Quantum computation and quantum information
Quantum computation and quantum information
A Free Object in Quantum Information Theory
Electronic Notes in Theoretical Computer Science (ENTCS)
How to Randomly Flip a Quantum Bit
Electronic Notes in Theoretical Computer Science (ENTCS)
Classical Representations of Qubit Channels
Electronic Notes in Theoretical Computer Science (ENTCS)
Teleportation with an imperfect state
Theoretical Computer Science
| Hi-index | 0.00 |
We answer a question posed by Martin et al. at MFPS XXVI in the affirmative: the free affine monoid over a finite involution group has a quantum representation, in addition to the classical representation already shown to exist in [Martin, K., J. Feng, and S. Krishnan. A Free Object in Quantum Information Theory. Electronic Notes in Theoretical Computer Science 267 (2010), 35-47]. In particular, this implies that in every dimension there are non-trivial classes of quantum channels that have classical representations which were not present in the lower dimensions. En route to establishing this result, we give two characterizations of the diagonal n-qubit channels (one of which is stated in [Bourdon, P.S, and H.T. Williams, Unital quantum operations on the Bloch ball and Bloch region, Phys. Rev. A. 69 (2004), 022314]) and necessary conditions for a Bloch matrix to satisfy.