Entanglement in the stabilizer formalism

By David Fattal, Toby S. Cubitt, Yoshihisa Yamamoto, Sergey Bravyi, Isaac L. Chuang. 2004

184 citations recorded by the source corpus.

We define a multi-partite entanglement measure for stabilizer states, which can be computed efficiently from a set of generators of the stabilizer group. Our measure applies to qubits, qudits and continuous variables.

Subfields: Applied Mathematics, Artificial Intelligence, Atomic and Molecular Physics, and Optics

View Paper: https://www.semanticscholar.org/paper/c6482b69bcf795d53f1ca3ce333e8751c7d5db7e

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In Applied Mathematics

In Artificial Intelligence

In Atomic and Molecular Physics, and Optics

Citations in the corpus

Correcting Quantum Errors with Entanglement (2006, background): “ors for S such that S can be decomposed into an “isotropic” subgroup SI generated by a set of commuting generators, and a “symplectic” subgroup SS generated by a set of anti-commuting generator pairs (13). Lemma 1. Given any arbitrary subgroup V in Gn that has 2m distinct elements up to overall phas”
Ground state entanglement and geometric entropy in the Kitaev model (2004, methodology): “[20] which uses a similar formalism in the context of stabilizer states.”
Statistical mechanics of quantum error correcting codes (2020, methodology): “We can directly compute its Rényi entropies [37],”
Suppressing quantum errors by scaling a surface code logical qubit (2022, unknown): “The validity of operations described follow from general theory of entanglement for stabilizer states[97].”
Dynamical Purification Phase Transition Induced by Quantum Measurements (2019, background): “In addition, partial traces, which map pure stabilizer states to mixed stabilizer states, and entanglement of stabilizer states can also be efficiently computed in a time O(L(3)) [42, 43, 54].”
Graphical calculus for Gaussian pure states (2010, background): “…closely related to the stabilizer formalism for Gaussian pure states, which, though utilized to some extent for a proof of the CV version of the Gottesman-Knill theorem [45] and often mentioned as a straightforward generalization from ﬁnite-dimensional systems [46], has not been fully explored yet.”