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**Question 1**: The bell state for a 2-qubit system has been defined in Neilsen and Chuang's book as the set of maximally entangled states spanned by $\{|00\rangle + |11\rangle, |00\rangle - |11\rangle, |01\rangle + |10\rangle, |01\rangle- |10\rangle \}$. What is the higher dimensional definition of a Bell state for an n-qubits system?

**Question 2**: More specificity, Consider the toric code on a $L\times L$ lattice. There are $2L^2$ qubits on it. Consider the minimal case when $L=3$, ie. we have $18$ qubits. How does the code space look like? Is it some sort of "bell-state" for these qubits? Is it possible to explicitly write the code space for this as in the case of say, a repetition code.

Thanks!

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Does this GHZ article help?

– Mark S – 2019-06-08T02:16:06.210I see, but what about other linear combinations? Its still not clear and well-motivated to me.The GHZ state is just one state whereas there are more than one bell state. Is the toric code space a GHZ state? – John Jacob – 2019-06-08T10:41:38.840

1I don't think of a"Bell state" (singular) as the

setof the four enumerated states - a pair of qubits are in a Bell state (singular) if they are in one of the four enumerated Bell states (plural). Similarly it might be ok to think of a qubit being in a superposition of $\vert 010\rangle+\vert 101\rangle$ as being in a "GHZ" state. – Mark S – 2019-06-08T12:27:07.210