# RepLAB: A Computational/Numerical Approach to Representation Theory

@article{Rosset2019RepLABAC, title={RepLAB: A Computational/Numerical Approach to Representation Theory}, author={Denis Rosset and Felipe Montealegre-Mora and Jean-Daniel Bancal}, journal={arXiv: Quantum Physics}, year={2019} }

We present a MATLAB/Octave toolbox to decompose finite dimensionial representations of compact groups. Surprisingly, little information about the group and the representation is needed to perform that task. We discuss applications to semidefinite programming.

## 6 Citations

Mutually unbiased bases and symmetric informationally complete measurements in Bell experiments

- PhysicsScience Advances
- 2021

The first example of an extremal point of the quantum set of correlations that admits physically inequivalent quantum realizations is presented, and the results elaborately demonstrate the foundational and practical relevance of the two most important discrete Hilbert space structures to the field of quantum nonlocality.

Certifying Numerical Decompositions of Compact Group Representations

- Computer Science, MathematicsArXiv
- 2021

A performant and rigorous algorithm for certifying that a matrix is close to being a projection onto an irreducible subspace of a given group representation, as well as a software implementation that can interface with RepLAB.

Mutually unbiased bases: polynomial optimization and symmetry

- Mathematics, Computer Science
- 2021

Sum-of-squares proofs for the (well-known) fact that there do not exist d+ 2 mutually unbiased bases in dimensions d = 2, 3, 4, 5, 6, 7, 8 are obtained.

Noncommutative polynomial optimization under symmetry

- Mathematics
- 2021

We present a general framework to exploit the symmetries present in the Navascués-PironioAćın semidefinite relaxations that approximate invariant noncommutative polynomial optimization problems. We…

Universal Approximation Under Constraints is Possible with Transformers

- Computer Science, MathematicsArXiv
- 2021

A quantitative constrained universal approximation theorem which guarantees that for any convex or non-convex compact set K and any continuous function f : R → K, there is a probabilistic transformer F̂ whose randomized outputs all lie in K and whose expected output uniformly approximates f .

Bounding and Simulating Contextual Correlations in Quantum Theory

- Computer Science
- 2020

The information cost of simulating contextuality is introduced, which quantifies the additional information required to simulate contextual correlations in either classical or quantum models, and it is shown that the simulation cost can be efficiently bounded using a variant of the hierarchy of semidefinite relaxations.

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