# What does the centered dot notation mean in the expression $|+\rangle|+\rangle\otimes(\cdot)$?

In the expression $$|+\rangle|+\rangle \otimes(\cdot)$$, what does the centered dot represent? I have come across a definition of the centered dot previously, similar to the one given here, but I am just querying to see if this means anything different in this context.

Edit:

This comes from the three qubit phase flip code in Nielsen and Chaung, section 10.1.2, page 431. For this specific example, the measurement of $$X_1X_2$$ gives $$+1$$ for the state $$|+\rangle|+\rangle \otimes(\cdot)$$.

• Does not seem possible to infer without a context. Perhaps $(\cdot)$ here just means anything (in the brackets)? Sep 13, 2022 at 19:56

## 1 Answer

Read in the context of Nielsen and Chuang it's clear that $$(\cdot)$$ is acting as a wildcard for extra, dummy or unspecified qubits, as @NikitaNemkov hinted.

Quoting from my copy of N+C:

...Measurement of the observables $$X_1X_2$$ and $$X_2X_3$$ corresponds to comparing the sign of qubits one and two, and two and three, respectively, in the sense that measurement of $$X_1X_2$$, for example, gives $$+1$$ for states like $$|+\rangle|+\rangle\otimes(\cdot)$$ or $$|-\rangle|-\rangle$$, and $$-1$$ for states like $$|+\rangle|-\rangle\otimes(\cdot)$$ or $$|-\rangle|+\rangle\otimes(\cdot)$$.

The first two qubits are $$X_1X_2$$ while the other qubits (e.g. $$X_3$$) could be represented by $$(\cdot)$$.