Papers โบ The Isomorphism of 3-Qubit Hadamards and Eโ
The Isomorphism of 3-Qubit Hadamards and Eโ
J. G. Moxness
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This paper presents several notable properties of the matrix ๐ shown to be related to the isomorphism between Hโ and Eโ. The most significant of these properties is that ๐.๐ is to rank 8 matrices what the golden ratio is to numbers. That is to say, the difference between it and its inverse is the identity element, albeit with a twist. Specifically, ๐.๐-(๐.๐)โปยน is the reverse identity matrix or standard involutory permutation matrix of rank 8. It has the same palindromic characteristic polynomial coefficients as the normalized 3-qubit Hadamard matrix with 8-bit binary basis states, which is known to be isomorphic to E8 through its (8,4) Hamming code.
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