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

Author

Chai Wah Wu, Jul 16 2014

Keywords

• nonn

Comments

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.

Links

• 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.

Crossrefs

Cf. A245290, A229865.

Formula

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

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