The aim of this paper is to establish a mathematical fundamental of complex duality quantum computers(CDQCs) acting on vector-states(pure states) and operator-states(mixed states),respectively.A CDQC consists of a com...The aim of this paper is to establish a mathematical fundamental of complex duality quantum computers(CDQCs) acting on vector-states(pure states) and operator-states(mixed states),respectively.A CDQC consists of a complex divider,a group of quantum gates represented by unitary operators,or quantum operations represented by completely positive and trace-preserving mappings,and a complex combiner.It is proved that the divider and the combiner of a CDQC are an isometry and a contraction,respectively.It is proved that the divider and the combiner of a CDQC acting on vector-states are dual,and in the finite dimensional case,it is proved that the divider and the combiner of a CDQC acting on operator-states(matrix-states) are also dual.Lastly,the loss of an input state passing through a CDQC is measured.展开更多
基金supported by the National Natural Science Foundation of China (Grant Nos. 10571113 and 11171197)the Fundamental Research Funds for the Central Universities (Grant No. GK201002006)
文摘The aim of this paper is to establish a mathematical fundamental of complex duality quantum computers(CDQCs) acting on vector-states(pure states) and operator-states(mixed states),respectively.A CDQC consists of a complex divider,a group of quantum gates represented by unitary operators,or quantum operations represented by completely positive and trace-preserving mappings,and a complex combiner.It is proved that the divider and the combiner of a CDQC are an isometry and a contraction,respectively.It is proved that the divider and the combiner of a CDQC acting on vector-states are dual,and in the finite dimensional case,it is proved that the divider and the combiner of a CDQC acting on operator-states(matrix-states) are also dual.Lastly,the loss of an input state passing through a CDQC is measured.
