Related papers: Uncertainty Relation for the Discrete Fourier Tran…
In this short note we show how the Generalised Uncertainty Principle (GUP) and the Extended Uncertainty Principle (EUP), two of the most common generalised uncertainty relations proposed in the quantum gravity literature, can be derived…
We analyze entropic uncertainty relations for two orthogonal measurements on a $N$-dimensional Hilbert space, performed in two generic bases. It is assumed that the unitary matrix $U$ relating both bases is distributed according to the Haar…
We derive a new memory-assisted entropic uncertainty relation for non-degenerate Hermitian observables where both quantum correlations, in the form of conditional von Neumann entropy, and quantum discord between system and memory play an…
The spread of the wave-function, or quantum uncertainty, is a key notion in quantum mechanics. At leading order, it is characterized by the quadratic moments of the position and momentum operators. These evolve and fluctuate independently…
The uncertainty principle is considered to be one of the most striking features in quantum mechanics. In the textbook literature, uncertainty relations usually refer to the preparation uncertainty which imposes a limitation on the spread of…
Conventional quantum uncertainty relations (URs) contain dispersions of two observables. Generalized URs are known which contain three or more dispersions. They are derived here starting with suitable generalized Cauchy inequalities. It is…
We formulate uncertainty relations for arbitrary finite number of incompatible observables. Based on the sum of variances of the observables, both Heisenberg-type and Schr\"{o}dinger-type uncertainty relations are provided. These new lower…
In this paper, we extend the coupled fractional Fourier transform of a complex valued functions to that of the quaternion valued functions on $\mathbb{R}^4$ and call it the quaternion coupled fractional Fourier transform (QCFrFT). We obtain…
Based on mixedness definition as M=1-tr(\r{ho}^2), we obtain a new variance-based uncertainty equality along with an inequality for Hermitian operators of a single-qubit system. The obtained uncertainty equality can be used as a measure of…
We present a general framework and procedure to derive uncertainty relations for observables of quantum systems in a covariant manner. All such relations are consequences of the positive semidefiniteness of the density matrix of a general…
In its original formulation, Heisenberg's uncertainty principle describes a trade-off relation between the error of a quantum measurement and the thereby induced disturbance on the measured object. However, this relation is not valid in…
Indirect measurement can be used to read out the outcome of a quantum system without resorting to a straightforward approach, and it is the foundation of the measurement uncertainty relations that explain the incompatibility of conjugate…
The example of nonpositive trace-class Hermitian operator for which Robertson-Schroedinger uncertainty relation is fulfilled is presented. The partial scaling criterion of separability of multimode continuous variable system is discussed in…
The uncertainty principle sets a bound on our ability to predict the measurement outcomes of two incompatible observables which are measured on a quantum particle simultaneously. In quantum information theory, the uncertainty principle can…
Quantum uncertainty relations impose fundamental limits on the joint knowledge that can be acquired from complementary observables: perfect knowledge of a quantum state in one basis implies maximal indetermination in all other mutually…
Uncertainty relations (URs) like the Heisenberg-Robertson or the time-energy UR are often considered to be hallmarks of quantum theory. Here, a simple derivation of these URs is presented based on a single classical inequality from…
For a pair of observables, they are called "incompatible", if and only if the commutator between them does not vanish, which represents one of the key features in quantum mechanics. The question is, how can we characterize the…
Thermodynamic uncertainty relations quantify how the signal-to-noise ratio of a given observable is constrained by dissipation. Fluctuation relations generalize the second law of thermodynamics to stochastic processes. We show that any…
We consider the uncertainty bound on the sum of variances of two incompatible observables in order to derive a corresponding steering inequality. Our steering criterion when applied to discrete variables yields the optimum steering range…
A new uncertainty relation (UR) is obtained for a system of N identical pure entangled particles if we use symmetrized observables when deriving the inequality. This new expression can be written in a form where we identify a term which…