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authorPrefetch2024-09-29 22:15:59 +0200
committerPrefetch2024-09-29 22:15:59 +0200
commitfda947364c33ea7f6273a7f3ad1e8898edbe1754 (patch)
tree2c393568e58c100b3fad465f23a17089eb3a06d7 /source/know/concept/no-cloning-theorem
parent766d05aac6f701fa85b7ceed1ce3a473a62cae55 (diff)
Improve knowledge base
Diffstat (limited to 'source/know/concept/no-cloning-theorem')
-rw-r--r--source/know/concept/no-cloning-theorem/index.md8
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.