98 citations · 979 across the 73 of their papers we have counts for
7 papers · 1 filter
Non-commutative calculus, optimal transport and functional inequalities in dissipative quantum systems
Eric A. Carlen, Jan Maas
We study dynamical optimal transport metrics between density matrices associated to symmetric Dirichlet forms on finite-dimensional -algebras. Our setting covers arbitrary ske…
Recovery map stability for the Data Processing Inequality
Eric A. Carlen, Anna Vershynina
The Data Processing Inequality (DPI) says that the Umegaki relative entropy is non-increasing under the action of completely positive trace…
Gradient flow and entropy inequalities for quantum Markov semigroups with detailed balance
Eric A. Carlen, Jan Maas
We study a class of ergodic quantum Markov semigroups on finite-dimensional unital -algebras. These semigroups have a unique stationary state , and we are concerned with th…
Entropy and entanglement bounds for reduced density matrices of fermionic states
Eric A. Carlen, Elliott H. Lieb, Robin Reuvers
Unlike bosons, fermions always have a non-trivial entanglement. Intuitively, Slater determinantal states should be the least entangled states. To make this intuition precise we inv…
A Minkowski Type Trace Inequality and Strong Subadditivity of Quantum Entropy II: Convexity and Concavity
Eric A. Carlen, Elliott H. Lieb
We revisit and prove some convexity inequalities for trace functions conjectured in the earlier part I. The main functional considered is Φ_{p,q}(A_1,A_2,...,A_m) = (trace((\sum_{j…
A Minkowski Type Trace Inequality and Strong Subadditivity of Quantum Entropy
Eric A. Carlen, Elliott H. Lieb
We consider the following trace function on n-tuples of positive operators: Φ_p(A_1,A_2,...,A_n) = Trace (\sum_{j=1}^n A_j^p)^{1/p} and prove that it is jointly concave for 0<p\le…