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The entanglement properties of a multiparty pure state are invariant under local unitary transformations. The stabilizer dimension of a multiparty pure state characterizes how many types of such local unitary transformations existing for the state. We find that the stabilizer dimension of an $n$-qubit ($nge 2$) graph state is associated with three specific configurations in its graph. We further show that the stabilizer dimension of an $n$-qubit ($nge 3$) graph state is equal to the degree of irreducible two-qubit correlations in the state.
Stabilizer states are eigenvectors of maximal commuting sets of operators in a finite Heisenberg group. States that are far from being stabilizer states include magic states in quantum computation, MUB-balanced states, and SIC vectors. In prime dimen
The generation and verification of large-scale entanglement are essential to the development of quantum technologies. In this paper, we present an efficient scheme to generate genuine multipartite entanglement of a large number of qubits by using the
A fundamental problem in quantum computation and quantum information is finding the minimum quantum dimension needed for a task. For tasks involving state preparation and measurements, this problem can be addressed using only the input-output correla
We present an algorithm for manipulating quantum information via a sequence of projective measurements. We frame this manipulation in the language of stabilizer codes: a quantum computation approach in which errors are prevented and corrected in part
We give necessary and sufficient conditions for the existence of stabilizer codes $[[n,k,3]]$ of distance 3 for qubits: $n-kge lceillog_2(3n+1)rceil+epsilon_n$ where $epsilon_n=1$ if $n=8frac{4^m-1}3+{pm1,2}$ or $n=frac{4^{m+2}-1}3-{1,2,3}$ for some