Codes of Maximal Distance and Highly Entangled Subspaces

Seminar date and time: 
Tuesday, 4 December, 2018 - 15:00
ICFO Barcelona
Felix Huber
GIQ Seminar Room (C5/262)

We present new bounds on the existence of quantum maximum distance separable 
codes (QMDS): the length n of all non-trivial QMDS codes with local dimension 
D and distance d is bounded by n ≤ D^2 + d − 2. We obtain their weight 
distribution by investigating families of QMDS codes, and present additional 
bounds that arise from Rains’ shadow inequalities. Our main result can be seen 
as a generalization of bounds that are known for the two special cases of 
stabilizer QMDS codes and absolutely maximally entangled states, and confirms 
the quantum MDS conjecture in the special case of distance-three codes. 
Because the existence of QMDS codes is directly linked to that of highly 
entangled subspaces (in which every vector has uniform r-body marginals) of 
maximal dimension, our methods directly carry over to address questions in 
multipartite entanglement.

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