Unordered Tuples in Quantum Computation
Quantum Algebra
2015-11-06 v4
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.
Cite
@article{arxiv.1409.1020,
title = {Unordered Tuples in Quantum Computation},
author = {Robert Furber and Bas Westerbaan},
journal= {arXiv preprint arXiv:1409.1020},
year = {2015}
}
Comments
In Proceedings QPL 2015, arXiv:1511.01181