Related papers: Entropic time-energy uncertainty relations: An alg…
We outline a new model in which generalised uncertainty relations, that govern the behaviour of microscopic world, and dark energy, that determines the large-scale evolution of the Universe, are intrinsically linked via the quantum…
Traditional thermodynamic trade-off relations usually apply to quantities that depend linearly on probability distributions. In contrast, many important information-theoretic measures, such as entropies, are nonlinear and therefore…
Strong and general entropic and geometric Heisenberg limits are obtained, for estimates of multiparameter unitary displacements in quantum metrology, such as the estimation of a magnetic field from the induced rotation of a probe state in…
A prominent formulation of the uncertainty principle identifies the fundamental quantum feature that no particle may be prepared with certain outcomes for both position and momentum measurements. Often the statistical uncertainties are…
Uncertainty relations for a pair of arbitrary measurements and for a single measurement are posed in the form of inequalities using the Renyi entropies. The formulation deals with discrete observables. Both the relations with…
Entropic uncertainty relations are powerful tools, especially in quantum cryptography. They typically bound the amount of uncertainty a third-party adversary may hold on a measurement outcome as a result of the measurement overlap. However,…
In this paper we show that the existence of a primarily discrete space-time may be a fruitful assumption from which we may develop a new approach of statistical thermodynamics in pre-relativistic conditions. The discreetness of space-time…
Several results of black holes thermodynamics can be considered as firmly founded and formulated in a very general manner. From this starting point we analyse in which way these results may give us the opportunity to gain a better…
Uncertainty relations play a central role in quantum mechanics. Entropic uncertainty relations in particular have gained significant importance within quantum information, providing the foundation for the security of many quantum…
Physical systems that power motion and create structure in a fixed amount of time dissipate energy and produce entropy. Whether living or synthetic, systems performing these dynamic functions must balance dissipation and speed. Here, we…
By collecting both quantum and gravitational principles, a space-time uncertainty relation $(\delta t)(\delta r)^{3}\geqslant\pi r^{2}l_{p}^{2}$ is derived. It can be used to facilitate the discussion of several profound questions, such as…
We consider the problem of guessing the realization of a random variable but under more general Tsallis' non-extensive entropic framework rather than the classical Maxwell-Boltzman-Gibbs-Shannon framework. We consider both the conditional…
In this paper we review various information-theoretic characterizations of the approach to equilibrium in biological systems. The replicator equation, evolutionary game theory, Markov processes and chemical reaction networks all describe…
We present a general approach to quantum entanglement and entropy that is based on algebras of observables and states thereon. In contrast to more standard treatments, Hilbert space is an emergent concept, appearing as a representation…
The emergence of a direction of time in statistical mechanics from an underlying time-reversal-invariant dynamics is explained by examining a simple model. The manner in which time-reversal symmetry is preserved and the role of initial…
The time energy uncertainty relation has been a controversial issue since the advent of quantum theory, with respect to appropriate formalisation, validity and possible meanings. A comprehensive account of the development of this subject up…
We consider the question of entropic uncertainty relations for prime power dimensions. In order to improve upon such uncertainty relations for higher dimensional quantum systems, we derive a tight lower bound amount of entropy for multiple…
We employ quantum relative entropy to establish the relation between the measurement uncertainty and its disturbance on a state in the presence (and absence) of quantum memory. For two incompatible observables, we present the…
Heisenberg's intuition was that there should be a tradeoff between measuring a particle's position with greater precision and disturbing its momentum. Recent formulations of this idea have focused on the question of how well two…
We extend the definition of algebraic entropy to semi-discrete (difference-differential) equations. Calculating the entropy for a number of integrable and non integrable systems, we show that its vanishing is a characteristic feature of…