2022 Winter Semester

During the 2022 winter semester, the seminar took place on Thursdays at 11:00 a.m. in the Josef Stefan lecture room (Faculty of Physics, Strudlhofgasse 4, 3rd floor, room 3329), generally in person if the situation reg. the COVID pandemic allowed this. 

Gauging quantum states with non-anomalous matrix product operator symmetries
Abstract: Gauging a global symmetry of a system amounts to introducing new degrees of freedom whose transformation rule makes the overall system observe a local symmetry. In quantum systems there can be obstructions to gauging a global symmetry. When this happens the symmetry is dubbed anomalous. Such obstructions are related to the fact that the global symmetry cannot be written as a tensor product of local operators. We study non-local symmetries that have an additional structure: they take the form of a matrix product operator (MPO). We exploit the tensor network structure of the MPOs to construct local operators from them satisfying the same group relations, that is, we are able to localize even anomalous MPOs. For non-anomalous MPOs, we use these local operators to explicitly gauge the MPO symmetry of a one-dimensional quantum state obtaining non-trivial gauged states. We show that our gauging procedure satisfies all the required properties as the standard on-site case does. We also show how this procedure is naturally represented in matrix product states protected by MPO symmetries. In the case of anomalous MPOs, we shed light on the obstructions to gauging these symmetries.

(date/time/location: 27.10.2022, 11:00, Josef Stefan lecture hall, Strudlhofgasse 4, 3rd floor, room 3329)

Tensor networks generating the same states
Abstract: In this talk I will review different scenarios where a state has two different natural tensor network descriptions. To understand the structure of these states, one has to be able to relate the two descriptions to each other. I will show how to derive such a relation for a restricted class of tensors.

(date/time/location: 03.11.2022, 11:45, Josef Stefan lecture hall, Strudlhofgasse 4, 3rd floor, room 3329)

Christopher Popp (University of Vienna)

Bound Entanglement of Bell Diagonal Pairs of Qudits
Abstract: For dimension d ≥ 3, a form of entanglement exists that is hard to detect and called bound entanglement due to the fact that such entangled states cannot be used for entanglement distillation. Up to this date, no efficient solution is known to differentiate bound entangled from separable states. We address and compare this problem named separability problem for a family of bipartite Bell diagonal qudits with special algebraic and geometric structures and applications in quantum information processing tasks in different dimensions. Using analytical and numerical methods, we successfully classify large shares of representative Bell diagonal PPT states for d = 3 and d=4. Via those representative states, we are able to estimate the volumes of separable and bound entangled states among PPT qudits. Comparing the structure of bound entangled states and their detectors, we find considerable differences in the detection capabilities for different dimensions and relate those to differences of the Euclidean geometry for qutrits (d = 3) and ququarts (d = 4). A detailed visual analysis of the set of separable Bell diagonal states in both dimensions allows a conjecture relating the group structure of Bell diagonal states of the analyzed family to necessary and sufficient mixing conditions for separable states.

Based on:
Almost complete solution for the NP-hard separability problem of Bell diagonal qutrits
(https://www.nature.com/articles/s41598-022-16225-z)
Bound Entanglement of Bell Diagonal Pairs of Qutrits and Ququarts: A Comparison
(https://arxiv.org/abs/2209.15267)

(date/time/location: 10.11.2022, 11:00, Josef Stefan lecture hall, Strudlhofgasse 4, 3rd floor, room 3329)

Martin Renner (University of Vienna)

Simulating qubit correlations with classical communication
Abstract: Bell's famous theorem shows that quantum correlations cannot be reproduced by local hidden variables. However, it is possible to simulate quantum entanglement when the parties are allowed to send some classical information. For the simplest case of projective measurements on two maximally entangled qubits, Toner and Bacon (Phys. Rev. Lett. 91, 187904, 2003) proved that already a single bit is sufficient. At the same time, all previously known protocols to simulate non-maximally entangled qubit pairs require more resources. Here, we improve these protocols and show that two weakly entangled qubits can be simulated with a single bit as well. We also study the case of positive operator-valued measurements (POVMs) and show that two bits are sufficient to simulate local POVMs on any entangled qubit pair. For the latter case, previously known protocols required an unbounded amount of communication in the worst case.

(date/time/location: 17.11.2022, 11:00, Josef Stefan lecture hall, Strudlhofgasse 4, 3rd floor, room 3329)

Bram Vanhecke (University of Vienna):

Some scaling methods for infinite tensor network calculations
Abstract: Finite size calculations for critical systems, be they performed by ED, MC or other, enjoy a generic and well understood scaling behaviour of the couplings and observables with respect to the system size. The ready availability and robustness of this 'scaling hypothesis' -with system size- has proven very practical and powerful. Tensor network calculations on the other hand may be performed in the thermodynamic limit, which is a nice feature but hinders direct application of the tried and tested finite size scaling methods. We will discuss some attempts at making an infinite tensor network equivalent of the old scaling hypothesis, for MPS, PEPS and bPEPS. We will show some of the benefits and shortcomings of this approach through some benchmark applications, and if time permits also an application to a critical QFT.

(date/time/location: 24.11.2022, 11:00, Josef Stefan lecture hall, Strudlhofgasse 4, 3rd floor, room 3329)

David Blanik (University of Vienna)

Topological Features of Electrodynamics on a Lattice
Abstract: I will introduce a somewhat novel approach to discretizing classical electrodynamics, based on the language of discrete differential forms. In this context I will discuss the interplay between the topology of the underlying discrete spacetime and gauge fixing of the path integral.
This talk is mainly based on work done by Derek Wise. (https://arxiv.org/abs/gr-qc/0510033)

(date/time/location: 15.12.2022, 11:00, Josef Stefan lecture hall, Strudlhofgasse 4, 3rd floor, room 3329)

Anna Francuz (University of Vienna)

Time evolution methods for 2D tensor network states
Abstract: In my talk, I will make a short overview of most common methods for simulating real time evolution using 2D tensor network states, focusing on the main challenges and trying to identify directions for improvement.

(date/time/location: 12.01.2023, 11:00, Josef Stefan lecture hall, Strudlhofgasse 4, 3rd floor, room 3329)

Mingru Yang (University of Vienna)

Detecting emergent conformal symmetry of 2+1D quantum Ising transition through a fuzzy sphere regularization
Abstract: In this talk, I will discuss a recent work on detecting emergent conformal symmetry at the 2+1D quantum Ising transition through the identification of the state-operator correspondence. By mapping the quantum Hamiltonian in a sphere to a long-range interacting fermionic chain through the lowest Landau level projection, the energy spectrum of a quite small system size agrees surprisingly well with the conformal bootstrapping data. This work might pave the way to study more complicated 3D CFT's.

Reference:
arXiv: 2210.13482, Wei Zhu, Chao Han, Emilie Huffman, Johannes S Hofmann, Yin-Chen He, Uncovering conformal symmetry in the 3D Ising transition: State-operator correspondence from a fuzzy sphere regularization.

(date/time/location: 19.11.2023, 11:00, Josef Stefan lecture hall, Strudlhofgasse 4, 3rd floor, room 3329)

Ilya Kull (University of Vienna)

Optimal bounds on the positivity of a matrix from a few moments
Abstract: I will discuss this paper by Gemma De las Cuevas, Tobias Fritz, and Tim Netzer, which deals with the problem of deciding whether a matrix M is positive semidefinite or not based on its m first moments: trace(M^k), k=1,...,m. This is relevant to the problem of determining whether a matrix-product operator is positive or not, as its low order moments can be computed efficiently.

(date/time/location: 26.01.2023, 11:00, Josef Stefan lecture hall, Strudlhofgasse 4, 3rd floor, room 3329)