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numerical-shadow:generalizations:restricted-numerical-shadow:w-numerical-shadow

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numerical-shadow:generalizations:restricted-numerical-shadow:w-numerical-shadow [2018/10/08 08:59]
plewandowska
numerical-shadow:generalizations:restricted-numerical-shadow:w-numerical-shadow [2019/10/01 12:44] (current)
rkukulski
Line 8: Line 8:
 where $\mu(\psi)$ denotes the unique unitarily invariant (Fubini-Study) measure on the set where $\mu(\psi)$ denotes the unique unitarily invariant (Fubini-Study) measure on the set
 $$ $$
-\Omega=\{\ket{\psi} \in \mathbb{C}^d:​ \ket{\psi} = \frac{1}{\sqrt{d}} \bigotimes_{i=1}^d U_i \left( \ket{10\ldots 0} + \ket{01 \ldots 0} + \ldots + \ket{00 \ldots 1} \right), \;​\braket{\psi}{\psi}=1\},+\Omega=\{\ket{\psi} \in \mathbb{C}^{2^d}: \ket{\psi} = \frac{1}{\sqrt{d}} \bigotimes_{i=1}^d U_i \left( \ket{10\ldots 0} + \ket{01 \ldots 0} + \ldots + \ket{00 \ldots 1} \right)\},
 $$ $$
 where $U_i \in SU(2)$. where $U_i \in SU(2)$.
 +
 +===== Example =====
 +W entanglement numerical shadow of a unitary matrix [(:​puchala2012restricted)]
 +$$ 
 +U=\text{diag}\left( 1,​e^{\frac{2 \ii \pi }{3}}, e^{\frac{2 \ii \pi }{3}}, e^{-\frac{2 \ii \pi }{3}}, e^{\frac{2 \ii \pi }{3}}, e^{-\frac{2 \ii \pi }{3}}, e^{-\frac{2 \ii \pi }{3}}, 1 \right)
 +$$
 +
 +{{ :​numerical-shadow:​w_shadow.png?​nolink |}}
numerical-shadow/generalizations/restricted-numerical-shadow/w-numerical-shadow.1538989170.txt.gz · Last modified: 2018/10/08 08:59 by plewandowska