A hyperdeterminant on fermionic Fock space

  • Frédéric Holweck

    Université Bourgogne Franche-Comté, Belfort Cedex, France
  • Luke Oeding

    Auburn University, USA
A hyperdeterminant on fermionic Fock space cover
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Twenty years ago, Cayley's hyperdeterminant, the degree four invariant of the polynomial ring , was popularized in modern physics as it separates genuine entanglement classes in the three-qubit Hilbert space and is connected to entropy formulas for special solutions of black holes. In this note, we compute the analogous invariant on the fermionic Fock space for , i.e., spin particles with four different locations, and show how this invariant projects to other well-known invariants in quantum information. We also give combinatorial interpretations of these formulas.

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Frédéric Holweck, Luke Oeding, A hyperdeterminant on fermionic Fock space. Ann. Inst. Henri Poincaré Comb. Phys. Interact. (2024), published online first

DOI 10.4171/AIHPD/187