2007/03/01 by Martin B. Plenio, Martin B Plenio · 9 citations
Computer Science · Physics and Astronomy · #Duality (order theory) #Eigenvalues and eigenvectors #Formalism (music) #Generalization #Quantum #Quantum Information and Cryptography #Quantum Mechanics and Applications #Quantum Mechanics and Non-Hermitian Physics #Stabilizer (aeronautics) #Transformation (genetics) #quant-ph
paper · pdf · doi:10.1080/09500340701275774
published in Journal of Modern Optics 54(13-15), 2193-2201 (Taylor & Francis) · Contribution to Special Issue in Journal of Modern Optics celebrating the 60th birthday of Peter Knight
arxiv created 2007/03/01 · openalex publication_date 2007/09/10 · arxiv updated 2015/06/26 · openalex created_date 2016/06/24 · openalex updated_date 2026/08/05
We consider the transformation of Hamilton operators under various sets of quantum operations acting simultaneously on all adjacent pairs of particles. We find mappings between Hamilton operators analogous to duality transformations as well as exact characterizations of ground states employing non-Hermitean eigenvalue equations and use this to motivate a generalization of the stabilizer formalism to non-Hermitean operators. The resulting class of states is larger than that of standard stabilizer states and allows for example for continuous variation of local entropies rather than the discrete values taken on stabilizer states and the exact description of certain ground states of Hamilton operators.