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70349424434
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A polynomial P is N -homogeneous if P (λx) = λN P (x).
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A polynomial P is N -homogeneous if P (λx) = λN P (x).
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Note that e and e□ are vectors with complex conjugated elements, i.e., e= er +i ei and e□ = er -i ei where er, ei □ Rk. Hence er, ei is an example for a real basis, being linearly independent since e ≡ e□. In fact, any real orthonormal basis of spanC (f1, f2, as long as they fulfill (iii).
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Note that e and e□ are vectors with complex conjugated elements, i.e., e= er +i ei and e□ = er -i ei where er, ei □ Rk. Hence er, ei is an example for a real basis, being linearly independent since e ≡ e□. In fact, any real orthonormal basis of spanC (f1, f2, as long as they fulfill (iii).
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35
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70349415345
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An example of a for four-qubit state where the maximizations over real and complex product vectors differ is |ψ□ = [| 0000 □ + | 0001 □ + | 0010 □ + | 0100 □ + | 1000 □ -2 (| 1110 □ + | 1101 □ + | 1011 □ + | 0111 □)] / 21.
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An example of a for four-qubit state where the maximizations over real and complex product vectors differ is |ψ□ = [| 0000 □ + | 0001 □ + | 0010 □ + | 0100 □ + | 1000 □ -2 (| 1110 □ + | 1101 □ + | 1011 □ + | 0111 □)] / 21.
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One can embed isometrically l1k (i.e., Rk with norm ∥□∥ 1) into Hk by a direct mapping into the diagonal. As c (N, l1k) = NN /N! for N≤k [17] and on the other hand c (N,E) ≤ NN /N! for any Banach space E, we have c (N, Hk) = NN /N! for N≤k.
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One can embed isometrically l1k (i.e., Rk with norm ∥ 1) into Hk by a direct mapping into the diagonal. As c (N, l1k) = NN /N! for N≤k [17] and on the other hand c (N,E) ≤ NN /N! for any Banach space E, we have c (N, Hk) = NN /N! for N≤k.
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