Related papers: Entropic Uncertainty Relations in Quantum Physics
The well-known Robertson-Schr\"odinger uncertainty relations have state-dependent lower bounds which are trivial for certain states. We present a general approach to deriving tight state-independent uncertainty relations for qubit…
Quantum states can be subjected to classical measurements, whose incompatibility, or uncertainty, can be quantified by a comparison of certain entropies. There is a long history of such entropy inequalities between position and momentum.…
The uncertainty principle sets limit on our ability to predict the values of two incompatible observables measured on a quantum particle simultaneously. This principle can be stated in various forms. In quantum information theory, it is…
We study the commutation relations, uncertainty relations and spectra of position and momentum operators within the framework of quantum group % symmetric Heisenberg algebras and their (Bargmann-) Fock representations. As an effect of the…
We introduce two uncertainty relations based on the state-dependent norm of commutators, utilizing generalizations of the B\"ottcher-Wenzel inequality. The first relation is mathematically proven, while the second, tighter relation is…
The uncertainty relation reveals the intrinsic difference between the classical world and the quantum world. We investigate the quantum uncertainty relation of quantum channel in qubit systems. Under two general measurement bases, we first…
The uncertainty relation is one of the key ingredients of quantum theory. Despite the great efforts devoted to this subject, most of the variance-based uncertainty relations are state-dependent and suffering from the triviality problem of…
We discuss the relationship between entropic uncertainty relations and entanglement. We present two methods for deriving separability criteria in terms of entropic uncertainty relations. Especially we show how any entropic uncertainty…
Commutator-based entropic uncertainty relations in multidimensional position and momentum spaces are derived, twofold generalizing previous entropic uncertainty relations for one-mode states. They provide optimal lower bounds and imply the…
For the power-law quantum wave packet in configuration space, the variance of the position observable may be divergent. Accordingly, the information-entropic formulation of the uncertainty principle becomes more appropriate than the…
The entropic uncertainty principle as outlined by Maassen and Uffink for a pair of non-degenerate observables in a finite level qusystem is generalized here to the case of a pair of arbitrary quantum measurements. In particular, our result…
Coherence of a quantum state intrinsically depends on the choice of the reference basis. A natural question to ask is the following: if we use two or more incompatible reference bases, can~there be some trade-off relation between the…
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…
The Heisenberg uncertainty relation, together with Robertson's generalisation, serves as a fundamental concept in quantum mechanics, showing that noncommutative pairs of observables cannot be measured precisely. In this study, we explore…
The uncertainty principle is an important principle in quantum theory. Based on this principle, it is impossible to predict the measurement outcomes of two incompatible observables, simultaneously. Uncertainty principle basically is…
We give a bound to the precision in the estimation of a parameter in terms of the expectation value of an observable. It is an extension of the Cramer-Rao inequality and of the Heisenberg uncertainty relation, where the estimation precision…
Bohr and Heisenberg suggested that the thermodynamical quantities of temperature and energy are complementary in the same way as position and momentum in quantum mechanics. Roughly speaking, their idea was that a definite temperature can be…
Under the scenario of generalized measurements, it can be questioned how much of quantum uncertainty can be attributed to measuring device, independent of the uncertainty in the measured system. On the course to answer the question, we…
After Shannon, entropy becomes a fundamental quantity to describe not only uncertainity or chaos of a system but also information carried by the system. Shannon's important discovery is to give a mathematical expression of the mutual…
We explore the uncertainty relation for unitary operators in a new way and find two uncertainty equalities for unitary operators, which are minimized by any pure states. Additionally, we derive two sets of uncertainty inequalities that…