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The notions of error and disturbance appearing in quantum uncertainty relations are often quantified by the discrepancy of a physical quantity from its ideal value. However, these real and ideal values are not the outcomes of simultaneous…
We develop a unified, information theoretic interpretation of the number-phase complementarity that is applicable both to finite-dimensional (atomic) and infinite-dimensional (oscillator) systems. The relevant uncertainty principle is…
Non-relativistic quantum theory is derived from information codified into an appropriate statistical model. The basic assumption is that there is an irreducible uncertainty in the location of particles: positions constitute a configuration…
In this paper we look at a particular realization of Popper's thought experiment with correlated quantum particles and argue that, from the point of view of a nonlinear quantum physics and contrary to the orthodox interpretation,…
We introduce a novel notion of invariance feedback entropy to quantify the state information that is required by any controller that enforces a given subset of the state space to be invariant. We establish a number of elementary properties,…
Uncertainty relations play a significant role in drawing a line between classical physics and quantum physics. Since the introduction by Heisenberg, these relations have been considerably explored. However, the effect of quantum…
The uncertainty principle is one of the key concepts in quantum theory. This principle states that it is not possible to measure two incompatible observables simultaneously and accurately. In quantum information theory, the uncertainty…
Consideration of the von Neumann measurement process underlying interference experiments shows that the uncertainty in the incoming wave, responsible for its interference, translates during measurement into an uncertainty at the measuring…
An effective formalism is developed to handle decaying two-state systems. Herewith, observables of such systems can be described by a single operator in the Heisenberg picture. This allows for using the usual framework in quantum…
The principle of maximum entropy is a broadly applicable technique for computing a distribution with the least amount of information possible constrained to match empirical data, for instance, feature expectations. We seek to generalize…
This paper examines the statistical mechanical and thermodynamical consequences of variable phase-space volume element $h_I=\bigtriangleup x_i\bigtriangleup p_i$. Varying $h_I$ leads to variations in the amount of measured information of a…
The Heisenberg uncertainty relation, which links the uncertainties of the position and momentum of a particle, has an important footprint on the quantum behavior of a physical system. Analogous to this principle, we propose that…
The Principle of Maximum Entropy is a rigorous technique for estimating an unknown distribution given partial information while simultaneously minimizing bias. However, an important requirement for applying the principle is that the…
Recently it was shown in [New J. Phys. 8, 330 (2006)] that the three dimensional Heisenberg uncertainty principle might be signifficantly sharpened if the relevant quantum state describes the particle in a central potential. I extend that…
In a previous study, it was shown that the Generalized Uncertainty Principle (GUP) can be derived from non-extensive entropies, particularly those depending only on the probability, denoted as $S_\pm$ in the literature. This finding reveals…
We exhibit three inequalities involving quantum measurement, all of which are sharp and state independent. The first inequality bounds the performance of joint measurement. The second quantifies the trade-off between the measurement quality…
Occurrence of spacetime singularities is one of the peculiar features of Einstein gravity, signalling limitation on probing short distances in spacetime. This alludes to the existence of a fundamental length scale in nature. On contrary,…
This thesis discusses the possibility of uncertainty relations for space and energy given a state of fixed entropy. In particular, it discusses the results in the paper of Dam/Nguyen. There, the authors propose a lower bound for the mixed…
Uncertainty principles for concentration of signals into truncated subspaces are considered. The ``classic'' uncertainty principle is explored as a special case of a more general operator framework. The time-bandwidth concentration problem…
Uncertainty principle, a fundamental principle in quantum physics, has been studied intensively via various uncertainty inequalities. Here we derive an uncertainty equality in terms of linear entropy, and show that the sum of uncertainty in…