Related papers: Optimal upper bound of entropic uncertainty relati…
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…
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 $et\ al.$…
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 analyze entropic uncertainty relations in a finite dimensional Hilbert space and derive several strong bounds for the sum of two entropies obtained in projective measurements with respect to any two orthogonal bases. We improve the…
The current study aims to examine uncertainty relations for measurements from generalized equiangular tight frames. Informationally overcomplete measurements are a valuable tool in quantum information processing, including tomography and…
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…
Entropic uncertainty relations $H(A)+H(B)\geqslant \gamma$ give a nonzero lower bound $\gamma$ to the sum of the Shannon entropies $H$ of the outcome probabilities of incompatible observables $A$ and $B$. They are better than the…
Given two orthornormal bases A and B, the basic form of the entropic uncertainty principle is stated in terms of the sum of the Shannon entropies of the probabilities of measuring A and B onto a given quantum state. State independent lower…
When an optimal measurement is made on a qubit and what we call an Unbiased Mixture of the resulting ensembles is taken, then the post measurement density matrix is shown to be related to the pre-measurement density matrix through a simple…
Uncertainty relations give upper bounds on the accuracy by which the outcomes of two incompatible measurements can be predicted. While established uncertainty relations apply to cases where the predictions are based on purely classical data…
One of the defining traits of quantum mechanics is the uncertainty principle which was originally expressed in terms of the standard deviation of two observables. Alternatively, it can be formulated using entropic measures, and can also be…
Various theories that aim at unifying gravity with quantum mechanics suggest modifications of the Heisenberg algebra for position and momentum. From the perspective of quantum mechanics, such modifications lead to new uncertainty relations…
We formulate some properties of a set of several mutually unbiased measurements. These properties are used for deriving entropic uncertainty relations. Applications of mutually unbiased measurements in entanglement detection are also…
Mutually unbiased bases (MUB) are an elusive discrete structure in Hilbert spaces. Many (complete sets of) MUB are group covariant, but little is known whether they can be sharply covariant in the sense that the generating groups can have…
We study mutually unbiased maximally entangled bases (MUMEB's) in bipartite system $\mathbb{C}^d\otimes\mathbb{C}^d (d \geq 3)$. We generalize the method to construct MUMEB's given in [16], by using any commutative ring $R$ with $d$…
The uncertainty of measurement on a quantum system can be reduced in presence of quantum memory [M. Berta et. al. Nature Phys. {\bf 6}, 659 (2010)]. By measurement on quantum memory, some information (non-classical information) is…
A set of $b$ mutually unbiased bases (MUBs) in $\mathbb{C}^d$ (for $d > 1$) comprises $bd$ vectors in $\mathbb{C}^d$, partitioned into $b$ orthogonal bases for $\mathbb{C}^d$ such that the pairwise angle between all vectors from distinct…
We study fine-grained uncertainty relations for several quantum measurements in a finite-dimensional Hilbert space. The proposed approach is based on exact calculation or estimation of the spectral norms of corresponding positive matrices.…
The mean king's problem with maximal mutually unbiased bases (MUB's) in general dimension d is investigated. It is shown that a solution of the problem exists if and only if the maximal number (d+1) of orthogonal Latin squares exists. This…
We construct inequalities between R\'{e}nyi entropy and the indexes of coincidence of probability distributions, based on which we obtain improved state-dependent entropic uncertainty relations for general symmetric informationally complete…