Chen Jianxin; Kribs David W.; Zeng Bei Univ Guelph Dept Math & Stat Guelph ON N1G 2W1 Canada. Chen Jianxin; Ji Zhengfeng; Kribs David W.; Zeng Bei Univ Waterloo Inst Quantum Comp Waterloo ON N2L 3G1 Canada. Ji Zhengfeng Chinese Acad Sci Inst Software State Key Lab Comp Sci Beijing Peoples R China. Klyachko Alexander Bilkent Univ Dept Math Ankara Turkey.
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. (C) 2012 American Institute of Physics. http://dx.doi.org/10.1063/1.3685644
English Abstract:
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. (C) 2012 American Institute of Physics. http://dx.doi.org/10.1063/1.3685644
Chen Jianxin,Ji Zhengfeng,Klyachko Alexander,et al. rank reduction for the local consistency problem[J]. JOURNAL OF MATHEMATICAL PHYSICS,2012-01-01,53(2):-.
