A completely entangled subspace of maximal dimension
نویسنده
چکیده
Consider a tensor product H = H1⊗H2⊗· · ·⊗Hk of finite dimensional Hilbert spaces with dimension of Hi = di, 1 ≤ i ≤ k. Then the maximum dimension possible for a subspace of H with no non-zero product vector is known to be d1d2 . . . dk− (d1 +d2 + · · ·+dk)+k−1. We obtain an explicit example of a subspace of this kind. We determine the set of product vectors in its orthogonal complement and show that it has the minimum dimension possible for an unextendible product basis of not necessarily orthogonal product vectors.
منابع مشابه
On the maximal dimension of a completely entangled subspace for finite level quantum systems
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 t...
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تاریخ انتشار 2004