All Mutually Unbiased Product Bases in Dimension Six
Daniel McNulty, Stefan Weigert
TL;DR
This paper classifies all mutually unbiased product bases in dimension six, proving that a complete set of seven such bases cannot include a triple of product bases, thus advancing understanding of quantum state measurement structures.
Contribution
It provides a complete classification of mutually unbiased product bases in dimension six and proves limitations on their arrangements.
Findings
Existence of several continuous families of pairs and two triples of mutually unbiased product bases.
No quadruple of mutually unbiased product bases exists in dimension six.
A complete set of seven mutually unbiased bases cannot contain a triple of product bases.
Abstract
All mutually unbiased bases in dimension six consisting of product states only are constructed. Several continuous families of pairs and two triples of mutually unbiased product bases are found to exist but no quadruple. The exhaustive classification leads to a proof that a complete set of seven mutually unbiased bases, if it exists, cannot contain a triple of mutually unbiased product bases.
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Taxonomy
TopicsFinite Group Theory Research · Graph theory and applications · graph theory and CDMA systems