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We introduce a new information-theoretic formulation of quantum measurement uncertainty relations, based on the notion of relative entropy between measurement probabilities. In the case of a finite-dimensional system and for any approximate…
Heisenberg's uncertainty principle states that the position and momentum of a particle cannot be sharply determined simultaneously. Standard-deviation and entropic formulations capture the spread of the probability distribution but say…
In this essay, we argue that certain aspects of the measurement require revision in Quantum Gravity. Using entropic arguments, we propose that the number of measurement outcomes and the accuracy (or the range) of the measurement are limited…
In the history of quantum mechanics, various types of uncertainty relationships have been introduced to accommodate different operational meanings of Heisenberg uncertainty principle. We derive an optimized entropic uncertainty relation…
For a particle in a box, the operator $-i\partial_x$ is not self-adjoint and thus does not qualify as the physical momentum. As a result, in general the Ehrenfest theorem is violated. Based upon a recently developed new concept for a…
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 derive an optimal bound on the sum of entropic uncertainties of two or more observables when they are sequentially measured on the same ensemble of systems. This optimal bound is shown to be greater than or equal to the bounds derived in…
The idea to base the uncertainty relation for photons on the electromagnetic energy distribution in space enabled us to derive a sharp inequality that expresses the uncertainty relation [Phys. Rev. Lett. {\bf 108}, 140401 (2012)]. An…
In this article we examine a Generalized Uncertainty Principle which differs from the Heisenberg Uncertainty Principle by terms linear and quadratic in particle momenta, as proposed by the authors in an earlier paper. We show that this…
The Heisenberg uncertainty principle is one of the fundamental pillars of quantum mechanics and quantum field theory. It is normally introduced by postulating the commutation relations $[\hat{x}^i, \hat{p}^j] = i\hbar \delta^{ij}$. However,…
We derive new inequalities for the probabilities of projective measurements in mutually unbiased bases of a qudit system. These inequalities lead to wider ranges of validity and tighter bounds on entropic uncertainty inequalities previously…
We discuss the information entropy for a general open pointer-based simultaneous measurement and show how it is bound from below. This entropic uncertainty bound is a direct consequence of the structure of the entropy and can be obtained…
Quantum phase transitions are often embodied by the critical behavior of purely quantum quantities such as entanglement or quantum fluctuations. In critical regions, we underline a general scaling relation between the entanglement entropy…
Uncertainty relations provide fundamental limits on what can be said about the properties of quantum systems. For a quantum particle, the commutation relation of position and momentum observables entails Heisenberg's uncertainty relation. A…
The uncertainty principle is the most important feature of quantum mechanics, which can be called the heart of quantum mechanics. This principle sets a lower bound on the uncertainties of two incompatible measurement. In quantum information…
By applying the Heisenberg's uncertainty principle for a macroscopic quantum gas formed by gravitational waves an expression for the universal bound on the entropy proposed by Bekenstein for any system of maximum radius R and total energy E…
We prove a lower bound on the relative entropy between two finite-dimensional states in terms of their entropy difference and the dimension of the underlying space. The inequality is tight in the sense that equality can be attained for any…
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…
The $D$-dimensional harmonic system (i.e., a particle moving under the action of a quadratic potential) is, together with the hydrogenic system, the main prototype of the physics of multidimensional quantum systems. In this work we…
Quantum processes can exhibit scenarios beyond a fixed order of events. We propose information inequalities that, when violated, constitute sufficient conditions to certify quantum processes without a fixed causal order -- causally…