Related papers: Entropic Bounds For Unitary Testers and Mutually U…
We reformulate the notion of uncertainty of pairs of unitary operators within the context of guessing games and derive an entropic uncertainty relation for a pair of such operators. We show how distinguishable operators are compatible while…
Entropic uncertainty relations are powerful tools, especially in quantum cryptography. They typically bound the amount of uncertainty a third-party adversary may hold on a measurement outcome as a result of the measurement overlap. However,…
Even though mutually unbiased bases and entropic uncertainty relations play an important role in quantum cryptographic protocols they remain ill understood. Here, we construct special sets of up to 2n+1 mutually unbiased bases (MUBs) in…
Entropic uncertainty relations, based on sums of entropies of probability distributions arising from different measurements on a given pure state, can be seen as a generalization of the Heisenberg uncertainty relation that is in many cases…
We prove tight entropic uncertainty relations for a large number of mutually unbiased measurements. In particular, we show that a bound derived from the result by Maassen and Uffink for 2 such measurements can in fact be tight for up to…
Entropic uncertainty relations provide an information-theoretic framework for quantifying the fundamental indeterminacy inherent in quantum mechanics. We propose more stringent quantum-memory-assisted entropic uncertainty relations for…
We investigate entropic uncertainty relations for two or more binary measurements, for example spin-$\frac{1}{2}$ or polarisation measurements. We argue that the effective anti-commutators of these measurements, i.e. the anti-commutators…
We have obtained the optimal upper bound of entropic uncertainty relation for $N$ Mutually Unbiased Bases (MUBs). We have used the methods of variational calculus for the states that can be written in terms of $N$ MUBs. Our result is valid…
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 prove that given a computable metric space and two computable measures, the set of points that have high universal uniform test scores with respect to the first measure will have a lower bound with respect to the second measure. This…
We consider entropic uncertainty relations for outcomes of the measurements of a quantum state in 3 or more mutually unbiased bases (MUBs), chosen from the standard construction of MUBs in prime dimension. We show that, for any choice of 3…
We consider the notion of unitary transformations forming bases for subspaces of $M(d,\mathbb{C})$ such that the square of Hilbert-Schmidt inner product of matrices from the differing bases is a constant. Moving from the qubit case,…
Entanglement is not only the resource that fuels many quantum technologies but also plays a key role for some of the most profound open questions of fundamental physics. Experiments controlling quantum systems at the single quantum level…
Entropic uncertainty relations express the quantum mechanical uncertainty principle by quantifying uncertainty in terms of entropy. Central questions include the derivation of lower bounds on the total uncertainty for given observables, the…
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…
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…
We present the entropic uncertainty relations for multiple measurement settings in quantum mechanics. Those uncertainty relations are obtained for both cases with and without the presence of quantum memory. They take concise forms which can…
A set of mutually unbiased bases (MUBs) is said to be unextendible if there does not exist another basis that is unbiased with respect to the given set. Here, we prove the existence of smaller sets of MUBs in prime-squared dimensions…
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…
In [Berta 2014 Entanglement], uncertainty relations in the presence of quantum memory was formulated for mutually unbiased bases using conditional collision entropy. In this paper, we generalize their results to the mutually unbiased…