For n≥3, the n-qubit Pauli group has no nonconstant Boolean-valued frame functions on stabiliser states, while the underlying symplectic theory admits exactly the linear and quadratic-refinement families, completing the classification of binary affine-symplectic Cameron-Liebler sets.
An algebraically closed family of informational n-qubit purity invariants
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abstract
We present a family of quadratics in Pauli expectation values, and prove that they constitute state-independent invariants for all n-qubit pure states. This family generalises the two-qubit `pentagon identities', discovered in the reconstruction programme of [P. A. H\"ohn, Quantum 1, 38 (2017), P. A. H\"ohn and C. S. P. Wever, Phys. Rev. A 95, 012102 (2017)], where they characterise the space of pure states, as well as the unitary group, and are interpreted as complementarity equalities in the Brukner-Zeilinger information measure. The generalisation to arbitrarily many qubits is nontrivial as it requires new tools which in turn reveal novel structural properties that are absent in the two-qubit case. A thorough analysis of these properties, and their relation with mutual unbiasedness and complementarity in the n-qubit Pauli group, can be found in two companion papers.
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Contextuality in the $n$-qubit Pauli group
For n≥3, the n-qubit Pauli group has no nonconstant Boolean-valued frame functions on stabiliser states, while the underlying symplectic theory admits exactly the linear and quadratic-refinement families, completing the classification of binary affine-symplectic Cameron-Liebler sets.