On the maximal dimension of a completely entangled subspace for finite level quantum systems
نویسنده
چکیده
LetHi be a finite dimensional complex Hilbert space of dimension di associated with a finite level quantum system Ai for i = i, 1, 2, . . . , k. A subspace S ⊂ H = HA1A2...Ak = H1 ⊗ H2 ⊗ . . . ⊗ Hk is said to be completely entangled if it has no nonzero product vector of the form u1 ⊗ u2 ⊗ . . . ⊗ uk with ui in Hi for each i. Using the methods of elementary linear algebra and the intersection theorem for projective varieties in basic algebraic geometry we prove that
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