메뉴 건너뛰기




Volumn 148, Issue 6, 2012, Pages 1040-1053

Relations for Certain Symmetric Norms and Anti-norms Before and After Partial Trace

Author keywords

Ky Fan norm; R nyi entropy; Schatten norm; Singular values; Symmetric anti norms; Tsallis entropy

Indexed keywords


EID: 84866534872     PISSN: 00224715     EISSN: None     Source Type: Journal    
DOI: 10.1007/s10955-012-0569-8     Document Type: Article
Times cited : (46)

References (49)
  • 2
    • 1142301536 scopus 로고    scopus 로고
    • Continuity of quantum conditional entropy
    • Alicki, R., Fannes, M.: Continuity of quantum conditional entropy. J. Phys. A, Math. Gen. 37, L55-L57 (2004).
    • (2004) J. Phys. A, Math. Gen. , vol.37
    • Alicki, R.1    Fannes, M.2
  • 3
    • 0001079995 scopus 로고
    • Concavity of certain maps of positive definite matrices and applications to Hadamard products
    • Ando, T.: Concavity of certain maps of positive definite matrices and applications to Hadamard products. Linear Algebra Appl. 26, 203-241 (1979).
    • (1979) Linear Algebra Appl. , vol.26 , pp. 203-241
    • Ando, T.1
  • 4
    • 27844558812 scopus 로고    scopus 로고
    • Continuity bounds on the quantum relative entropy
    • Audenaert, K. M. R., Eisert, J.: Continuity bounds on the quantum relative entropy. J. Math. Phys. 26, 102104 (2005).
    • (2005) J. Math. Phys. , vol.26 , pp. 102104
    • Audenaert, K.M.R.1    Eisert, J.2
  • 5
    • 82855170975 scopus 로고    scopus 로고
    • Continuity bounds on the quantum relative entropy-II
    • Audenaert, K. M. R., Eisert, J.: Continuity bounds on the quantum relative entropy-II. J. Math. Phys. 52, 112201 (2011).
    • (2011) J. Math. Phys. , vol.52 , pp. 112201
    • Audenaert, K.M.R.1    Eisert, J.2
  • 8
    • 80052101887 scopus 로고    scopus 로고
    • Norm and anti-norm inequalities for positive semi-definite matrices
    • Bourin, J.-C., Hiai, F.: Norm and anti-norm inequalities for positive semi-definite matrices. Int. J. Math. 22, 1121-1138 (2011).
    • (2011) Int. J. Math. , vol.22 , pp. 1121-1138
    • Bourin, J.-C.1    Hiai, F.2
  • 10
    • 77952310431 scopus 로고    scopus 로고
    • Metric-adjusted skew information: convexity and restricted forms of superadditivity
    • Cai, L., Hansen, F.: Metric-adjusted skew information: convexity and restricted forms of superadditivity. Lett. Math. Phys. 93, 1-13 (2010).
    • (2010) Lett. Math. Phys. , vol.93 , pp. 1-13
    • Cai, L.1    Hansen, F.2
  • 11
    • 64549104859 scopus 로고    scopus 로고
    • On the stability of generalized entropies
    • Cao, X., Luo, S.: On the stability of generalized entropies. J. Phys. A, Math. Theor. 42, 075205 (2009).
    • (2009) J. Phys. A, Math. Theor. , vol.42 , pp. 075205
    • Cao, X.1    Luo, S.2
  • 12
    • 79955368914 scopus 로고    scopus 로고
    • Lecture course given at "Entropy and the Quantum", Tucson, Arizona
    • Carlen, E. A.: Trace inequalities and quantum entropy: an introductory course. Lecture course given at "Entropy and the Quantum", Tucson, Arizona. http://www. mathphys. org/AZschool/material/AZ09-carlen. pdf (2009).
    • (2009) Trace inequalities and quantum entropy: An introductory course
    • Carlen, E.A.1
  • 13
    • 0016522050 scopus 로고
    • Completely positive linear maps on complex matrices
    • Choi, M.-D.: Completely positive linear maps on complex matrices. Linear Algebra Appl. 10, 285-290 (1975).
    • (1975) Linear Algebra Appl. , vol.10 , pp. 285-290
    • Choi, M.-D.1
  • 15
    • 0000142610 scopus 로고
    • On a theorem of Weyl concerning eigenvalues of linear transformations. I
    • Fan, K.: On a theorem of Weyl concerning eigenvalues of linear transformations. I. Proc. Natl. Acad. Sci. USA 35, 652-655 (1949).
    • (1949) Proc. Natl. Acad. Sci. USA , vol.35 , pp. 652-655
    • Fan, K.1
  • 16
    • 0000578987 scopus 로고
    • A continuity property of entropy density for spin lattice systems
    • Fannes, M.: A continuity property of entropy density for spin lattice systems. Commun. Math. Phys. 31, 291-294 (1973).
    • (1973) Commun. Math. Phys. , vol.31 , pp. 291-294
    • Fannes, M.1
  • 18
    • 33748091389 scopus 로고    scopus 로고
    • Extensions of Lieb's concavity theorem
    • Hansen, F.: Extensions of Lieb's concavity theorem. J. Stat. Phys. 124, 87-101 (2006).
    • (2006) J. Stat. Phys. , vol.124 , pp. 87-101
    • Hansen, F.1
  • 19
    • 33847193188 scopus 로고    scopus 로고
    • The Wigner-Yanase entropy is not subadditive
    • Hansen, F.: The Wigner-Yanase entropy is not subadditive. J. Stat. Phys. 126, 643-648 (2007).
    • (2007) J. Stat. Phys. , vol.126 , pp. 643-648
    • Hansen, F.1
  • 21
    • 80052040382 scopus 로고    scopus 로고
    • Quantum f-divergences and error correction
    • Hiai, F., Mosonyi, M., Petz, D., Bény, C.: Quantum f-divergences and error correction. Rev. Math. Phys. 23, 691-747 (2011).
    • (2011) Rev. Math. Phys. , vol.23 , pp. 691-747
    • Hiai, F.1    Mosonyi, M.2    Petz, D.3    Bény, C.4
  • 23
    • 33644629301 scopus 로고    scopus 로고
    • Generalised quantum entropies
    • Hu, X., Ye, Z.: Generalised quantum entropies. J. Math. Phys. 47, 023502 (2006).
    • (2006) J. Math. Phys. , vol.47 , pp. 023502
    • Hu, X.1    Ye, Z.2
  • 24
    • 35448975107 scopus 로고
    • Linear transformations which preserve trace and positive semidefiniteness of operators
    • Jamiołkowski, A.: Linear transformations which preserve trace and positive semidefiniteness of operators. Rep. Math. Phys. 3, 275-278 (1972).
    • (1972) Rep. Math. Phys. , vol.3 , pp. 275-278
    • Jamiołkowski, A.1
  • 25
    • 77958563426 scopus 로고    scopus 로고
    • A unified treatment of convexity of relative entropy and related trace functions, with conditions for equality
    • Jenčová, A., Ruskai, M. B.: A unified treatment of convexity of relative entropy and related trace functions, with conditions for equality. Rev. Math. Phys. 22, 1099-1121 (2010).
    • (2010) Rev. Math. Phys. , vol.22 , pp. 1099-1121
    • Jenčová, A.1    Ruskai, M.B.2
  • 26
    • 79960603161 scopus 로고    scopus 로고
    • Unified entropy, entanglement measures and monogamy of multi-party entanglement
    • Kim, J. S., Sanders, B.: Unified entropy, entanglement measures and monogamy of multi-party entanglement. J. Phys. A, Math. Theor. 44, 295303 (2011).
    • (2011) J. Phys. A, Math. Theor. , vol.44 , pp. 295303
    • Kim, J.S.1    Sanders, B.2
  • 27
    • 0012570835 scopus 로고
    • Instability of Rényi entropies
    • Lesche, B.: Instability of Rényi entropies. J. Stat. Phys. 27, 419-422 (1982).
    • (1982) J. Stat. Phys. , vol.27 , pp. 419-422
    • Lesche, B.1
  • 28
    • 36649022319 scopus 로고
    • Convex trace functions and the Wigner-Yanase-Dyson conjecture
    • Reprinted in: Loss, M., Ruskai, M.B. (eds.): Inequalities: Selecta of E.H. Lieb. Springer, Berlin (2002)
    • Lieb, E. H.: Convex trace functions and the Wigner-Yanase-Dyson conjecture. Adv. Math. 11, 267-288 (1973). Reprinted in: Loss, M., Ruskai, M. B. (eds.): Inequalities: Selecta of E. H. Lieb. Springer, Berlin (2002).
    • (1973) Adv. Math. , vol.11 , pp. 267-288
    • Lieb, E.H.1
  • 30
    • 0040404601 scopus 로고
    • Quantum entropy and quantum measurements
    • Lecture Notes in Physics, C. Bendjaballah, O. Hirota, and S. Reynaud (Eds.), Berlin: Springer
    • Lindblad, G.: Quantum entropy and quantum measurements. In: Bendjaballah, C., Hirota, O., Reynaud, S. (eds.) Quantum Aspects of Optical Communications. Lecture Notes in Physics, vol. 378, pp. 71-80. Springer, Berlin (1991).
    • (1991) Quantum Aspects of Optical Communications , vol.378 , pp. 71-80
    • Lindblad, G.1
  • 31
    • 44249099882 scopus 로고    scopus 로고
    • Superadditivity of Wigner-Yanase-Dyson information revisited
    • Luo, S., Zhang, Q.: Superadditivity of Wigner-Yanase-Dyson information revisited. J. Stat. Phys. 131, 1169-1177 (2008).
    • (2008) J. Stat. Phys. , vol.131 , pp. 1169-1177
    • Luo, S.1    Zhang, Q.2
  • 34
    • 0002988067 scopus 로고
    • Quasi-entropies for finite quantum systems
    • Petz, D.: Quasi-entropies for finite quantum systems. Rep. Math. Phys. 21, 57-65 (1986).
    • (1986) Rep. Math. Phys. , vol.21 , pp. 57-65
    • Petz, D.1
  • 35
    • 78149496229 scopus 로고    scopus 로고
    • Continuity and stability of partial entropic sums
    • Rastegin, A. E.: Continuity and stability of partial entropic sums. Lett. Math. Phys. 94, 229-242 (2010).
    • (2010) Lett. Math. Phys. , vol.94 , pp. 229-242
    • Rastegin, A.E.1
  • 36
    • 79551556050 scopus 로고    scopus 로고
    • Bounds on Shannon distinguishability in terms of partitioned measures
    • Rastegin, A. E.: Bounds on Shannon distinguishability in terms of partitioned measures. Quantum Inf. Process. 10, 123-138 (2011).
    • (2011) Quantum Inf. Process. , vol.10 , pp. 123-138
    • Rastegin, A.E.1
  • 37
    • 79959550749 scopus 로고    scopus 로고
    • Some general properties of unified entropies
    • Rastegin, A. E.: Some general properties of unified entropies. J. Stat. Phys. 143, 1120-1135 (2011).
    • (2011) J. Stat. Phys. , vol.143 , pp. 1120-1135
    • Rastegin, A.E.1
  • 38
    • 79959955244 scopus 로고    scopus 로고
    • Upper continuity bounds on relative q-entropy for q > 1
    • Rastegin, A. E.: Upper continuity bounds on relative q-entropy for q > 1. J. Math. Phys. 52, 062203 (2011).
    • (2011) J. Math. Phys. , vol.52 , pp. 062203
    • Rastegin, A.E.1
  • 39
    • 84856023638 scopus 로고    scopus 로고
    • On unified-entropy characterization of quantum channels
    • Rastegin, A. E.: On unified-entropy characterization of quantum channels. J. Phys. A, Math. Theor. 45, 045302 (2012).
    • (2012) J. Phys. A, Math. Theor. , vol.45 , pp. 045302
    • Rastegin, A.E.1
  • 40
    • 84862265749 scopus 로고    scopus 로고
    • Number-phase uncertainty relations in terms of generalized entropies
    • Rastegin, A. E.: Number-phase uncertainty relations in terms of generalized entropies. Quantum Inf. Comput. 12, 0742-0763 (2012).
    • (2012) Quantum Inf. Comput. , vol.12 , pp. 0742-0763
    • Rastegin, A.E.1
  • 42
    • 79959670153 scopus 로고    scopus 로고
    • Entropic characterization of quantum operations
    • Roga, W., Fannes, M., Życzkowski, K.: Entropic characterization of quantum operations. Int. J. Quantum Inf. 9, 1031-1045 (2011).
    • (2011) Int. J. Quantum Inf. , vol.9 , pp. 1031-1045
    • Roga, W.1    Fannes, M.2    Zyczkowski, K.3
  • 44
    • 33646516485 scopus 로고
    • Possible generalization of Boltzmann-Gibbs statistics
    • Tsallis, C.: Possible generalization of Boltzmann-Gibbs statistics. J. Stat. Phys. 52, 479-487 (1988).
    • (1988) J. Stat. Phys. , vol.52 , pp. 479-487
    • Tsallis, C.1
  • 45
    • 0034196177 scopus 로고    scopus 로고
    • On "partial" fidelities
    • Uhlmann, A.: On "partial" fidelities. Rep. Math. Phys. 45, 407-418 (2000).
    • (2000) Rep. Math. Phys. , vol.45 , pp. 407-418
    • Uhlmann, A.1
  • 46
    • 71549171306 scopus 로고    scopus 로고
    • University of Waterloo, Ontario, Waterloo
    • Watrous, J.: CS 798: Theory of quantum information, University of Waterloo, Ontario, Waterloo, 2008. http://www. cs. uwaterloo. ca/~watrous/quant-info/lecture-notes/.
    • (2008) CS 798: Theory of quantum information
    • Watrous, J.1
  • 47
    • 77949524530 scopus 로고    scopus 로고
    • Entropic uncertainty relations-a survey
    • Wehner, S., Winter, A.: Entropic uncertainty relations-a survey. New J. Phys. 12, 025009 (2010).
    • (2010) New J. Phys. , vol.12 , pp. 025009
    • Wehner, S.1    Winter, A.2
  • 48
    • 5844266551 scopus 로고
    • General properties of entropy
    • Wehrl, A.: General properties of entropy. Rev. Mod. Phys. 50, 221-260 (1978).
    • (1978) Rev. Mod. Phys. , vol.50 , pp. 221-260
    • Wehrl, A.1
  • 49
    • 34248366161 scopus 로고    scopus 로고
    • Uniform estimates on the Tsallis entropies
    • Zhang, Z.: Uniform estimates on the Tsallis entropies. Lett. Math. Phys. 80, 171-181 (2007).
    • (2007) Lett. Math. Phys. , vol.80 , pp. 171-181
    • Zhang, Z.1


* 이 정보는 Elsevier사의 SCOPUS DB에서 KISTI가 분석하여 추출한 것입니다.