Spectra of phase point operators in odd prime dimensions and the extended Clifford group

Abstract

We analyse the role of the Extended Clifford group in classifying the spectra of phase point operators within the framework laid out by Gibbons et al for setting up Wigner distributions on discrete phase spaces based on finite fields. To do so we regard the set of all the discrete phase spaces as a symplectic vector space over the finite field. Auxiliary results include a derivation of the conjugacy classes of $\mathrm{ESL}(2,{\mathbb{F}}_N)$.

arXiv commentLatex, 19pages

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• Qutrit Magic State Distillation Tight in Some Directions
• Efficient simulatability of continuous-variable circuits with large Wigner negativity
• Qutrit and Ququint Magic States
• Quantum Advantage in Information Retrieval
• Magic State Distillation with the Ternary Golay Code
• Bipartite entangled stabilizer mutually unbiased bases as maximum cliques of Cayley graphs
• Wigner distributions for finite state systems without redundant phase point operators
• Contextual bound states for qudit magic state distillation
• Classical codes in quantum state space
• Covariant mutually unbiased bases
• Studies of symmetries that give special quantum states the "right to exist"
• Quantum Tomography and Schwinger's Picture of Quantum Mechanics
• The Interplay between Quantum Contextuality and Wigner Negativity
• Maximally symmetric stabilizer MUBs in even prime-power dimensions