메뉴 건너뛰기




Volumn 31, Issue 1, 1999, Pages 16-24

The scalar curvature of the Bures metric on the space of density matrices

Author keywords

Bures metric; Density matrices; Scalar currature

Indexed keywords


EID: 0033177340     PISSN: 03930440     EISSN: None     Source Type: Journal    
DOI: 10.1016/S0393-0440(98)00068-0     Document Type: Article
Times cited : (19)

References (19)
  • 1
    • 0003355633 scopus 로고
    • Differential geometric methods in statistics
    • Springer, Berlin
    • S. Amari, Differential geometric methods in statistics, Lecture Notes in Statistics, vol. 28, Springer, Berlin, 1985.
    • (1985) Lecture Notes in Statistics , vol.28
    • Amari, S.1
  • 2
    • 0003365357 scopus 로고    scopus 로고
    • How and why to solve the operator equation AX - XB = Y
    • R. Bhatia, P. Rosenthal, How and why to solve the operator equation AX - XB = Y, Bull. London Math. Soc. 29 (1997) 1-21.
    • (1997) Bull. London Math. Soc. , vol.29 , pp. 1-21
    • Bhatia, R.1    Rosenthal, P.2
  • 3
    • 0000519707 scopus 로고
    • Statistical distance and the geometry of quantum states
    • S.L. Braunstein, C.M. Caves, Statistical distance and the geometry of quantum states, Phys. Rev. Lett. 72 (1994) 3439-3443.
    • (1994) Phys. Rev. Lett. , vol.72 , pp. 3439-3443
    • Braunstein, S.L.1    Caves, C.M.2
  • 4
    • 0030577976 scopus 로고    scopus 로고
    • Generalized uncertainty relations: Theory, examples, and Lorentz invariance
    • S.L. Braunstein, C.M. Caves, G.J. Milburn, Generalized uncertainty relations: Theory, examples, and Lorentz invariance, Ann. Phys. 247 (1996) 135-173.
    • (1996) Ann. Phys. , vol.247 , pp. 135-173
    • Braunstein, S.L.1    Caves, C.M.2    Milburn, G.J.3
  • 5
    • 0002443417 scopus 로고
    • On the Riemannian geometry of finite dimensional mixed states
    • J. Dittmann, On the Riemannian geometry of finite dimensional mixed states, Sem. S. Lie 3 (1993) 73-87.
    • (1993) Sem. S. Lie , vol.3 , pp. 73-87
    • Dittmann, J.1
  • 6
    • 0009135498 scopus 로고
    • Some properties of the Riemannian Bures metric on mixed states
    • J. Dittmann, Some properties of the Riemannian Bures metric on mixed states, J. Geom. Phys. 13 (1994) 203-206.
    • (1994) J. Geom. Phys. , vol.13 , pp. 203-206
    • Dittmann, J.1
  • 7
    • 85045720312 scopus 로고    scopus 로고
    • Yang-Mills equation and Bures metric
    • to appear
    • J. Dittmann, Yang-Mills equation and Bures metric, Lett. Math. Phys., to appear.
    • Lett. Math. Phys.
    • Dittmann, J.1
  • 10
    • 84985360120 scopus 로고
    • Die Fisher-information und symplektische strukturen
    • T. Friedrich, Die Fisher-information und symplektische strukturen, Math. Nachr. 153 (1991) 273-296.
    • (1991) Math. Nachr. , vol.153 , pp. 273-296
    • Friedrich, T.1
  • 11
    • 0009140173 scopus 로고    scopus 로고
    • Curvature in the geometry of canonical correlation
    • F. Hiai, D. Petz, G. Toth, Curvature in the geometry of canonical correlation, Stud. Sci. Math. Hung. 32 (1996) 235-249.
    • (1996) Stud. Sci. Math. Hung. , vol.32 , pp. 235-249
    • Hiai, F.1    Petz, D.2    Toth, G.3
  • 14
    • 0030501619 scopus 로고    scopus 로고
    • Monotone metrics on matrix spaces
    • D. Petz, Monotone metrics on matrix spaces, Linear Algebra Appl. 244 (1996) 81-96.
    • (1996) Linear Algebra Appl. , vol.244 , pp. 81-96
    • Petz, D.1
  • 15
    • 0009139884 scopus 로고
    • Matrix calculations for Lyapunov quadratic forms
    • R.A. Smith, Matrix calculations for Lyapunov quadratic forms, J. Differential Equations 2 (1966) 208-217.
    • (1966) J. Differential Equations , vol.2 , pp. 208-217
    • Smith, R.A.1
  • 16
    • 0000778175 scopus 로고    scopus 로고
    • Bures and statistical distance for squeezed thermal states
    • J. Twamley, Bures and statistical distance for squeezed thermal states, J. Phys. A 29 (1996) 3723-3731.
    • (1996) J. Phys. A , vol.29 , pp. 3723-3731
    • Twamley, J.1
  • 17
    • 0343012756 scopus 로고
    • Parallel transport and quantum holonomy
    • A. Uhlmann, Parallel transport and quantum holonomy, Rep. Math. Phys. 24 (1986) 229-240.
    • (1986) Rep. Math. Phys. , vol.24 , pp. 229-240
    • Uhlmann, A.1
  • 18
    • 0000024981 scopus 로고
    • A gauge field governing parallel transport along mixed states
    • A. Uhlmann, A gauge field governing parallel transport along mixed states, Lett. Math. Phys. 21 (1991) 229-236.
    • (1991) Lett. Math. Phys. , vol.21 , pp. 229-236
    • Uhlmann, A.1
  • 19
    • 0001606571 scopus 로고
    • The metric of Bures and the geometric phase
    • in: R. Gielerak et al. (Eds.), Kluwer Academic Publishers, Dordrecht
    • A. Uhlmann, The metric of Bures and the geometric phase, in: R. Gielerak et al. (Eds.), Groups and Related Topics, Kluwer Academic Publishers, Dordrecht, 1992.
    • (1992) Groups and Related Topics
    • Uhlmann, A.1


* 이 정보는 Elsevier사의 SCOPUS DB에서 KISTI가 분석하여 추출한 것입니다.