such as uncertainty relations, kinetic energy, value of an observable, probability distributions, the projection or collapse of a wave function postulate, and discrete versus continuous values, that appear…
The theory of quantum gravity is aimed to fuse general relativity with quantum theory into a more fundamental framework. The space of quantum gravity provides both the non-fixed causality of general relativity and the quantum uncertainty of…
Given are a first principles derivation and formulation of the probabilistic concepts that underly equilibrium quantum statistical mechanics. The transition to non-equilibrium probability is traversed briefly.
These lecture notes are an informal introduction to the theory of computational complexity and its links to quantum computing and statistical mechanics.
A heuristic derivation of quantum mechanics using information theory requires a foundational physical principle: the existence of a universal action reservoir, analogous to the energy reservoir of a canonical ensemble.
We give a non-technical introduction of the basic concepts of Quantum Information Theory along the distinction between possible and impossible machines. We then proceed to describe the mathematical framework of Quantum Information Theory.…
Quantum superposition, a cornerstone of quantum mechanics, enables systems to exist in multiple states simultaneously, giving rise to probabilistic outcomes. In quantum information science, conditional entropy has become a key metric for…
In one-dimensional case, it is shown that the basic principles of quantum mechanics are properties of the set of intermediate cardinality.
I give a brief introduction to many worlds or "no wavefunction collapse" quantum mechanics, suitable for non-specialists. I then discuss the origin of probability in such formulations, distinguishing between objective and subjective notions…
A common understanding of quantum mechanics (QM) among students and practical users is often plagued by a number of "myths", that is, widely accepted claims on which there is not really a general consensus among experts in foundations of…
We demonstrate that the concept of information offers a more complete description of complementarity than the traditional approach based on observables. We present the first experimental test of information complementarity for two-qubit…
In quantum mechanics, outcomes of measurements on a state have a probabilistic interpretation while the evolution of the state is treated deterministically. Here we show that one can also treat the evolution as being probabilistic in nature…
The concept of probability was prominent in the original foundations of quantum mechanics, and continues to be so today. Indeed, the controversies regarding objective and subjective interpretations of probability have again become active. I…
A succinct statement and justification of all the principles necessary to understand and evaluate interpretations of quantum mechanics is given. These principles provide strong constraints on interpretations. They imply the particle-like…
We discuss the notion of integrability in quantum mechanics. Starting from a review of some definitions commonly used in the literature, we propose a different set of criteria, leading to a classification of models in terms of different…
The geometry of Quantum Mechanics in the context of uncertainty and complementarity, and probability is explored. We extend the discussion of geometry of uncertainty relations in wider perspective. Also, we discuss the geometry of…