Steve Flammia

Steve Flammiasflammia

Aug 11 2017 16:00 UTC
Steve Flammia scited Quantum Deconvolution
Aug 09 2017 19:20 UTC
Aug 08 2017 20:18 UTC
Aug 08 2017 20:17 UTC
Aug 07 2017 02:30 UTC
Steve Flammia scited A fermionic de Finetti theorem
Aug 04 2017 05:16 UTC
Aug 02 2017 05:43 UTC
Aug 01 2017 02:00 UTC
Algebraic number theory relates SIC-POVMs in dimension $d>3$ to those in dimension $d(d-2)$. We define a SIC in dimension $d(d-2)$ to be aligned to a SIC in dimension $d$ if and only if the squares of the overlap phases in dimension $d$ appear as a subset of the overlap phases in dimension $d(d-2)$ in a specified way. We give 19 (mostly numerical) examples of aligned SICs. We conjecture that given any SIC in dimension $d$ there exists an aligned SIC in dimension $d(d-2)$. In all our examples the aligned SIC has lower dimensional equiangular tight frames embedded in it. If $d$ is odd so that a natural tensor product structure exists, we prove that the individual vectors in the aligned SIC have a very special entanglement structure, and the existence of the embedded tight frames follows as a theorem. If $d-2$ is an odd prime number we prove that a complete set of mutually unbiased bases can be obtained by reducing an aligned SIC to this dimension.
Jul 24 2017 18:08 UTC
Jul 21 2017 15:08 UTC
Jul 21 2017 13:43 UTC

Actually, there is even earlier work that shows this result. In [arXiv:1109.6887][1], Magesan, Gambetta, and Emerson showed that for any Pauli channel the diamond distance to the identity is equal to the trace distance between the associated Choi states. They prefer to phrase their results in terms of the "average error rate", but this is just another name for the process infidelity, up to a scaling factor. Magesan's thesis contains a more readable proof, IMO.

[1]: https://arxiv.org/abs/1109.6887

Jul 21 2017 12:37 UTC
Jul 21 2017 12:36 UTC