Related Experiment Video
Updated: Aug 6, 2025

Scalable Quantum Integrated Circuits on Superconducting Two-Dimensional Electron Gas Platform
Published on: August 2, 2019
Curvature-Dimension Conditions for Symmetric Quantum Markov Semigroups
Melchior Wirth1, Haonan Zhang1
1Institute of Science and Technology Austria (ISTA), Am Campus 1, 3400 Klosterneuburg, Austria.
Abstract:
Following up on the recent work on lower Ricci curvature bounds for quantum systems, we introduce two noncommutative versions of curvature-dimension bounds for symmetric quantum Markov semigroups over matrix algebras. Under suitable such curvature-dimension conditions, we prove a family of dimension-dependent functional inequalities, a version of the Bonnet-Myers theorem and concavity of entropy power in the noncommutative setting. We also provide examples satisfying certain curvature-dimension conditions, including Schur multipliers over matrix algebras, Herz-Schur multipliers over group algebras and generalized depolarizing semigroups.
Related Concept Videos
Gauss's Law: Cylindrical Symmetry
Symmetric Member in Bending
Routh-Hurwitz Criterion I
To apply the Routh-Hurwitz criterion, a Routh table is constructed. The table's rows are labeled with powers of the complex frequency variable s, starting from the...
Routh-Hurwitz Criterion II
The first scenario occurs when a singular zero appears in the first column of the Routh table. This situation creates a division by zero issues. To resolve this, a small positive or negative number, denoted as epsilon (∈), is substituted for the zero. The stability analysis proceeds by assuming a sign for ∈. If ∈ is positive, any sign change in the first...
Woodward–Hoffmann Selection Rules and Microscopic Reversibility
Curve Equations

