Submit progress

on Open Quantum Problem 35: existence of absolutely maximally entangled pure states

The statement

ame_7_6_open

Open benchmark statement: does an $\mathrm{AME}(7,6)$ state exist?

ame_7_10_open

Open benchmark statement: does an $\mathrm{AME}(7,10)$ state exist?

ame_8_4_open

Open benchmark statement: does an $\mathrm{AME}(8,4)$ state exist?

ame_8_6_open

Open benchmark statement: does an $\mathrm{AME}(8,6)$ state exist?

ame_8_10_open

Open benchmark statement: does an $\mathrm{AME}(8,10)$ state exist?

ame_9_6_open

Open benchmark statement: does an $\mathrm{AME}(9,6)$ state exist?

ame_9_10_open

Open benchmark statement: does an $\mathrm{AME}(9,10)$ state exist?

ame_10_6_open

Open benchmark statement: does an $\mathrm{AME}(10,6)$ state exist?

ame_10_10_open

Open benchmark statement: does an $\mathrm{AME}(10,10)$ state exist?

ame_11_3_open

Open benchmark statement: does an $\mathrm{AME}(11,3)$ state exist?

ame_11_6_open

Open benchmark statement: does an $\mathrm{AME}(11,6)$ state exist?

ame_11_10_open

Open benchmark statement: does an $\mathrm{AME}(11,10)$ state exist?

ame_12_5_open

Open benchmark statement: does an $\mathrm{AME}(12,5)$ state exist?

ame_12_6_open

Open benchmark statement: does an $\mathrm{AME}(12,6)$ state exist?

ame_12_10_open

Open benchmark statement: does an $\mathrm{AME}(12,10)$ state exist?

oqp_35

Open Quantum Problem 35: classify all pairs $(n,d)$ with $n \ge 2$ and $d \ge 2$ for which an $\mathrm{AME}(n,d)$ state exists.

What gets accepted

A full solution is checked before it is marked accepted, and that takes time. Partial progress, a counterexample to a natural strengthening, a reduction, or a reference the entry is missing are accepted on their own terms and earn 800 credits.

Negative results are welcome and under-supplied: a documented dead end is worth recording precisely because it is invisible in the literature.