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Daily Overview |
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CA2: Computer Algebra Location: D406 Session Chair: Anne Frühbis-Krüger Session Chair: Alheydis Geiger | |
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Matroid isomorphism games and quantum automorphisms TU Berlin, Germany Matroids admit many equivalent axiom systems to characterise them. The fact that bases, circuits, etc., can all define the same matroid means that invariants are preserved across these descriptions. For example, an automorphism preserving the circuit structure will necessarily preserve the bases as well. That is, the automorphism group with respect to circuits coincides with the automorphism group with respect to bases. We discuss whether this persists for the quantum analogues of isomorphism and automorphism, defined via non-local games. This framework comes from quantum information, where players' winning strategies correspond to isomorphisms of the underlying structures. In this generalisation, classical cryptomorphism breaks down: two classically non-isomorphic matroids can be quantum isomorphic with respect to bases but not with respect to circuits, for example. These quantum generalisations can be computed via non-commutative Gröbner basis computations, carried out using the computer algebra system OSCAR. We discuss algorithms and the limitations of this approach. | |
