The quantum information manifold for ε-bounded forms

1999/10/19 by M. R. Grasselli, Matheus R. Grasselli, R. F. Streater · 1 citation
Computer Science · Mathematics · Physics and Astronomy · #Mathematical Analysis and Transform Methods #Quantum Information and Cryptography #advanced mathematical theories #math-ph #math.FA #math.MP #msc:53C80 #msc:58B20

paper · pdf · doi:10.1016/s0034-4877(00)90003-x

published as Reports on Mathematical Physics, Vol. 46 (2000), 325-335. · 12 pages, report to Torun Conference, 1999

arxiv created 1999/10/19 · openalex publication_date 2000/12/01 · arxiv updated 2009/11/30 · openalex created_date 2016/06/24 · openalex updated_date 2026/07/28

Abstract

Let H be a self-adjoint operator bounded below by 1, and let V be a small form perturbation such that RVS has finite norm, where R is the resolvent at zero to the power 1/2 +epsilon, and S is the resolvent to the power 1/2-epsilon. Here, epsilon lies between 0 and 1/2. If the Gibbs state defined by H is sufficiently regular, we show that the free energy is an analytic function of V in the sense of Frechet, and that the family of density operators defined in this way is an analytic manifold modelled on a Banach space.

Citations

• The Bogoliubov inner product in quantum statistics

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