Thats a unique idea.You should consider the following idea to enhance your idea so that it would impact uniquely: Unitary error bases generalize the Pauli matrices to higher dimensional systems. Two basic constructions of unitary error bases are known: An algebraic construction by Knill that yields nice error bases, and a combinatorial construction by rner that yields shift-and-multiply bases. An open problem posed by Schlingemann and rner relates these two constructions and asks whether each nice error basis is equivalent to a shift-and-multiply basis.  solve this problem and show that the ansr is negative. Hover,  find that nice error bases have more structure than one can anticipate from their definition. In particular,  show that nice error bases can be written in a form in which at least half of the matrix entries are 0.
['Andreas Klappenecker', 'Martin Rötteler']
I am writing a research paper on a idea On the monomiality of nice error bases
[{"from": "human", "value": "I am writing a research paper on a idea On the monomiality of nice error bases"}, {"from": "gpt", "value": "Thats a unique idea.You should consider the following idea to enhance your idea so that it would impact uniquely: Unitary error bases generalize the Pauli matrices to higher dimensional systems. Two basic constructions of unitary error bases are known: An algebraic construction by Knill that yields nice error bases, and a combinatorial construction by rner that yields shift-and-multiply bases. An open problem posed by Schlingemann and rner relates these two constructions and asks whether each nice error basis is equivalent to a shift-and-multiply basis.  solve this problem and show that the ansr is negative. Hover,  find that nice error bases have more structure than one can anticipate from their definition. In particular,  show that nice error bases can be written in a form in which at least half of the matrix entries are 0."}]