diff options
Diffstat (limited to 'source/know/concept/no-cloning-theorem')
| -rw-r--r-- | source/know/concept/no-cloning-theorem/index.md | 8 |
1 files changed, 4 insertions, 4 deletions
diff --git a/source/know/concept/no-cloning-theorem/index.md b/source/know/concept/no-cloning-theorem/index.md index 840a598..9c8b11d 100644 --- a/source/know/concept/no-cloning-theorem/index.md +++ b/source/know/concept/no-cloning-theorem/index.md @@ -30,14 +30,14 @@ $$\begin{aligned} \ket{0} \ket{?} \:\:\longrightarrow\:\: \ket{0} \ket{0} - \qquad \quad + \qquad \qquad \ket{1} \ket{?} \:\:\longrightarrow\:\: \ket{1} \ket{1} \end{aligned}$$ If we feed this machine a superposition $$\ket{\psi} = \alpha \ket{0} + \beta \ket{1}$$, -we *want* the following behaviour: +we *want* the following behavior: $$\begin{aligned} \Big( \alpha \ket{0} + \beta \ket{1} \Big) \ket{?} @@ -47,7 +47,7 @@ $$\begin{aligned} &= \Big( \alpha^2 \ket{0} \ket{0} + \alpha \beta \ket{0} \ket{1} + \alpha \beta \ket{1} \ket{0} + \beta^2 \ket{1} \ket{1} \Big) \end{aligned}$$ -Note the appearance of the cross terms with a factor of $$\alpha \beta$$. +Note the appearance of the cross-terms with a factor of $$\alpha \beta$$. The problem is that the fundamental linearity of quantum mechanics dictates different behaviour: @@ -59,7 +59,7 @@ $$\begin{aligned} \end{aligned}$$ This is clearly not the same as before: we have a contradiction, -which implies that such a general cloning machine cannot ever exist. +which implies that such a general cloning machine cannot exist. |