Clifford covariance of Wigner functions, positive representation of Pauli measurement, and cohomology

22 Oct 2021  ·  Robert Raussendorf, Cihan Okay, Michael Zurel, Polina Feldmann ·

The scheme of quantum computation with magic states, and in particular the role of the Wigner function as an indicator of quantumness, motivate the question of when Clifford-covariant Wigner functions exist, and when Wigner functions exist that represent Pauli measurements positively. This question has been settled affirmatively for all odd dimensions... Here, we discuss the case of even dimension, for Wigner functions obtained from operator bases. We find that such Clifford-covariant Wigner functions do not exist in any even dimension, and furthermore, Pauli measurement cannot be positively represented by them in any even dimension whenever the number of qudits is n >= 2. read more

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Quantum Physics