Talks

This talk was about proving a superexponential decay of the Belavkin–Staszewski conditional mutual information for local, translation-invariant Gibbs states in one dimension at arbitrary positive temperature. By combining this result with a strengthened recovery bound, my collaborators and I constructed a matrix product operator approximation of these Gibbs states that achieves subpolynomial complexity in $N/\varepsilon$, where $N$ is the system size and $\varepsilon$ the reconstruction error in trace distance. Using local tomography combined with the MPO reconstruction, I then proposed an algorithm for reconstructing such Gibbs states from measurement data with runtime polynomial in $N/\varepsilon$.

The talk was about investigating semigroup evolutions in bosonic quantum systems, focusing on how to handle the mathematical complications that arise from unbounded creation and annihilation operators. Together with my coauthors we developed a framework using non-commutative Sobolev spaces and adapted generation theorems to make these quantum evolutions mathematically rigorous, with applications in perturbation analysis of quantum error correction codes.

The talk was about investigating semigroup evolutions in bosonic quantum systems, focusing on how to handle the mathematical complications that arise from unbounded creation and annihilation operators. Together with my coauthors we developed a framework using non-commutative Sobolev spaces and adapted generation theorems to make these quantum evolutions mathematically rigorous, with applications in perturbation analysis of quantum error correction codes.

This talk was about introducing the almost locally affine (ALAFF) method that we based on proofs by Alicki, Fannes, and Winter, to prove continuity bounds for various entropic quantities. As a proof of concept we applied the method to the Umegaki relative entropy, recovering known almost tight bounds and proving new continuity bounds. Then we examined the use of it on the Belavkin-Staszewski relative entropy, yielding novel explicit bounds for BS-conditional entropy, BS-mutual and BS-conditional mutual information.

This talk was about introducing the almost locally affine (ALAFF) method that we based on proofs by Alicki, Fannes, and Winter, to prove continuity bounds for various entropic quantities. As a proof of concept we applied the method to the Umegaki relative entropy, recovering known almost tight bounds and proving new continuity bounds. Then we examined the use of it on the Belavkin-Staszewski relative entropy, yielding novel explicit bounds for BS-conditional entropy, BS-mutual and BS-conditional mutual information.