Unordered Tuples in Quantum Computation

Robert Furber
(Radboud Universiteit Nijmegen)
Bas Westerbaan
(Radboud Universiteit Nijmegen)

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.

In Chris Heunen, Peter Selinger and Jamie Vicary: Proceedings of the 12th International Workshop on Quantum Physics and Logic (QPL 2015), Oxford, U.K., July 15-17, 2015, Electronic Proceedings in Theoretical Computer Science 195, pp. 196–207.
Published: 4th November 2015.

ArXived at: http://dx.doi.org/10.4204/EPTCS.195.15 bibtex PDF
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