Bures metric

In mathematics, in the area of quantum information geometry, the Bures metric (named after Donald Bures)[1] or Helstrom metric (named after Carl W. Helstrom)[2] defines an infinitesimal distance between density matrix operators defining quantum states. It is a quantum generalization of the Fisher information metric, and is identical to the Fubini–Study metric[3] when restricted to the pure states alone.

  1. ^ Bures, Donald (1969). "An extension of Kakutani's theorem on infinite product measures to the tensor product of semifinite *-algebras" (PDF). Transactions of the American Mathematical Society. 135. American Mathematical Society (AMS): 199. doi:10.1090/s0002-9947-1969-0236719-2. ISSN 0002-9947.
  2. ^ Helstrom, C.W. (1967). "Minimum mean-squared error of estimates in quantum statistics". Physics Letters A. 25 (2). Elsevier BV: 101–102. Bibcode:1967PhLA...25..101H. doi:10.1016/0375-9601(67)90366-0. ISSN 0375-9601.
  3. ^ Facchi, Paolo; Kulkarni, Ravi; Man'ko, V.I.; Marmo, Giuseppe; Sudarshan, E.C.G.; Ventriglia, Franco (2010). "Classical and quantum Fisher information in the geometrical formulation of quantum mechanics". Physics Letters A. 374 (48): 4801–4803. arXiv:1009.5219. Bibcode:2010PhLA..374.4801F. doi:10.1016/j.physleta.2010.10.005. ISSN 0375-9601. S2CID 55558124.