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Volumn 80, Issue 3, 2009, Pages

Geometric measure of entanglement for symmetric states

Author keywords

[No Author keywords available]

Indexed keywords

GEOMETRIC MEASURES; HOMOGENEOUS POLYNOMIALS; MULTILINEAR FORMS; QUANTUM STATE; SPIN MODELS; SYMMETRIC STATE;

EID: 70349436052     PISSN: 10502947     EISSN: 10941622     Source Type: Journal    
DOI: 10.1103/PhysRevA.80.032324     Document Type: Article
Times cited : (134)

References (43)
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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).
    • 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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    • 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.
    • 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.
    • 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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