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Volumn 4, Issue 2, 2001, Pages 173-182

On the uniqueness of the Chentsov metric in quantum information geometry

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EID: 0035628303     PISSN: 02190257     EISSN: None     Source Type: Journal    
DOI: 10.1142/S0219025701000462     Document Type: Article
Times cited : (51)

References (22)
  • 1
    • 0003355633 scopus 로고
    • Differential Geometric Methods in Statistics
    • Springer-Verlag
    • S.-I. Amari, Differential Geometric Methods in Statistics, Lecture Notes in Statistics, Vol. 28 (Springer-Verlag, 1985).
    • (1985) Lecture Notes in Statistics , vol.28
    • Amari, S.-I.1
  • 2
    • 0001777754 scopus 로고
    • Information geometry
    • S.-I. Amari, Information geometry, Contemp. Math. 203 (1985) 81-95.
    • (1985) Contemp. Math. , vol.203 , pp. 81-95
    • Amari, S.-I.1
  • 6
    • 0347117897 scopus 로고    scopus 로고
    • The quantum information manifold for ε-bounded forms
    • to appear math-hp/9910031
    • M. R. Grasselli and R. F. Streater, The quantum information manifold for ε-bounded forms, to appear in Rep. Math. Phys., math-hp/9910031.
    • Rep. Math. Phys.
    • Grasselli, M.R.1    Streater, R.F.2
  • 7
    • 0002559620 scopus 로고
    • Noncommutative extension of the information geometry
    • eds. V. P. Balavkin, O. Hirota and R. L. Hudson (Plenum Press)
    • H. Hasegawa, Noncommutative extension of the information geometry, in Quantum Communication and Measurement, eds. V. P. Balavkin, O. Hirota and R. L. Hudson (Plenum Press, 1995), pp. 327-337.
    • (1995) Quantum Communication and Measurement , pp. 327-337
    • Hasegawa, H.1
  • 8
    • 0031066685 scopus 로고    scopus 로고
    • Exponential and mixture families in quantum statistics: Dual structures and unbiased parameter estimation
    • H. Hasegawa, Exponential and mixture families in quantum statistics: dual structures and unbiased parameter estimation, Rep. Math. Phys. 39 (1997) 49-68.
    • (1997) Rep. Math. Phys. , vol.39 , pp. 49-68
    • Hasegawa, H.1
  • 9
    • 0003096079 scopus 로고
    • α-divergence of the noncommutative information geometry
    • H. Hasegawa, α-divergence of the noncommutative information geometry, Rep. Math. Phys. 33 (1993) 87-93.
    • (1993) Rep. Math. Phys. , vol.33 , pp. 87-93
    • Hasegawa, H.1
  • 10
    • 0012458021 scopus 로고    scopus 로고
    • Noncommutative extension of information geometry II
    • eds. V. P. Belavkin, O. Hirota and R. L. Hudson (Plenum Press)
    • H. Hasegawa and D. Petz, Noncommutative extension of information geometry II, in Quantum Communication and Measurement, eds. V. P. Belavkin, O. Hirota and R. L. Hudson (Plenum Press, 1997) pp. 109-118.
    • (1997) Quantum Communication and Measurement , pp. 109-118
    • Hasegawa, H.1    Petz, D.2
  • 11
    • 12344271673 scopus 로고
    • Statistical mechanical theory of irreversible processes I
    • R. Kubo, Statistical mechanical theory of irreversible processes I, J. Phys. Soc. Jpn. 12 (1957) 570, also The fluctuation-dissipation theorem, Rep. Prog. Phys. 29 (1966) 255.
    • (1957) J. Phys. Soc. Jpn. , vol.12 , pp. 570
    • Kubo, R.1
  • 12
    • 33847327575 scopus 로고
    • The fluctuation-dissipation theorem
    • R. Kubo, Statistical mechanical theory of irreversible processes I, J. Phys. Soc. Jpn. 12 (1957) 570, also The fluctuation-dissipation theorem, Rep. Prog. Phys. 29 (1966) 255.
    • (1966) Rep. Prog. Phys. , vol.29 , pp. 255
  • 13
    • 0000514837 scopus 로고
    • Transport, collective motion and Brownian motion
    • H. Mori, Transport, collective motion and Brownian motion, Prog. Theor. Phys. 33 (1965) 423.
    • (1965) Prog. Theor. Phys. , vol.33 , pp. 423
    • Mori, H.1
  • 14
    • 0002486043 scopus 로고
    • Markov invariant geometry on state manifolds
    • E. A. Morozova and N. N. Chentsov, Markov invariant geometry on state manifolds (Russian), Ito. Nauki Tek. 36 (1990) 69-102.
    • (1990) Ito. Nauki Tek. , vol.36 , pp. 69-102
    • Morozova, E.A.1    Chentsov, N.N.2
  • 16
    • 0011632541 scopus 로고
    • Differential geometric aspects of quantum state estimation and relative entropy
    • eds. V. P. Balavkin, O. Hirota and R. L. Hudson (Plenum Press)
    • H. Nagaoka, Differential geometric aspects of quantum state estimation and relative entropy, in Quantum Communication and Measurement, eds. V. P. Balavkin, O. Hirota and R. L. Hudson (Plenum Press, 1995).
    • (1995) Quantum Communication and Measurement
    • Nagaoka, H.1
  • 17
    • 0002988067 scopus 로고
    • Quasi-entropies for finite quantum systems
    • D. Petz, Quasi-entropies for finite quantum systems, Rep. Math. Phys. 23 (1986) 57-65.
    • (1986) Rep. Math. Phys. , vol.23 , pp. 57-65
    • Petz, D.1
  • 18
    • 36449005102 scopus 로고
    • Geometry of canonical correlation on the state space of a quantum system
    • D. Petz, Geometry of canonical correlation on the state space of a quantum system, J. Math. Phys. 35 (1994) 780-795.
    • (1994) J. Math. Phys. , vol.35 , pp. 780-795
    • Petz, D.1
  • 19
    • 0030501619 scopus 로고    scopus 로고
    • Monotone metrics on matrix spaces
    • D. Petz, Monotone metrics on matrix spaces, Lin. Alg. Appl. 244 (1996) 81-96.
    • (1996) Lin. Alg. Appl. , vol.244 , pp. 81-96
    • Petz, D.1
  • 20
    • 0009130255 scopus 로고    scopus 로고
    • On the Riemannian metric of α-entropies of density matrices
    • D. Petz and H. Hasegawa, On the Riemannian metric of α-entropies of density matrices, Lett. Math. Phys. 38 (1996) 221-241.
    • (1996) Lett. Math. Phys. , vol.38 , pp. 221-241
    • Petz, D.1    Hasegawa, H.2
  • 21
    • 0030544975 scopus 로고    scopus 로고
    • Geometries of quantum states
    • D. Petz and C. Sudar, Geometries of quantum states, J. Math. Phys. 37 (1996) 2662-2673.
    • (1996) J. Math. Phys. , vol.37 , pp. 2662-2673
    • Petz, D.1    Sudar, C.2
  • 22
    • 0345993297 scopus 로고    scopus 로고
    • The information manifold for relatively bounded potentials
    • math-ph/9910035
    • R. F. Streater, The information manifold for relatively bounded potentials, Proc. Stecklov Inst. Math. 228 (2000) 205-223, math-ph/9910035.
    • (2000) Proc. Stecklov Inst. Math. , vol.228 , pp. 205-223
    • Streater, R.F.1


* 이 정보는 Elsevier사의 SCOPUS DB에서 KISTI가 분석하여 추출한 것입니다.