Mutually unbiased bases and trinary operator sets for N qutrits

Journal Article · Thu Jul 01 04:00:00 EDT 2004 · Physical Review. A

DOI:https://doi.org/10.1103/PhysRevA.70.012302· OSTI ID:20643874

Lawrence, Jay ^[1]

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1. Department of Physics and Astronomy, Dartmouth College, Hanover, New Hampshire 03755 (United States)

A compete orthonormal basis of N-qutrit unitary operators drawn from the Pauli group consists of the identity and 9{sup N}-1 traceless operators. The traceless ones partition into 3{sup N}+1 maximally commuting subsets (MCS's) of 3{sup N}-1 operators each, whose joint eigenbases are mutually unbiased. We prove that Pauli factor groups of order 3{sup N} are isomorphic to all MCS's and show how this result applies in specific cases. For two qutrits, the 80 traceless operators partition into 10 MCS's. We prove that 4 of the corresponding basis sets must be separable, while 6 must be totally entangled (and Bell-like). For three qutrits, 728 operators partition into 28 MCS's with less rigid structure, allowing for the coexistence of separable, partially entangled, and totally entangled (GHZ-like) bases. However a minimum of 16 GHZ-like bases must occur. Every basis state is described by an N-digit trinary number consisting of the eigenvalues of N observables constructed from the corresponding MCS.

• OSTI ID: 20643874
• Journal Information: Physical Review. A, Journal Name: Physical Review. A Journal Issue: 1 Vol. 70; ISSN 1050-2947; ISSN PLRAAN
• Country of Publication: United States
• Language: English

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