

A245291


Number of normalized graph Laplacian matrices of nonempty labeled graphs of 2n vertices that are entangled in C^2 x C^n as density matrices in quantum mechanics.


2



0, 32, 27648, 258473984, 34924795002880, 73692421593384353792, 2475385863878910456755126272, 1329190247836700110425361699261382656, 11417938846687390120116281062224453749176270848, 1569274711573306070659025854469940650153499575743856771072
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OFFSET

1,2


COMMENTS

Since entanglement is not invariant under graph isomorphism, all 2^(n(2n1))1 nonzero Laplacian matrices are treated as different. A nonzero Laplacian matrix not equal to the complete graph is entangled in C^2 x C^n if and only if its complement is. Since the complete graph is not entangled, this means that a(n) is even for all n.


LINKS

Table of n, a(n) for n=1..10.
C. W. Wu, Conditions for separability in generalized Laplacian matrices and diagonally dominant matrices as density matrices, Physics Letters A, 351 (2006), 1822.
C. W. Wu, Graphs whose normalized Laplacian matrices are separable as density matrices in quantum mechanics, arXiv:1407.5663, 2014.


FORMULA

A245290(n) + A245291(n) = 2^(n*(2*n1))1.
A245291(n) = 2^(n*(2*n1))2^(n*(n1))*A229865(n).


CROSSREFS

Cf. A245290, A229865.
Sequence in context: A230914 A232596 A123393 * A016937 A074800 A320859
Adjacent sequences: A245288 A245289 A245290 * A245292 A245293 A245294


KEYWORD

nonn


AUTHOR

Chai Wah Wu, Jul 16 2014


STATUS

approved



