Schedule
All talks at Abels Utsikt (12th floor) on Niels Henrik Abels hus building, University of Oslo, Blindern campus
Monday
9:30–10:30 Lyudmila Turowska
Break
11:00–12:00 Francesca La Piana
Lunch Break
14:00–14:30 Ian Thompson
14:30–15:00 Zhao Zhang
Break
15:30–16:30 Josse van Dobben de Bruyn
Tuesday
9:30–10:30 Tim Netzer
Break
11:00–12:00 David Roberson
Lunch Break
14:00–15:00 Francisco Gutiérrez
Break
15:30–16:00 Nina Kiefer
16:00–17:00 Problem / discussion session
19:00– Workshop dinner
Wednesday
10:00–10:30 Björn Schäfer
Break
11:00–12:00 Alexander Müller–Hermes
Talks
Francisco Gutiérrez: Quantum query algorithms via completely bounded polynomials.
In this talk, we will start by introducing query complexity, a model of computing where rigorous separations between classical and quantum algorithms can be proven. For instance, Grover's and Shor's algorithms fall into this model. Later, we will revisit a connection between quantum query algorithms and completely bounded forms, proven via the Christensen-Sinclair factorization theorem. Motivated by this characterization, we will talk about three results we have proven during my PhD: 1) an alternative proof of the Christensen and Sinclair factorization theorem via semidefinite programming, 2) a particular case of the Aaronson and Ambainis conjecture of Fourier analysis, which in its 'final form' implies that exponential quantum-classical separations can only occur for certain 'structured' problems, 3) and an upper bound to the ℓ1 norm of the Fourier coefficients of quantum query algorithms, which establishes a limitation on the power of quantum query algorithms.
Jonas Eidesen: Quantum error correction: Projective error models, stabilizer codes, and Clifford codes.
We study error models corresponding to nice error bases, introduced by Knill (1996), and nice error frames, introduced by Chien and Waldron (2017), using the language of projective representation theory. If V is a finite dimensional Hilbert space, a projective error model on V is a pair (G, π) where G is a finite group and π is a projectively faithful irreducible projective representation of G on V . In this language we generalize the definitions of Clifford codes and stabilizer codes, the latter we call weak stabilizer codes. We give a group cohomological criteria to determine when a stabilizer code is non-trivial. For Clifford codes we give a description of the detectable errors in terms of the group L of logical operations of the code, and the group S of stabilizers of the code, generalizing results by Knill (1996), and Klappenecker and Rötteler (2002). In the special case where the projective error model (G, π) on V corresponds to a nice error basis, we are able to characterize the Clifford codes that are also weak stabilizer codes as precisely the Clifford codes for which |G| = |L| · |S|, generalizing results by Klappenecker and Rötteler (2004), and Nicolás, Martínez, and Grassl (2010). We also present infinite families of non-stabilizer Clifford codes, as well as infinite families of non-Clifford weak stabilizer codes.
Francesca La Piana
Alexander Müller-Hermes: Limit formulas for norms of tensor power operators and the problem of entanglement annihilation
I will explain some recent results on tensor powers of linear operators between Banach spaces and ordered vector spaces. In the setting of Banach spaces I will explain how tensor-stable contractions, i.e., operators for which all tensor powers are contractive when viewed as operators from the injective into the projective tensor product spaces, are characterized by the dual of the Hilbert space factorization norm. I will then review implications of this result for a related problem in the theory of ordered vector spaces and make a connection to long-standing open problems in quantum information theory. Joint work with Guillaume Aubrun and Francesca La Piana.
Tim Netzer: Spectrahedra, Operator Systems and Magic Squares
We explain how (free) spectrahedra, matrix convex sets and operator systems are related. We then focus on different types of magic squares as examples of such sets, and review some results on their classification.
David Roberson: Group Invariant Quantum Latin Squares
Quantum strategies for the graph isomorphism game are given by quantum permutation matrices whose entries are projections with every row/column summing to identity. Requiring that each of these projections has rank 1 (and replacing each projection with a unit vector that spans the space it projects onto) yields the special case of a quantum Latin square: a square of unit vectors where every row/column forms an orthonormal basis. If the input graphs for the graph isomorphism game are Cayley graphs, then any winning classical/quantum correlation for the game can be "regularized" to a group-invariant correlation, i.e., one where the probabilities depend only on the quotient of the two inputs and the quotient of the two outputs. This somewhat motivates the definition of group invariant quantum Latin squares (introduced in arXiv:2501.00196), where the rows and columns are indexed by finite group G and G' and the inner product of the (a,b)-entry and (c,d)-entry depends only on a-1c ∈ G and b-1d ∈ G'. We will see that, up to unitary equivalence, such quantum Latin squares are in bijective correspondence to the trace-preserving isomorphisms of the group algebras of G and G'. Moreover, in the abelian case, the convex hull of the quantum correlations produced by group invariant quantum Latin squares is a unitary transformation of the set of classical group invariant correlations. We will also discuss some further motivations/connections, and some open questions.
Lyudmila Turowska: Self-testing: an operator-algebraic approach
In contrast to classical physics, quantum states can be entangled—that is, linked in such a way that measurements performed on one particle are correlated with measurements on another, regardless of the distance between them. This phenomenon, known as Bell nonlocality, gives the appearance that one particle instantaneously influences the other. Previous work has shown that certain correlations can only be produced by preparing a specific entangled state and performing particular measurements.
Self-testing is a framework that aims to identify those correlations that uniquely determine both the quantum state and the measurements used to produce them, up to local isometries. Beyond its significance in Quantum Information Theory, self-testing has played a crucial role in developments in quantum complexity theory and in progress toward resolving Connes’ embedding problem, motivating its study within the context of operator algebras.
In this talk, I will review recent results on self-testing, with a particular focus on how they relate to questions concerning states on tensor products of associated C*-algebras. This talk is based on joint work with Jason Crann and Ivan G. Todorov.
Josse van Dobben de Bruyn: Mermin–Peres magic rectangles modulo odd primes
The Mermin–Peres square and similar examples show that a linear system over ℤ/2ℤ with no classical solutions can have an operator solution, paving the way for the rich theory of linear constraint system (LCS) games. LCS games over ℤ/2ℤ are quite well understood and have been used to prove deep results in QIT, including undecidability in nonlocal games and separations between correlation sets. By contrast, LCS games over ℤ/dℤ with d odd remain poorly understood, and no Mermin–Peres-like (finite-dimensional) pseudotelepathy scenarios are known in this setting. This problem has received considerable attention from researchers in nonlocal games, noncommutative constraint satisfaction problems, and contextuality, and it was recently conjectured by Chung, Okay and Sikora that no such examples exist. In this talk, I will use graph theory to explain why it is harder to get pseudotelepathy modulo odd numbers, and I will present the first known examples of Mermin–Peres-like magic rectangles with finite-dimensional operators of odd prime order. This talk is based on joint work with David Roberson and runs parallel to recent work of Slofstra and Zhang, who found the first such examples in the infinite-dimensional (quantum commuting) setting.
Nina Kiefer: Complete Classification of Quantum Graphs on M2
Over the past few years, the theory of quantum graphs has emerged as a field of growing interest. In 2022, Matsuda and Gromada have given concrete examples by classifying the undirected quantum graphs on the quantum space M2. Based on the solid theory of directed quantum graphs developed in 2024, it became possible to complete the classification of quantum graphs on M2 also in the directed case. We observe that there is a far bigger range of directed quantum graphs than of undirected quantum graphs on M2. This talk is based on a joint work with Björn Schäfer.
Björn Schäfer: Two Partitions of Unity
The universal C*-algebra generated by two projections can be described as algebra of continuous functions from [0,1] to M2. This was first observed by Pedersen and reflects Halmos' famous Two Projection Theorem. In this talk we present a class of C*-algebras generated by two partitions of unity associated to bipartite graphs. Besides classifying isomorphism in this class of C*-algebras, we present a generalization of Pedersen's/Halmos' theorem to higher dimensions.
Ian Thompson: The noncommutative Choquet boundary and approximation theory
A well-studied question in approximation theory is to investigate when convergence for a collection of continuous functions promotes to automatic convergence for a much broader class of functions. One such result of Šaškin provides an abstract characterization in terms of Choquet theory. Around 15 years ago, Arveson had proposed an extension to Šaškin's work in terms of noncommutative Choquet theory; describing when an operator system completely determines its generating C*-algebra. For this talk, I will discuss recent developments surrounding Arveson's conjecture as well as an application toward Cuntz-Pimsner C*-algebras. This is based on joint works with Raphaël Clouâtre and Adam Dor-On.
Zhao Zhang: Reconciling Translational Invariance and Hierarchy
Tensor networks are not only numerical tools for describing ground states of quantum many-body systems, but also conceptual aids for understanding their entanglement structures. The proper way to understand tensor networks themselves is through explicit examples of solvable ground states that they represent exactly. In fact, this has historically been how tensor networks for gapped ground states, such as the matrix product state (MPS) and the projected entangled paired state (PEPS), emerged as an elegant analytical framework from numerical techniques like the density matrix renormalization group. However, for gapless ground states, generically described by the multiscale entanglement renormalization ansatz (MERA), a corresponding exactly solvable model has so far been missing. This is because the hierarchical structure of MERA intrinsically breaks the translational invariance. We identify a condition for MERA to be compatible with translational invariance by examining equivalent networks of rank-3 tensors. The condition is satisfied by the previously constructed hierarchical tensor network for the Motzkin and Fredkin chains, which can be considered a non-unitary generalization to the MERA. The hierarchical TN description is complemented by a translationally invariant MPS alternative, which is used to derive the power-law decay of the correlation function and critical exponents of a $q$-deformation phase transition.