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The equality $G({\\bf a},{\\bf b})= 4[\\langle \\psi|P({\\bf a})\\otimes P({\\bf b})|\\psi\\rangle-\\langle \\psi|P({\\bf a})\\otimes{\\bf 1}|\\psi\\rangle\\langle \\psi|{\\bf 1}\\otimes P({\\bf b})|\\psi\\rangle]=0$ for any two projection operators $P({\\bf a})$ and $P({\\bf b})$ provides a necessary and sufficient separability criterion in the case of a separable pure state $\\rho=|\\psi\\rangle\\langle\\psi|$. 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Oh, Kazuo Fujikawa, Koichiro Umetsu, Sixia Yu","submitted_at":"2016-03-06T06:15:33Z","abstract_excerpt":"The practically useful criteria of separable states $\\rho=\\sum_{k}w_{k}\\rho_{k}$ in $d=2\\times2$ are discussed. The equality $G({\\bf a},{\\bf b})= 4[\\langle \\psi|P({\\bf a})\\otimes P({\\bf b})|\\psi\\rangle-\\langle \\psi|P({\\bf a})\\otimes{\\bf 1}|\\psi\\rangle\\langle \\psi|{\\bf 1}\\otimes P({\\bf b})|\\psi\\rangle]=0$ for any two projection operators $P({\\bf a})$ and $P({\\bf b})$ provides a necessary and sufficient separability criterion in the case of a separable pure state $\\rho=|\\psi\\rangle\\langle\\psi|$. 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