Related papers: Uncertainty relations based on mutually unbiased m…
We derive strong variance-based uncertainty relations for arbitrary two and more unitary operators by re-examining the mathematical foundation of the uncertainty relation. This is achieved by strengthening the celebrated Cauchy-Schwarz…
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…
Characterization and certification of nonlocal correlations is one of the the central topics in quantum information theory. In this work, we develop the detection methods of entanglement and steering based on the universal uncertainty…
The entropic uncertainty principle in the form proven by Maassen and Uffink yields a fundamental inequality that is prominently used in many places all over the field of quantum information theory. In this work, we provide a family of…
We establish a general connection between entropic uncertainty relations, Einstein-Podolsky-Rosen steering, and joint measurability. Specifically, we construct steering inequalities from any entropic uncertainty relation, given that the…
Quantum mechanical uncertainty relations for position and momentum are expressed in the form of inequalities involving the Renyi entropies. The proof of these inequalities requires the use of the exact expression for the (p,q)-norm of the…
We address an information-theoretic approach to noise and disturbance in quantum measurements. Properties of corresponding probability distributions are characterized by means of both the R\'{e}nyi and Tsallis entropies. Related…
We consider two (natural) families of observables $O_k$ for systems with dimension $d=3,4,5$: the spin observables $S_x$, $S_y$ and $S_z$, and the observables that have mutually unbiased bases as eigenstates. We derive tight entropic…
The uncertainty relation for continuous variables due to Byalinicki-Birula and Mycielski expresses the complementarity between two $n$-uples of canonically conjugate variables $(x_1,x_2,\cdots x_n)$ and $(p_1,p_2,\cdots p_n)$ in terms of…
Measuring incomplete sets of mutually unbiased bases constitutes a sensible approach to the tomography of high-dimensional quantum systems. The unbiased nature of these bases optimizes the uncertainty hypervolume. However, imposing…
We utilize quantum superposition principle to establish the improvable upper and lower bounds on the stronger uncertainty relation, i.e., the "weighted-like" sum of the variances of observables. Our bounds include some free parameters which…
We analyze various uncertainty measures for spatial diffusion processes. In this manifestly non-quantum setting, we focus on the existence issue of complementary pairs whose joint dispersion measure has strictly positive lower bound.
In quantum mechanics, the variance-based Heisenberg-type uncertainty relations are a series of mathematical inequalities posing the fundamental limits on the achievable accuracy of the state preparations. In contrast, we construct and…
In this paper we derive a new quantum entropic uncertainty relation, bounding the conditional smooth quantum min entropy based on the result of a measurement using a two outcome POVM and the failure probability of a classical sampling…
The well-known Robertson-Schroedinger uncertainty relations miss an irreducible lower bound. This is widely attributed to the lower bound's state-dependence. Therefore, Abbott \emph{et al.} introduced a general approach to derive tight…
Entropic uncertainty relations demonstrate the intrinsic uncertainty of nature from an information-theory perspective. Recently, a quantum-memory-assisted entropic uncertainty relation for multiple measurements was proposed by Wu $et\ al.$…
An entropic approach to formulating uncertainty relations for the number-annihilation pair is considered. We construct some normal operator that traces the annihilation operator as well as commuting quadratures with a complete system of…
The uncertainty principle can be expressed in entropic terms, also taking into account the role of entanglement in reducing uncertainty. The information exclusion principle bounds instead the correlations that can exist between the outcomes…
In many areas of engineering and sciences, decision rules and control strategies are usually designed based on nominal values of relevant system parameters. To ensure that a control strategy or decision rule will work properly when the…
We introduce a new concept called as the mutual uncertainty between two observables in a given quantum state which enjoys similar features like the mutual information for two random variables. Further, we define the conditional uncertainty…