90010 Belfort Cedex, FR ... tiple qubits ¸½¼¸½½¸¾¼, representation theory and Jordan algebras for the black-hole/qubit correspondence¿¸ ¸ , and geometries ...
D4
D X P(H) = P X H X
X ∩ H ⊂ X D ! X " 2 × 2 × 2 × 2 # SLOCC D 4
15
4
4
! " # ! $%%&% # '( )
*" + ! , +
,
- .
/0 1 , ! #2 3 43%& ! -
'( )
5 )6 '7 8 1 ,6 89%:: # ; )
$
%
& ' ( # ) * + "#, ' , ' - SU(2) # ! , '
A − D − E . - % SU(2) A sl (C) x +x +···+x = 0 D so (C) x +x x +x +···+x = 0 E e x +x +x +···+x = 0 e x x + x + x + · · · + x = 0 E E e x +x +x +···+x = 0 * ADE / SU(2) !0 * 1 '
2 3 - / ADE 4 *
- 0 5 0 X - G 6 - P(g) X g 7
n
n+1
n
2n
2 2
n+1 1
n−1 1
6
6
4 1
7
7
3 1 2
8
8
5 1
2 k
2 1 2
3 2
2 3
2 3
3 2
3 2
2 k
2 k
2 3
2 3
2 k
2 k
-' ADE # 85 5 . , ' D ' - so(8) 2 D 3 / ) SO(4) × SO(4) ⊂ SO(8) M (C) " ,'