According to this wikipedia page the initial state in Deutsch–Jozsa algorithm is written as follows: $$|0\rangle^{\otimes n} |1\rangle$$

shouldn't it look like this?:

$$|0\rangle^{\otimes n} \otimes |1\rangle$$


1 Answer 1


This is just a convention. People tend to write $|01 \rangle$ instead of $|0 \rangle \otimes |1\rangle $, but they mean the same thing. In this case, $$ \overbrace{|0\rangle \otimes |0\rangle \otimes \cdots \otimes |0\rangle}^{n \ \ times} \otimes|1\rangle = |0\rangle^{\otimes n} \otimes |1\rangle = |0\rangle^{\otimes n} |1\rangle$$

So it is just a matter of notation.


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