01124nas a2200181 4500008004100000245005300041210005300094260001500147300001100162490000700173520063000180100001800810700001800828700002400846700002100870700001400891856003700905 2012 eng d00aRank Reduction for the Local Consistency Problem0 aRank Reduction for the Local Consistency Problem c2012/02/09 a0222020 v533 a We address the problem of how simple a solution can be for a given quantum
local consistency instance. More specifically, we investigate how small the
rank of the global density operator can be if the local constraints are known
to be compatible. We prove that any compatible local density operators can be
satisfied by a low rank global density operator. Then we study both fermionic
and bosonic versions of the N-representability problem as applications. After
applying the channel-state duality, we prove that any compatible local channels
can be obtained through a global quantum channel with small Kraus rank.
1 aChen, Jianxin1 aJi, Zhengfeng1 aKlyachko, Alexander1 aKribs, David, W.1 aZeng, Bei uhttp://arxiv.org/abs/1106.3235v2