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|Computes the s(k)-norm of a vector|
|Other toolboxes required||none|
|Related functions|| KyFanNorm|
|Usable within CVX?||no|
- VEC: A vector living in bipartite space.
- K (optional, default 1): A positive integer.
- DIM (optional, by default has both subsystems of equal dimension): A 1-by-2 vector containing the dimensions of the subsystems that VEC lives on.
Sum of squares of eigenvalues of reduced density matrix
The square of the s(k)-vector norm is equal to the Ky Fan k-norm of the vector's reduced density matrix:
>> v = RandomStateVector(9); >> [SkVectorNorm(v,1)^2, KyFanNorm(PartialTrace(v*v'),1)] ans = 0.7754 0.7754 >> [SkVectorNorm(v,2)^2, KyFanNorm(PartialTrace(v*v'),2)] ans = 0.9333 0.9333 >> [SkVectorNorm(v,3)^2, KyFanNorm(PartialTrace(v*v'),3)] ans = 1.0000 1.0000
Click on "expand" to the right to view the MATLAB source code for this function.
- N. Johnston and D. W. Kribs. A Family of Norms With Applications in Quantum Information Theory. J. Math. Phys., 51:082202, 2010. E-print: arXiv:0909.3907 [quant-ph]