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Volumn 2, Issue SPEC. ISS., 2002, Pages 540-555

Multipartite entanglement and hyperdeterminants

Author keywords

Duality; Hyperdeterminant; Multipartite entanglement; Stochastic LOCC

Indexed keywords

ELECTRON ENERGY ANALYZERS; QUBITS; STOCHASTIC SYSTEMS;

EID: 0347269195     PISSN: 15337146     EISSN: None     Source Type: Journal    
DOI: None     Document Type: Article
Times cited : (70)

References (36)
  • 2
    • 19944381927 scopus 로고    scopus 로고
    • review articles (2001) in Quant. Info. Comp. 1.
    • (2001) Quant. Info. Comp. , vol.1
  • 8
    • 19944420508 scopus 로고    scopus 로고
    • note
    • SLOCC was tied to SL × SL in [4]. Since we treat |Ψ> as a ray, i.e., an unnormalized vector, we rather relate SLOCC to GL × GL.
  • 9
    • 19944395571 scopus 로고    scopus 로고
    • note
    • The local rank can be defined as the rank of the reduced density matrix traced out for all except one party. Note that this definition is applicable to the multipartite case.
  • 11
    • 14344280810 scopus 로고    scopus 로고
    • and references therein.
    • H.K. Lo and S. Popescu (2001), Phys. Rev. A 63, 022301; and references therein.
    • (2001) Phys. Rev. A , vol.63 , pp. 022301
    • Lo, H.K.1    Popescu, S.2
  • 12
    • 19944414372 scopus 로고    scopus 로고
    • quant-ph/0206111; to be published in
    • A. Miyake (2002), quant-ph/0206111; to be published in Phys. Rev. A.
    • (2002) Phys. Rev. A
    • Miyake, A.1
  • 16
    • 0003686930 scopus 로고
    • (Graduate Texts in Mathematics 133, Springer-Verlag, New York), However, no preliminary knowledge of algebraic geometry is required in the text
    • As an excellent textbook of algebraic geometry, e.g., J. Harris (1992), Algebraic Geometry: A First Course (Graduate Texts in Mathematics 133, Springer-Verlag, New York), However, no preliminary knowledge of algebraic geometry is required in the text.
    • (1992) Algebraic Geometry: A First Course
    • Harris, J.1
  • 17
    • 0035472193 scopus 로고    scopus 로고
    • and references therein
    • A. Miyake and M. Wadati (2001), Phys. Rev. A 64, 042317; and references therein.
    • (2001) Phys. Rev. A , vol.64 , pp. 042317
    • Miyake, A.1    Wadati, M.2
  • 18
    • 85111346742 scopus 로고    scopus 로고
    • note
    • 3 so that it is separable (not genuine 4-partite entangled).
  • 20
    • 0347090644 scopus 로고
    • reprinted Cambridge Univ. Press, London/New York
    • reprinted (1889) in his Collected Mathematical Papers (Cambridge Univ. Press, London/New York) 1, 80.
    • (1889) Collected Mathematical Papers , vol.1 , pp. 80
  • 24
    • 0003094020 scopus 로고
    • reprinted (Birkhäuser-Verlag, Basel)
    • reprinted (1953) in Gesammelte Abhandlungen (Birkhäuser-Verlag, Basel) 2, 9.
    • (1953) Gesammelte Abhandlungen , vol.2 , pp. 9
  • 26
    • 19944421126 scopus 로고    scopus 로고
    • note
    • If there exists a noninvertible local operation between SLOCC orbits, some of local ranks decrease. Note that the converse is generally not the case. However in our examples in Sec.4, we do find some noninvertible local operations for the decrease of local ranks.
  • 27
    • 19944411540 scopus 로고    scopus 로고
    • note
    • The tensor rank means the number of terms in the minimal decomposition of |Ψ> in Eq.(1) by separable states. It coincides with the local rank in the bipartite ease
  • 33
    • 0034652055 scopus 로고    scopus 로고
    • n| is invariant up to sign under permutations of the parties.
    • (2000) J. Mod. Opt. , vol.47 , pp. 355
    • Vidal, G.1
  • 36
    • 19944373465 scopus 로고    scopus 로고
    • J.G. Luque and J.Y. Thibon (2002), quant-ph/0212069.
    • J.G. Luque and J.Y. Thibon (2002), quant-ph/0212069.


* 이 정보는 Elsevier사의 SCOPUS DB에서 KISTI가 분석하여 추출한 것입니다.