Open AccessQuantum Entanglement Criterion for Rank of Block Matrix Vector Group Based on Density Matrix
Author(s) -
Guangrong Liu
Publication year - 2019
Publication title -
journal of physics. conference series
Language(s) - English
Resource type - Journals
SCImago Journal Rank - 0.21
H-Index - 85
eISSN - 1742-6596
pISSN - 1742-6588
DOI - 10.1088/1742-6596/1325/1/012137
Subject(s) - quantum entanglement , rank (graph theory) , density matrix , mathematics , quantum discord , matrix (chemical analysis) , quantum state , group (periodic table) , pure mathematics , state (computer science) , quantum mechanics , state vector , quantum , combinatorics , physics , algorithm , chemistry , chromatography
The determination of quantum state separability is the basic problem of quantum entanglement theory. By judging the rank of the matrix vector group formed by the density matrix block, the necessary and sufficient conditions for the separation of quantum pure States are given, and the necessary conditions for the separation of quantum mixed States are given, too. In the composite system 2 × 2, the rank of the vector group corresponding to the divisible pure state is 1, and the rank corresponding to the entangled state is 4.