## How can I invert the least significant bit of a certain term of a superposed state?

3

Say I have

$$\dfrac{1}{\sqrt{2}}\bigl(|1\rangle|221\rangle|0\rangle + |3\rangle|73\rangle|2\rangle\bigr).$$

How can I change that into

$$\dfrac{1}{\sqrt{2}}\bigl(|1\rangle|221\rangle|1\rangle + |3\rangle|73\rangle|2\rangle\bigr)?$$

What do you mean by a certain term? If it is what it I think you are saying then you are not following linearity. But I just want to clarify. – AHusain – 2019-03-14T22:28:04.203

Assuming that your last spin is of dimension 3, why not just apply the unitary $$\left(\begin{array}{ccc} 0 & 1 & 0 \\ 1 & 0 & 0 \\ 0 & 0 & 1 \end{array}\right)?$$