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We report on experimental studies on entanglement quantification and verification based on uncertainty relations for systems consisting of two qubits. The new proposed measure is shown to be invariant under local unitary transformations, by…
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…
We derive several entanglement criteria for bipartite continuous variable quantum systems based on the Shannon entropy. These criteria are more sensitive than those involving only second-order moments, and are equivalent to well-known…
Uncertainty relations lie at the very core of quantum mechanics, and form the cornerstone of essentially all quantum cryptographic applications. In particular, they play an important role in cryptographic protocols in the…
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…
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 improve the entropic uncertainty relations for position and momentum coarse-grained measurements. We derive the continuous, coarse-grained counterparts of the discrete uncertainty relations based on the concept of majorization. The…
We introduce a new information-theoretic formulation of quantum measurement uncertainty relations, based on the notion of relative entropy between measurement probabilities. In the case of a finite-dimensional system and for any approximate…
Uncertainty principle is one of the cornerstones of quantum theory. In the literature, there are two types of uncertainty relations, the operator form concerning the variances of physical observables and the entropy form related to entropic…
We introduce a complete set of complementary quantities in bipartite, two-dimensional systems. Complementarity then relates the quantitative entanglement measure concurrence which is a bipartite property to the single-particle quantum…
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…
Having the quantum correlations in a general bipartite state in mind, the information accessible by simultaneous measurement on both subsystems is shown never to exceed the information accessible by measurement on one subsystem, which, in…
We derive an exact uncertainty relation for arbitrary quantum states of finite-dimensional Hilbert spaces. For any given $k$-partition of a $d$-dimensional multipartite system, we introduce the total uncertainty as the sum of the…
We derive a classification and a measure of classical- and quantum-correlation of multipartite qubit, qutrit, and in general, $n$-level systems, in terms of SU$(n)$ representations of density matrices. We compare the measure for the case of…
Using the relative entropy of total correlation, we derive an expression relating the mutual information of $n$-partite pure states to the sum of the mutual informations and entropies of its marginals and analyze some of its implications.…
Quantum information-theoretic approach has been identified as a way to understand the foundations of quantum mechanics as early as 1950 due to Shannon. However there hasn't been enough advancement or rigorous development of the subject. In…
Uncertainty relations and quantum entanglement are pivotal concepts in quantum theory. Beyond their fundamental significance in shaping our understanding of the quantum world, they also underpin crucial applications in quantum information…
An entanglement measure for a bipartite quantum system is a state functional that vanishes on separable states and that does not increase under separable (local) operations. It is well-known that for pure states, essentially all…
We conjecture a new entropic uncertainty principle governing the entropy of complementary observations made on a system given side information in the form of quantum states, generalizing the entropic uncertainty relation of Maassen and…
We provide a generalized treatment of uncertainties, von Neumann entropy, and squeezing in entangled bipartite pure state of two-level atoms. We observe that when the bipartite state is entangled, though the von Neumann entropy of the…