-
2
-
-
19944381927
-
-
review articles (2001) in Quant. Info. Comp. 1.
-
(2001)
Quant. Info. Comp.
, vol.1
-
-
-
8
-
-
19944420508
-
-
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
-
-
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.
-
-
-
-
10
-
-
3943078830
-
-
The enjoyable word "onion" can be seen in A. Acín, D. Bruß, M. Lewenstein, and A. Sanpera (2001), Phys. Rev. Lett. 87, 040401, although their picture was drawn for mixed states.
-
(2001)
Phys. Rev. Lett.
, vol.87
, pp. 040401
-
-
Acín, A.1
Bruß, D.2
Lewenstein, M.3
Sanpera, A.4
-
11
-
-
14344280810
-
-
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
-
-
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
-
-
(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
-
-
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
-
-
note
-
3 so that it is separable (not genuine 4-partite entangled).
-
-
-
-
20
-
-
0347090644
-
-
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
-
-
-
22
-
-
0004057454
-
-
(Birkhäuser, Boston), Chapter 14
-
I.M. Gelfand, M.M. Kapranov, and A.V. Zelevinsky (1994), Discriminants, Resultants, and Multidimensional Determinants (Birkhäuser, Boston), Chapter 14.
-
(1994)
Discriminants, Resultants, and Multidimensional Determinants
-
-
Gelfand, I.M.1
Kapranov, M.M.2
Zelevinsky, A.V.3
-
24
-
-
0003094020
-
-
reprinted (Birkhäuser-Verlag, Basel)
-
reprinted (1953) in Gesammelte Abhandlungen (Birkhäuser-Verlag, Basel) 2, 9.
-
(1953)
Gesammelte Abhandlungen
, vol.2
, pp. 9
-
-
-
26
-
-
19944421126
-
-
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
-
-
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
-
-
-
-
29
-
-
0036577113
-
-
F. Verstraete, J. Dehaene, B. De Moor, and H. Verscheide (2002), Phys. Rev. A 65, 052112.
-
(2002)
Phys. Rev. A
, vol.65
, pp. 052112
-
-
Verstraete, F.1
Dehaene, J.2
De Moor, B.3
Verscheide, H.4
-
33
-
-
0034652055
-
-
n| is invariant up to sign under permutations of the parties.
-
(2000)
J. Mod. Opt.
, vol.47
, pp. 355
-
-
Vidal, G.1
-
34
-
-
0141782139
-
-
M. Lewenstein, B. Kraus, J.I. Cirac, and P. Horodecki (2000), Phys. Rev. A 62, 052310;
-
(2000)
Phys. Rev. A
, vol.62
, pp. 052310
-
-
Lewenstein, M.1
Kraus, B.2
Cirac, J.I.3
Horodecki, P.4
-
36
-
-
19944373465
-
-
J.G. Luque and J.Y. Thibon (2002), quant-ph/0212069.
-
J.G. Luque and J.Y. Thibon (2002), quant-ph/0212069.
-
-
-
|