Symmetries and entanglement of stabilizer states

Abstract

Stabilizer states constitute a set of pure states which plays a dominant role in quantum error correction, measurement--based quantum computation, and quantum communication. Central in these applications are the local symmetries of these states. We characterize all local symmetries of arbitrary stabilizer states and provide an algorithm which determines them. We demonstrate the usefulness of these results by showing that the additional local symmetries find applications in entanglement theory and quantum error correction.

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Cited by in corpus (13)

• LIMDD: A Decision Diagram for Simulation of Quantum Computing Including Stabilizer States
• Transformations of Stabilizer States in Quantum Networks
• On Groups in the Qubit Clifford Hierarchy
• Measurement outcomes that do not occur and their role in entanglement transformations
• Symmetric hypergraph states: Entanglement quantification and robust Bell nonlocality
• State transformations within entanglement classes containing permutation-symmetric states
• Classification of four qubit states and their stabilisers under SLOCC operations
• Designing locally maximally entangled quantum states with arbitrary local symmetries
• Identifying families of multipartite states with non-trivial local entanglement transformations
• Level-rank duality of SU(2)k Chern-Simons theory, and of hypergraph and magic states
• Generalized Code Distance through Rotated Logical States in Quantum Error Correction
• Classification of qubit cellular automata on hypercubic lattices
• Hypergraph States in SU(N)1, N odd prime, Chern-Simons Theory