Unordered Tuples in Quantum Computation
arXiv:1409.1020 · doi:10.4204/EPTCS.195.15
Abstract
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.
arXiv commentIn Proceedings QPL 2015, arXiv:1511.01181