Dienstag, 07.10.2025: Functional Inequalities in Open and Closed Quantum Systems: Continuity, Correlations and Applications
Paul Gondolf
I will begin the talk with a brief overview of four of the six projects I have pursued during my thesis, covering
quantum information theory, many-body physics, functional analysis, and semigroup theory. The focus will
then be on the fifth project, “Energy-Preserving Evolutions over Bosonic Systems”.
Motivated by experimental realisations of bosonic cat codes, which provide a hardware implementation of
partially self-correcting qubits, we aimed to better understand their mathematical underpinnings. In contrast to
Gaussian semigroups, whose generators are quadratic in annihilation and creation operators and have been
extensively studied from a mathematical perspective, cat codes and more generally higher-order polynomials
have received little attention. To address this gap, we build on and extend earlier work by Davies, who
generalised the GKSL form to unbounded operators to prove the semigroup generation theorems of Hille–
Yosida and Feller–Miyadera–Phillips, although only for an ambiguous extension of the original operator in
general.
In our setting, we not only relax the prior requirements of Davies’ scheme but also show that the semigroup is
generated by the original operator itself, provided this operator preserves the moments of the number
operator. Since this condition is relatively straightforward to verify, our framework applies both to Gaussian
semigroups, such as the quantum Ornstein–Uhlenbeck process, and to all but one multimode cat gate. Rather
than discussing these examples and the multimode extension in detail, however, I will highlight the
advantages of the framework beyond generation theory, particularly its use in perturbation bounds, where in
certain cases one can recover 1 -> 1 norm bounds known from the bounded setting.
The talk will conclude with an outlook and possible directions for future research.
| Uhrzeit: |
09:30 |
| Ort: |
B9N22 |
| Gruppe: |
Promotionsvortrag |
| Einladender: |
Capel, Lemm |
