dorsal/arxiv
View SchemaMutually Unbiased Bases and Trinary Operator Sets for N Qutrits
| Authors | Jay Lawrence |
|---|---|
| Categories | |
| ArXiv ID | quant-ph/0403095 |
| URL | https://arxiv.org/abs/quant-ph/0403095 |
| DOI | 10.1103/PhysRevA.70.012302 |
| Journal | Phys. Rev. A 70, 012302 (2004) |
Abstract
A complete orthonormal basis of N-qutrit unitary operators drawn from the Pauli Group consists of the identity and 9^N-1 traceless operators. The traceless ones partition into 3^N+1 maximally commuting subsets (MCS's) of 3^N-1 operators each, whose joint eigenbases are mutually unbiased. We prove that Pauli factor groups of order 3^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.
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"abstract": "A complete orthonormal basis of N-qutrit unitary operators drawn from the\nPauli Group consists of the identity and 9^N-1 traceless operators. The\ntraceless ones partition into 3^N+1 maximally commuting subsets (MCS\u0027s) of\n3^N-1 operators each, whose joint eigenbases are mutually unbiased. We prove\nthat Pauli factor groups of order 3^N are isomorphic to all MCS\u0027s, and show how\nthis result applies in specific cases. For two qutrits, the 80 traceless\noperators partition into 10 MCS\u0027s. We prove that 4 of the corresponding basis\nsets must be separable, while 6 must be totally entangled (and Bell-like). For\nthree qutrits, 728 operators partition into 28 MCS\u0027s with less rigid structure\nallowing for the coexistence of separable, partially-entangled, and totally\nentangled (GHZ-like) bases. However, a minimum of 16 GHZ-like bases must occur.\nEvery basis state is described by an N-digit trinary number consisting of the\neigenvalues of N observables constructed from the corresponding MCS.",
"arxiv_id": "quant-ph/0403095",
"authors": [
"Jay Lawrence"
],
"categories": [
"quant-ph"
],
"doi": "10.1103/PhysRevA.70.012302",
"journal_ref": "Phys. Rev. A 70, 012302 (2004)",
"title": "Mutually Unbiased Bases and Trinary Operator Sets for N Qutrits",
"url": "https://arxiv.org/abs/quant-ph/0403095"
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