Rostock 2019 – wissenschaftliches Programm
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Q: Fachverband Quantenoptik und Photonik
Q 27: Quantum Information (Concepts and Methods) II
Q 27.2: Vortrag
Mittwoch, 13. März 2019, 11:00–11:15, S HS 001 Chemie
Codes of Maximal Distance and Highly Entangled Subspaces — •Felix Huber1,2,3 and Markus Grassl4 — 1ICFO Barcelona, 08860 Castelldefels, Spain — 2Institute for Theoretical Physics, University of Cologne, 50937 Cologne, Germany — 3Theoretical Quantum Optics, University of Siegen, 57068 Siegen — 4Max Planck Institute for the Science of Light, 91058 Erlangen, Germany
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 ≤ D2 + 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.