Magic informationally complete POVMs with permutations

Abstract

Eigenstates of permutation gates are either stabilizer states (for gates in the Pauli group) or magic states, thus allowing universal quantum computation [M. Planat and Rukhsan-Ul-Haq, Preprint 1701.06443]. We show in this paper that a subset of such magic states, when acting on the generalized Pauli group, define (asymmetric) informationally complete POVMs. Such IC-POVMs, investigated in dimensions $2$ to $12$, exhibit simple finite geometries in their projector products and, for dimensions $4$ and $8$ and $9$, relate to two-qubit, three-qubit and two-qutrit contextuality.

11 pages, 6 figures, 1 table, a few complements and corrections

References in corpus (8)

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Cited by in corpus (9)

• The SIC Question: History and State of Play
• Qutrit and Ququint Magic States
• Informationally complete characters for quark and lepton mixings
• The Poincaré half-plane for informationally complete POVMs
• Group geometrical axioms for magic states of quantum computing
• Quantum computation and measurements from an exotic space-time R4
• Quantum computing, Seifert surfaces and singular fibers
• Quantum computing with Bianchi groups
• Quantum Tomography and Schwinger's Picture of Quantum Mechanics