I wanted to evaluate a bipartite entanglement using von Neumann entropy. It's been said in some references that the von Neuman entropy can be defined by the symplectic eigenvalues of reduced density matrix of one subsystem. Now I have to know about symplectic eigenvalues.
Sounds like "symplectic eigenvalues" refers to the eigenvalues of a symplectic matrix. The latter refers to a square matrix, say 2n-by-2n M, which fulfills matrix equation
M^T J M = J, where J is also 2n-by-2n and has block structure J = [0 I_n ; -I_n 0]
(am using matlab notation here, can't do anything fancier) and I_n is n-by-n identity matrix. You have to google for some articles on these, they are not very much discussed in linear algebra books. Unless there is a recent one, correct me anyone if I'm wrong.
Hi, I think the attached links may be useful.
http://issnla2010.ba.cnr.it/Lecture/symplectic%20eigenvalue%20problem.pdf
https://www.ime.usp.br/~piccione/Downloads/LecturesIME.pdf
http://webzoom.freewebs.com/cvdegosson/symplectic%20group.pdf
http://planetmath.org/symplecticmatrix
http://www2.mpi-magdeburg.mpg.de/mpcsc/benner/pub/bf3.ps.gz
http://www.sciencedirect.com/science/article/pii/S0024379597100490
Entropy: A concept that is not a physical quantity
https://www.researchgate.net/publication/230554936_Entropy_A_concept_that_is_not_a_physical_quantity
- Badges
- Science topic
- Similar topics
- Mathematics