Related papers: How complex is the quantum motion?
A short historical overview is given on the development of our knowledge of complex dynamical systems with special emphasis on ergodicity and chaos, and on the semiclassical quantization of integrable and chaotic systems. The general trace…
Why do quantum evolutions occur and why do they stop at certain points? In classical thermodynamics affinity was introduced to predict in which direction an irreversible process proceeds. In this paper the quantum mechanical counterpart of…
It is often stated that quantum mechanics only makes statistical predictions and that a quantum state is described by the various probability distributions associated with it. Can we describe a quantum state completely in terms of…
The intuition that a long history is required for the emergence of complexity in natural systems is formalized using the notion of depth. The depth of a system is defined in terms of the number of parallel computational steps needed to…
Depth is a complexity measure for natural systems of the kind studied in statistical physics and is defined in terms of computational complexity. Depth quantifies the length of the shortest parallel computation required to construct a…
Quantum mechanics is usually presented starting from a series of postulates about the mathematical framework. In this work we show that those same postulates can be derived by assuming that measurements are discrete interactions: that is,…
General Theory of Relativity and Quantum theory gives two different description of the same mother nature in the big and small scale respectively. Mathematical languages of these two theories are entirely different, one is geometric while…
Quantum machine learning (QML) holds promise for accelerating pattern recognition, optimization, and data analysis, but the conditions under which it can truly outperform classical approaches remain unclear. Existing research often…
The uncertainty of a quantum state is given by the composition of two components. The first is called the quantum component and is given by the probability distribution of an observable relative to the state. The second is the classical…
The interaction between two parts in a compound quantum system may be reconsidered more completely than before and some new understandings and conclusions different from current quantum mechanics are obtained, including the conservation law…
Using semiclassical methods, it is possible to construct very accurate approximations in the short wavelength limit of quantum dynamics that rely exclusively on classical dynamical input. For systems whose classical realization is strongly…
How useful is a quantum dynamical operation for quantum information processing? Motivated by this question we investigate several strength measures quantifying the resources intrinsic to a quantum operation. We develop a general theory of…
Universality of quantum mechanics -- its applicability to physical systems of quite different nature and scales -- indicates that quantum behavior can be a manifestation of general mathematical properties of systems containing…
We study the effects of dynamical imperfections in quantum computers. By considering an explicit example, we identify different regimes ranging from the low-frequency case, where the imperfections can be considered as static but with…
The notion of "closed systems" in Quantum Mechanics is discussed. For this purpose, we study two models of a quantum-mechanical system $P$ spatially far separated from the "rest of the universe" $Q$. Under reasonable assumptions on the…
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…
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 discuss a number of comments on quant-ph/9801061, and propose to introduce the concept of 'Causal Indistinguishability'. The incompatibility between Quantum Mechanics and Nonlocal Causality appears to be unavoidable: upholding of Quantum…
Quantum mechanics---the theory describing the fundamental workings of nature---is famously counterintuitive: it predicts that a particle can be in two places at the same time, and that two remote particles can be inextricably and…
Two major deviations from causality in the existing formulations of quantum mechanics, related respectively to quantum chaos and indeterminate wave reduction, are eliminated within the new, universal concept of dynamic complexity. The…