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Unordered Tuples in Quantum Computation

It is well known that the C*-algebra of an ordered pair of qubits is M_2 (x) M_2. What about unordered pairs? We show in detail that M_3 (+) C is the C*-algebra of an unordered pair of qubits. Then we use Schur-Weyl duality to characterize the C*-algebra of an unordered n-tuple of d-level quantum systems. Using some further elementary representation theory and number theory, we characterize the quantum cycles. We finish with a characterization of the von Neumann algebra for unordered words.

preprint2015arXivOpen access
Robert FurberBas Westerbaan
math.QA
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Robert FurberBas Westerbaan

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