A245290 -id:A245290 - cp's OEIS frontend

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.

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

Offset: 1

Chai Wah Wu, Jul 16 2014

nonn

Since entanglement is not invariant under graph isomorphism, all 2^(n(2n-1))-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.

Chai Wah Wu, Conditions for separability in generalized Laplacian matrices and diagonally dominant matrices as density matrices, Physics Letters A, 351 (2006), 18-22.
Chai Wah Wu, Graphs whose normalized Laplacian matrices are separable as density matrices in quantum mechanics, arXiv:1407.5663 [quant-ph], 2014.

Cf. A245290, A229865.

A245290(n) + a(n) = 2^(n*(2*n-1))-1.

a(n) = 2^(n*(2*n-1))-2^(n*(n-1))*A229865(n).

cp's OEIS Frontend

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.

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