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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 $|+\rangle|+\rangle \otimes(\cdot)$.

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

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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 $(\cdot)$.

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