Numerical Shadow

The web resource on numerical range and numerical shadow

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numerical-shadow:generalizations:restricted-numerical-shadow:ghz-numerical-shadow [2018/10/08 08:58]
numerical-shadow:generalizations:restricted-numerical-shadow:ghz-numerical-shadow [2019/10/01 12:45] (current)
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 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{2}} \bigotimes_{i=1}^d U_i \left( \ket{0}^{\otimes d} + \ket{1}^{\otimes d} \right), \;​\braket{\psi}{\psi}=1\},+\Omega=\{\ket{\psi} \in \mathbb{C}^{2^d}: \ket{\psi} = \frac{1}{\sqrt{2}} \bigotimes_{i=1}^d U_i \left( \ket{0}^{\otimes d} + \ket{1}^{\otimes d} \right)\},
 $$ $$
 where $U_i \in SU(2)$ where $U_i \in SU(2)$
 +===== Example =====
 +GHZ entangled 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:​ghz_shadow.png?​nolink |}}
numerical-shadow/generalizations/restricted-numerical-shadow/ghz-numerical-shadow.1538989114.txt.gz · Last modified: 2018/10/08 08:58 by plewandowska