appunti-steffo/7 - Introduction to quantum information processing/1 - Concetti base/prodotto tensoriale.md

Operazione tra due tensore che risulta in un tensore di ordine superiore.

\Huge \otimes

Può essere vista come l'applicazione di un "pattern" moltiplicato: \left[ \begin{matrix} {\color{Gray} In} & {\color{Gray} Out_{\ket{0}}} & {\color{Gray} Out_{\ket{1}}} \ {\color{Gray} \ket{0}} & 0 & 1 \ {\color{Gray} \ket{1}} & 1 & 0 \ \end{matrix} \right] \otimes \left[ \begin{matrix} {\color{Gray} In} & {\color{Gray} Out_{\ket{0}}} & {\color{Gray} Out_{\ket{1}}} \ {\color{Gray} \ket{0}} & {\color{blue} 0} & {\color{green} 1} \ {\color{Gray} \ket{1}} & {\color{red} 2} & {\color{orange} 3} \ \end{matrix} \right] = \ \quad \ \left[ \begin{matrix} {\color{Gray} In} & {\color{Gray} Out_{\ket{00}}} & {\color{Gray} Out_{\ket{01}}} & {\color{Gray} Out_{\ket{10}}} & {\color{Gray} Out_{\ket{11}}} \ {\color{Gray} \ket{00}} & {\color{blue} 0} & {\color{blue} 0} & {\color{green} 0} & {\color{green} 1} \ {\color{Gray} \ket{01}} & {\color{blue} 0} & {\color{blue} 0} & {\color{green} 1} & {\color{green} 0} \ {\color{Gray} \ket{10}} & {\color{red} 0} & {\color{red} 2} & {\color{orange} 0} & {\color{orange} 3} \ {\color{Gray} \ket{11}} & {\color{red} 2} & {\color{red} 0} & {\color{orange} 3} & {\color{orange} 0} \ \end{matrix} \right]