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Volumn 78, Issue 6, 2008, Pages

Structural approximations to positive maps and entanglement-breaking channels

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[No Author keywords available]

Indexed keywords

OPTICAL PROJECTORS;

EID: 57649136859     PISSN: 10502947     EISSN: 10941622     Source Type: Journal    
DOI: 10.1103/PhysRevA.78.062105     Document Type: Article
Times cited : (91)

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    • For a general unitary symplectic invariant operator AΓ AJ, although it can happen [see Eq. 62].
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    • Note that P+ P+J =0= P+J P+, since Φ+ (1J) Φ+ =0, which implies [P+, P+J] =0. Also [P+J, FJ] = [P+, F]J =0, because F Φ+ = Φ+ . Finally, [F, FJ] ik = Ji,Jk - Ji,Jk =0 for any basis vector ik.
    • Note that P+ P+J =0= P+J P+, since Φ+ (1J) Φ+ =0, which implies [P+, P+J] =0. Also [P+J, FJ] = [P+, F]J =0, because F Φ+ = Φ+. Finally, [F, FJ] ik = Ji,Jk - Ji,Jk =0 for any basis vector ik.
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    • Observe that (P+ A A′ FB B′) T A′ B′ = (dB / dA) FA A′ P+ B B′ and analogously (P+ A A′ 1B B′) T A′ B′ = (1/ dA) FA A′ 1B B′, and (1A A′ FB B′) T A′ B′ = dB 1A A′ P+ B B′.
    • Observe that (P+ A A′ FB B′) T A′ B′ = (dB / dA) FA A′ P+ B B′ and analogously (P+ A A′ 1B B′) T A′ B′ = (1/ dA) FA A′ 1B B′, and (1A A′ FB B′) T A′ B′ = dB 1A A′ P+ B B′.
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    • The other possibilities give nothing new as (J1) P+ (J† 1) = P+J and, trivially, JJF J† J† =F.
    • The other possibilities give nothing new as (J1) P+ (J† 1) = P+J and, trivially, JJF J† J† =F.


* 이 정보는 Elsevier사의 SCOPUS DB에서 KISTI가 분석하여 추출한 것입니다.