Lauritz van Luijk
@lvanluijk.bsky.social
Reposted by Lauritz van Luijk
We're a group of fun, loving, and fun-loving people welcoming more :)
November 7, 2025 at 3:45 PM
We're a group of fun, loving, and fun-loving people welcoming more :)
The thesis is based on a series of works with my wonderful collaborators @stotti-alex.bsky.social, Reinhard Werner, and @arrr.de. I'm grateful for the wonderful time I had as a PhD student in Hanover!
October 13, 2025 at 9:01 AM
The thesis is based on a series of works with my wonderful collaborators @stotti-alex.bsky.social, Reinhard Werner, and @arrr.de. I'm grateful for the wonderful time I had as a PhD student in Hanover!
With Simon Becker, Niklas Galke and Robert Salzmann.
The paper is inspired by doi.org/10.1103/Phys..., where Burgarth et al show unexpectedly slow Trotter convergence rates of N^{-¼} for the Coulomb dynamics of certain states. We quantitatively link such slow rates to certain regularity properties.
The paper is inspired by doi.org/10.1103/Phys..., where Burgarth et al show unexpectedly slow Trotter convergence rates of N^{-¼} for the Coulomb dynamics of certain states. We quantitatively link such slow rates to certain regularity properties.
Strong error bounds for Trotter and strang-splittings and their implications for quantum chemistry
Efficient error estimates for the Trotter product formula are central in quantum computing, mathematical physics, and numerical simulations. However, the Trotter error's dependency on the input state ...
doi.org
October 1, 2025 at 1:29 PM
With Simon Becker, Niklas Galke and Robert Salzmann.
The paper is inspired by doi.org/10.1103/Phys..., where Burgarth et al show unexpectedly slow Trotter convergence rates of N^{-¼} for the Coulomb dynamics of certain states. We quantitatively link such slow rates to certain regularity properties.
The paper is inspired by doi.org/10.1103/Phys..., where Burgarth et al show unexpectedly slow Trotter convergence rates of N^{-¼} for the Coulomb dynamics of certain states. We quantitatively link such slow rates to certain regularity properties.
Main takeaway:
Haag duality and the uniqueness of purifications are equivalent, but not automatic in bipartite systems with infinitely many DoF. E.g., they can fail in certain bipartitions of topologically ordered systems.
Haag duality and the uniqueness of purifications are equivalent, but not automatic in bipartite systems with infinitely many DoF. E.g., they can fail in certain bipartitions of topologically ordered systems.
September 17, 2025 at 10:22 AM
Main takeaway:
Haag duality and the uniqueness of purifications are equivalent, but not automatic in bipartite systems with infinitely many DoF. E.g., they can fail in certain bipartitions of topologically ordered systems.
Haag duality and the uniqueness of purifications are equivalent, but not automatic in bipartite systems with infinitely many DoF. E.g., they can fail in certain bipartitions of topologically ordered systems.
By our result, the Uhlmann property must also fail. But can we understand this explicitly?
Yes: Creating a pair of anyons in the two cones leaves the B-marginal unchanged. With unitaries in A, the anyons can't be removed. The resulting states remain perfectly distinguishable from the ground state.
Yes: Creating a pair of anyons in the two cones leaves the B-marginal unchanged. With unitaries in A, the anyons can't be removed. The resulting states remain perfectly distinguishable from the ground state.
September 17, 2025 at 10:22 AM
By our result, the Uhlmann property must also fail. But can we understand this explicitly?
Yes: Creating a pair of anyons in the two cones leaves the B-marginal unchanged. With unitaries in A, the anyons can't be removed. The resulting states remain perfectly distinguishable from the ground state.
Yes: Creating a pair of anyons in the two cones leaves the B-marginal unchanged. With unitaries in A, the anyons can't be removed. The resulting states remain perfectly distinguishable from the ground state.
Example: The ground state sector of the surface code on an infinite square lattice. Let A be two disjoint cones, and let B be the complement (see below). Then tomography holds, but it was shown by P. Naaijkens in doi.org/10.1063/1.48... that Haag duality fails.
September 17, 2025 at 10:22 AM
Example: The ground state sector of the surface code on an infinite square lattice. Let A be two disjoint cones, and let B be the complement (see below). Then tomography holds, but it was shown by P. Naaijkens in doi.org/10.1063/1.48... that Haag duality fails.
For systems with finitely many DoF, all three are equivalent. In the general case, where subsystems are modeled by von Neumann factors on the full system’s Hilbert space, we prove:
Haag duality ⇔ Uhlmann property ⇒ tomography.
The converse to the second implication does not hold.
Haag duality ⇔ Uhlmann property ⇒ tomography.
The converse to the second implication does not hold.
September 17, 2025 at 10:22 AM
For systems with finitely many DoF, all three are equivalent. In the general case, where subsystems are modeled by von Neumann factors on the full system’s Hilbert space, we prove:
Haag duality ⇔ Uhlmann property ⇒ tomography.
The converse to the second implication does not hold.
Haag duality ⇔ Uhlmann property ⇒ tomography.
The converse to the second implication does not hold.
Uhlmann property: Pure states with equal A-marginals are connected by unitaries of Bob, up to arbitrarily small error. In other words: Purifications of A-states are unique, modulo their obvious symmetries.
September 17, 2025 at 10:22 AM
Uhlmann property: Pure states with equal A-marginals are connected by unitaries of Bob, up to arbitrarily small error. In other words: Purifications of A-states are unique, modulo their obvious symmetries.
A bipartite system is a system composed of two subsystems. We investigate three formalizations of what "composed of" means:
Tomography: States are uniquely determined by correlation experiments.
Haag duality: Observables belong to Alice if and only if they commute with all of Bob’s observables.
Tomography: States are uniquely determined by correlation experiments.
Haag duality: Observables belong to Alice if and only if they commute with all of Bob’s observables.
September 17, 2025 at 10:22 AM
A bipartite system is a system composed of two subsystems. We investigate three formalizations of what "composed of" means:
Tomography: States are uniquely determined by correlation experiments.
Haag duality: Observables belong to Alice if and only if they commute with all of Bob’s observables.
Tomography: States are uniquely determined by correlation experiments.
Haag duality: Observables belong to Alice if and only if they commute with all of Bob’s observables.
Reposted by Lauritz van Luijk
For the math folks on here: NSF has suspended Terry Tao's grant. www.nsf.gov/awardsearch/...
NSF Award Search: Award # 2347850
Structure theory for measure-preserving systems, additive combinatorics, and correlations of multiplicative functions
www.nsf.gov
July 31, 2025 at 10:44 PM
For the math folks on here: NSF has suspended Terry Tao's grant. www.nsf.gov/awardsearch/...