# John B. DeBrotajdebrota

May 11 2017 14:59 UTC
Mar 27 2017 14:18 UTC
Mar 27 2017 02:00 UTC
The appearance of negative terms in quasiprobability representations of quantum theory is known to be inevitable, and, due to its equivalence with the onset of contextuality, of central interest in quantum computation and information. Until recently, however, nothing has been known about how much negativity is necessary in a quasiprobability representation. Zhu proved that the upper and lower bounds with respect to one type of negativity measure are saturated by quasiprobability representations which are in one-to-one correspondence with the elusive symmetric informationally complete quantum measurements (SICs). We define a family of negativity measures which includes Zhu's as a special case and consider another member of the family which we call "sum negativity." We prove a sufficient condition for local maxima in sum negativity and find exact global maxima in dimensions $3$ and $4$. Notably, we find that Zhu's result on the SICs does not generally extend to sum negativity, although the analogous result does hold in dimension $4$. Finally, the Hoggar lines in dimension $8$ make an appearance in a conjecture on sum negativity.
Jan 20 2017 17:16 UTC
Jan 20 2017 17:16 UTC
Jan 20 2017 17:15 UTC
Jan 20 2017 17:15 UTC
Jan 20 2017 17:15 UTC
Jan 20 2017 17:12 UTC
Jan 20 2017 16:55 UTC
John B. DeBrota scited SICs and Algebraic Number Theory
Sep 30 2016 02:00 UTC
This essay constitutes a review of the information geometric approach to renormalization developed in the recent works of Bény and Osborne as well as a detailed work-through of some of their contents. A noncommutative generalization of information geometry allows one to treat quantum state distinguishability in geometric terms with an intuitive empirical interpretation, allowing for an information theoretic prescription of renormalization which incorporates both the condensed matter and quantum field theoretic approaches.
Sep 13 2016 14:03 UTC
Sep 13 2016 14:03 UTC
Sep 13 2016 14:03 UTC
Sep 12 2016 14:30 UTC
John B. DeBrota scited Struggles with the Continuum
May 06 2016 15:45 UTC