306 citations · 1.4k across the 39 of their papers we have counts for
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A refinement of Reznick's Positivstellensatz with applications to quantum information theory
Alexander Müller-Hermes, Ion Nechita, David Reeb
In his solution of Hilbert's 17th problem Artin showed that any positive definite polynomial in several variables can be written as the quotient of two sums of squares. Later Rezni…
Bounds on Information Combining With Quantum Side Information
Christoph Hirche, David Reeb
"Bounds on information combining" are entropic inequalities that determine how the information (entropy) of a set of random variables can change when these are combined in certain…
Fundamental energy cost for quantum measurement
Kais Abdelkhalek, Yoshifumi Nakata, David Reeb
Measurements and feedback are essential in the control of any device operating at the quantum scale and exploiting the features of quantum physics. As the number of quantum compone…
Measurement Uncertainty for Finite Quantum Observables
René Schwonnek, David Reeb, Reinhard F. Werner
Measurement uncertainty relations are lower bounds on the errors of any approximate joint measurement of two or more quantum observables. The aim of this paper is to provide method…
Monotonicity of the Quantum Relative Entropy Under Positive Maps
Alexander Müller-Hermes, David Reeb
We prove that the quantum relative entropy decreases monotonically under the application of any positive trace-preserving linear map, for underlying separable Hilbert spaces. This…
Positivity of linear maps under tensor powers
Alexander Müller-Hermes, David Reeb, Michael M. Wolf
We investigate linear maps between matrix algebras that remain positive under tensor powers, i.e., under tensoring with copies of themselves. Completely positive and completely…