Summary: Maximal vectors in Hilbert space
and quantum entanglement
Quantum Information Theory is quantum mechanics in matrix
algebras - the algebras B(H) with H finite dimensional. I'll stay
in that context for this talk; but much of the following discussion
generalizes naturally to infinite dimensional Hilbert spaces.
We discuss separability of states, entanglement of states, and
propose a numerical measure of entanglement in an abstract
context. Then we apply that to compute maximally entangled
vectors and states of tensor products H = H1 · · · HN.
Not discussed: the physics of entanglement, how/why it is a
resource for quantum computing, the EPR paradox, Bell's