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

Operazione tra due matrice che risulta in una matrice più grande: \Huge \otimes

Si calcola nel seguente modo:

\begin{bmatrix} {\color{navy} 0} & {\color{blue} 1} \ {\color{dodgerblue} 2} & {\color{deepskyblue} 3} \ \end{bmatrix} \otimes \begin{bmatrix} {\color{darkred} 4} & {\color{red} 5}\ {\color{firebrick} 6} & {\color{indianred} 7} \end{bmatrix}

\begin{bmatrix} {\color{navy} 0} \cdot {\color{darkred} 4} & {\color{blue} 1} \cdot {\color{darkred} 4} & {\color{navy} 0} \cdot {\color{red} 5} & {\color{blue} 1} \cdot {\color{red} 5} \ {\color{dodgerblue} 2} \cdot {\color{darkred} 4} & {\color{deepskyblue} 3} \cdot {\color{darkred} 4} & {\color{dodgerblue} 2} \cdot {\color{red} 5} & {\color{deepskyblue} 3} \cdot {\color{red} 5} \ {\color{navy} 0} \cdot {\color{firebrick} 6} & {\color{blue} 1} \cdot {\color{firebrick} 6} & {\color{navy} 0} \cdot {\color{indianred} 7} & {\color{blue} 1} \cdot {\color{indianred} 7} \ {\color{dodgerblue} 2} \cdot {\color{firebrick} 6} & {\color{deepskyblue} 3} \cdot {\color{firebrick} 6} & {\color{dodgerblue} 2} \cdot {\color{indianred} 7} & {\color{deepskyblue} 3} \cdot {\color{indianred} 7} \ \end{bmatrix}

\begin{bmatrix} 0 & 4 & 0 & 5 \ 8 & 12 & 10 & 15 \ 0 & 6 & 0 & 7 \ 12 & 18 & 14 & 21 \end{bmatrix}

Rappresenta la combinazione di due o più qbit. \ket{0} \otimes \ket{1}

\ket{01}

\begin{bmatrix} 1 \ 0 \end{bmatrix} \otimes \begin{bmatrix} 0 \ 1 \end{bmatrix}

\begin{bmatrix} 0 \cdot 0 \ 1 \cdot 1 \ 0 \cdot 1 \ 0 \cdot 1 \end{bmatrix}

\begin{bmatrix} 0 \ 1 \ 0 \ 0 \end{bmatrix}