id	author	title	date	pages	extension	mime	words	sentence	flesch	summary	cache	txt
ap-7656	Zhao, Hui; Liu, Yu-Qiu; Wang, Zhi-Xi; Fei, Shao-Ming	A note on entanglement classification for tripartite mixed states	2022	6	.pdf	application/pdf	4056	204	73	− T 1|23 2 ( ∑ pi|φi⟩⟨φi|)∥tr ≤ ∑ pi∥T 1|23 1 (|φi⟩⟨φi|) − T 1|23 2 (|φi⟩⟨φi|)∥tr, namely, ∥T 1|23 1 (ρ) − T 1|23 2 (ρ)∥tr ≤ √ 6. (2) If ρ = |φ⟩⟨φ| is 2|13 separable, we have |φ2|13⟩ = |φ2⟩ ⊗ |φ13⟩ ∈ H2 2 ⊗ H6 13, where H6 13 = H2 1 ⊗ H3 3 . For any mixed state ρ =∑ pi|φi⟩⟨φi| ∈ H2 1 ⊗H2 2 ⊗H3 3 , ∑ pi = 1, 0 < pi ≤ 1, we have: (1) If ρ is 1|23 separable, then ∥T 1|23 1 −T 1|23 2 ∥tr ≤ √ 6; (2) If ρ is 2|13 separable, then ∥T 2|13 1 −T 2|13 2 ∥tr ≤ √ 6; (3) If ρ is 3|12 separable, then ∥T 3|12 1 −T 3|12 2 ∥tr ≤ √ 3. Proof (1) If ρ = |φ⟩⟨φ| is 1|23 separable, we have |φ1|23⟩ = |φ1⟩ ⊗ |φ23⟩ ∈ H2 1 ⊗ H6 23, where H6 23 = H2 2 ⊗H3 3 .	cache/ap-7656.pdf	txt/ap-7656.txt