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Volumn 54, Issue 5, 2013, Pages

Quantum logarithmic Sobolev inequalities and rapid mixing

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EID: 84878589101     PISSN: 00222488     EISSN: None     Source Type: Journal    
DOI: 10.1063/1.4804995     Document Type: Article
Times cited : (138)

References (47)
  • 1
    • 0001429116 scopus 로고
    • Logarithmic sobolev inequalities
    • 10.2307/2373688
    • Gross L. Logarithmic sobolev inequalities. Am. J. Math. 1975, 97(4):1061-1083. 10.2307/2373688.
    • (1975) Am. J. Math. , vol.97 , Issue.4 , pp. 1061-1083
    • Gross, L.1
  • 2
    • 0002236459 scopus 로고
    • Logarithmic sobolev inequalities and contractivity properties of semigroups
    • 10.1007/BFb0074091
    • Gross L. Logarithmic sobolev inequalities and contractivity properties of semigroups. Lect. Notes Math. 1993, 1563:54-88. 10.1007/BFb0074091.
    • (1993) Lect. Notes Math. , vol.1563 , pp. 54-88
    • Gross, L.1
  • 3
    • 0030487036 scopus 로고    scopus 로고
    • Logarithmic sobolev inequalities for finite Markov chains
    • 10.1214/aoap/1034968224
    • Diaconis P. Saloff-Coste L. Logarithmic sobolev inequalities for finite Markov chains. Ann. Appl. Probab. 1996, 6(3):695-750. 10.1214/aoap/1034968224.
    • (1996) Ann. Appl. Probab. , vol.6 , Issue.3 , pp. 695-750
    • Diaconis, P.1    Saloff-Coste, L.2
  • 5
    • 0347466412 scopus 로고    scopus 로고
    • Lectures on logarithmic sobolev inequalities
    • (Springer).
    • Guionnet A. Zegarlinski B. Lectures on logarithmic sobolev inequalities. Séminaire de Probabilités, XXXVI 2003, 1801:1-134. and (Springer)., Vol. pp.
    • (2003) Séminaire de Probabilités, XXXVI , vol.1801 , pp. 1-134
    • Guionnet, A.1    Zegarlinski, B.2
  • 6
    • 3543009193 scopus 로고
    • On the generators of quantum dynamical semigroups
    • 10.1007/BF01608499
    • Lindblad G. On the generators of quantum dynamical semigroups. Commun. Math. Phys. 1976, 48(2):119-130. 10.1007/BF01608499.
    • (1976) Commun. Math. Phys. , vol.48 , Issue.2 , pp. 119-130
    • Lindblad, G.1
  • 7
    • 21144484566 scopus 로고
    • Optimal hypercontractivity for fermi fields and related non-commutative integration inequalities
    • 10.1007/BF02100048
    • Carlen E.A. Lieb E.H. Optimal hypercontractivity for fermi fields and related non-commutative integration inequalities. Commun. Math. Phys. 1993, 155(1):27-46. 10.1007/BF02100048.
    • (1993) Commun. Math. Phys. , vol.155 , Issue.1 , pp. 27-46
    • Carlen, E.A.1    Lieb, E.H.2
  • 8
    • 0033540129 scopus 로고    scopus 로고
    • Hypercontractivity in noncommutative Lp spaces
    • 10.1006/jfan.1998.3342
    • Olkiewicz R. Zegarlinski B. Hypercontractivity in noncommutative Lp spaces. J. Funct. Anal. 1999, 161(1):246-285. 10.1006/jfan.1998.3342.
    • (1999) J. Funct. Anal. , vol.161 , Issue.1 , pp. 246-285
    • Olkiewicz, R.1    Zegarlinski, B.2
  • 10
    • 0003598758 scopus 로고
    • Lp spaces associated with von Neumann algebras
    • (Copenhagen University).
    • Terp M. Lp spaces associated with von Neumann algebras. Notes, Math. Institute 1981, 3. (Copenhagen University)., Vol.
    • (1981) Notes, Math. Institute , vol.3
    • Terp, M.1
  • 12
    • 77949537092 scopus 로고    scopus 로고
    • Thermodynamic stability criteria for a quantum memory based on stabilizer and subsystem codes
    • 10.1088/1367-2630/12/2/025013
    • Chesi S. Loss D. Bravyi S. Terhal B.M. Thermodynamic stability criteria for a quantum memory based on stabilizer and subsystem codes. New J. Phys. 2010, 12:025013. 10.1088/1367-2630/12/2/025013.
    • (2010) New J. Phys. , vol.12 , pp. 025013
    • Chesi, S.1    Loss, D.2    Bravyi, S.3    Terhal, B.M.4
  • 13
    • 70249086538 scopus 로고    scopus 로고
    • Quantum computation and quantum-state engineering driven by dissipation
    • 10.1038/nphys1342
    • Verstraete F. Wolf M.M. Cirac J.I. Quantum computation and quantum-state engineering driven by dissipation. Nat. Phys. 2009, 5(9):633-636. 10.1038/nphys1342.
    • (2009) Nat. Phys. , vol.5 , Issue.9 , pp. 633-636
    • Verstraete, F.1    Wolf, M.M.2    Cirac, J.I.3
  • 15
    • 67650902389 scopus 로고    scopus 로고
    • Quantum mechanical evolution towards thermal equilibrium
    • 10.1103/PhysRevE.79.061103
    • Linden N. Popescu S. Short A.J. Winter A. Quantum mechanical evolution towards thermal equilibrium. Phys. Rev. E 2009, 79:061103. 10.1103/PhysRevE.79.061103.
    • (2009) Phys. Rev. E , vol.79 , pp. 061103
    • Linden, N.1    Popescu, S.2    Short, A.J.3    Winter, A.4
  • 17
    • 0032667067 scopus 로고    scopus 로고
    • Cryptographic distinguishability measures for quantum-mechanical states
    • 10.1109/18.761271
    • Fuchs C.A. Van De Graaf J. Cryptographic distinguishability measures for quantum-mechanical states. IEEE Trans. Inf. Theory 1999, 45(4):1216-1227. 10.1109/18.761271.
    • (1999) IEEE Trans. Inf. Theory , vol.45 , Issue.4 , pp. 1216-1227
    • Fuchs, C.A.1    Van De Graaf, J.2
  • 18
    • 78650704416 scopus 로고    scopus 로고
    • The χ2-divergence and mixing times of quantum markov processes
    • 10.1063/1.3511335
    • Temme K. Kastoryano M.J. Ruskai M.B. Wolf M.M. Verstraete F. The χ2-divergence and mixing times of quantum markov processes. J. Math. Phys. 2010, 51(12):122201-122201. 10.1063/1.3511335.
    • (2010) J. Math. Phys. , vol.51 , Issue.12 , pp. 122201-122201
    • Temme, K.1    Kastoryano, M.J.2    Ruskai, M.B.3    Wolf, M.M.4    Verstraete, F.5
  • 21
    • 0002262781 scopus 로고    scopus 로고
    • On logarithmic Sobolev inequalities, Csiszar-Kullback inequalities, and the rate of convergence to equilibrium for Fokker-Planck type equations
    • (Techn. Univ., Fachbereich Mathematik(3)).
    • Arnold A. Markowich P. Toscani G. Unterreiter A. On logarithmic Sobolev inequalities, Csiszar-Kullback inequalities, and the rate of convergence to equilibrium for Fokker-Planck type equations. Preprint-Reihe Mathematik 1998, and (Techn. Univ., Fachbereich Mathematik(3)).
    • (1998) Preprint-Reihe Mathematik
    • Arnold, A.1    Markowich, P.2    Toscani, G.3    Unterreiter, A.4
  • 22
    • 0002000391 scopus 로고
    • Existence and uniqueness of physical ground states
    • 10.1016/0022-1236(72)90057-2
    • Gross L. Existence and uniqueness of physical ground states. J. Funct. Anal. 1972, 10(1):52-109. 10.1016/0022-1236(72)90057-2.
    • (1972) J. Funct. Anal. , vol.10 , Issue.1 , pp. 52-109
    • Gross, L.1
  • 23
    • 84972558081 scopus 로고
    • Hypercontractivity and logarithmic sobolev inequalities for the Clifford-Dirichlet form
    • 10.1215/S0012-7094-75-04237-4
    • Gross L. Hypercontractivity and logarithmic sobolev inequalities for the Clifford-Dirichlet form. Duke Math. J. 1975, 42(3):383-396. 10.1215/S0012-7094-75-04237-4.
    • (1975) Duke Math. J. , vol.42 , Issue.3 , pp. 383-396
    • Gross, L.1
  • 24
    • 0001260297 scopus 로고    scopus 로고
    • On quantum stochastic dynamics and noncommutative Lp spaces
    • 10.1007/BF00714401
    • Majewski A.W. Zegarlinski B. On quantum stochastic dynamics and noncommutative Lp spaces. Lett. Math. Phys. 1996, 36(4):337-349. 10.1007/BF00714401.
    • (1996) Lett. Math. Phys. , vol.36 , Issue.4 , pp. 337-349
    • Majewski, A.W.1    Zegarlinski, B.2
  • 26
    • 0000112360 scopus 로고
    • Generators of dynamical semigroups
    • 10.1016/0022-1236(79)90085-5
    • Davies E.B. Generators of dynamical semigroups. J. Funct. Anal. 1979, 34(3):421-432. 10.1016/0022-1236(79)90085-5.
    • (1979) J. Funct. Anal. , vol.34 , Issue.3 , pp. 421-432
    • Davies, E.B.1
  • 27
    • 0033240088 scopus 로고    scopus 로고
    • Monotone Riemannian metrics and relative entropy on noncommutative probability spaces
    • 10.1063/1.533053
    • Lesniewski A. Ruskai M.B. Monotone Riemannian metrics and relative entropy on noncommutative probability spaces. J. Math. Phys. 1999, 40:5702. 10.1063/1.533053.
    • (1999) J. Math. Phys. , vol.40 , pp. 5702
    • Lesniewski, A.1    Ruskai, M.B.2
  • 28
    • 0002988067 scopus 로고
    • Quasi-entropies for finite quantum systems
    • 10.1016/0034-4877(86)90067-4
    • Petz D. Quasi-entropies for finite quantum systems. Rep. Math. Phys. 1986, 23(1):57-65. 10.1016/0034-4877(86)90067-4.
    • (1986) Rep. Math. Phys. , vol.23 , Issue.1 , pp. 57-65
    • Petz, D.1
  • 29
    • 0030501619 scopus 로고    scopus 로고
    • Monotone metrics on matrix spaces
    • 10.1016/0024-3795(94)00211-8
    • Petz D. Monotone metrics on matrix spaces. Linear Algebra Appl. 1996, 244:81-96. 10.1016/0024-3795(94)00211-8.
    • (1996) Linear Algebra Appl. , vol.244 , pp. 81-96
    • Petz, D.1
  • 30
    • 77955733714 scopus 로고    scopus 로고
    • A quantum version of Wielandt's inequality
    • 10.1109/TIT.2010.2054552
    • Sanz M. Pérez-García D. Wolf M.M. Cirac J.I. A quantum version of Wielandt's inequality. IEEE Trans. Inf. Theory 2010, 56(9):4668-4673. 10.1109/TIT.2010.2054552.
    • (2010) IEEE Trans. Inf. Theory , vol.56 , Issue.9 , pp. 4668-4673
    • Sanz, M.1    Pérez-García, D.2    Wolf, M.M.3    Cirac, J.I.4
  • 32
    • 0011634607 scopus 로고
    • The detailed balance condition in quantum statistical mechanics
    • 10.1063/1.526164
    • Majewski W.A. The detailed balance condition in quantum statistical mechanics. J. Math. Phys. 1984, 25(3):614-616. 10.1063/1.526164.
    • (1984) J. Math. Phys. , vol.25 , Issue.3 , pp. 614-616
    • Majewski, W.A.1
  • 33
    • 0032475781 scopus 로고    scopus 로고
    • Detailed balance and quantum dynamical maps
    • 10.1088/0305-4470/31/39/013
    • Majewski W.A. Streater R.F. Detailed balance and quantum dynamical maps. J. Phys. A: Math. Gen. 1998, 31:7981. 10.1088/0305-4470/31/39/013.
    • (1998) J. Phys. A: Math. Gen. , vol.31 , pp. 7981
    • Majewski, W.A.1    Streater, R.F.2
  • 34
    • 0002925263 scopus 로고
    • L'hypercontractivité et son utilisation en théorie des semigroupes
    • (Springer).
    • Bakry D. L'hypercontractivité et son utilisation en théorie des semigroupes. Lectures on Probability Theory 1994, 1-114. (Springer)., pp.
    • (1994) Lectures on Probability Theory , pp. 1-114
    • Bakry, D.1
  • 35
  • 36
    • 36749116101 scopus 로고
    • Entropy production for quantum dynamical semigroups
    • 10.1063/1.523789
    • Spohn H. Entropy production for quantum dynamical semigroups. J. Math. Phys. 1978, 19:1227. 10.1063/1.523789.
    • (1978) J. Math. Phys. , vol.19 , pp. 1227
    • Spohn, H.1
  • 37
    • 40849102414 scopus 로고    scopus 로고
    • Fluctuations of quantum currents and unravelings of master equations
    • 10.1007/s10955-008-9500-8
    • Dereziński J. De Roeck W. Maes C. Fluctuations of quantum currents and unravelings of master equations. J. Stat. Phys. 2008, 131(2):341-356. 10.1007/s10955-008-9500-8.
    • (2008) J. Stat. Phys. , vol.131 , Issue.2 , pp. 341-356
    • Dereziński, J.1    De Roeck, W.2    Maes, C.3
  • 38
    • 34249767236 scopus 로고
    • Approach to equilibrium of Glauber dynamics in the one phase region
    • 10.1007/BF02101929
    • Martinelli F. Olivieri E. Approach to equilibrium of Glauber dynamics in the one phase region. Commun. Math. Phys. 1994, 161(3):447-486. 10.1007/BF02101929.
    • (1994) Commun. Math. Phys. , vol.161 , Issue.3 , pp. 447-486
    • Martinelli, F.1    Olivieri, E.2
  • 41
    • 0344551997 scopus 로고    scopus 로고
    • Inequalities for trace norms of 2x2 block matrices
    • 10.1007/s00220-003-0955-9
    • King C. Inequalities for trace norms of 2x2 block matrices. Commun. Math. Phys. 2003, 242:531-545. 10.1007/s00220-003-0955-9.
    • (2003) Commun. Math. Phys. , vol.242 , pp. 531-545
    • King, C.1
  • 42
    • 70349538979 scopus 로고    scopus 로고
    • How long can a quantum memory withstand depolarizing noise?
    • 10.1103/PhysRevLett.103.080501
    • Pastawski F. Kay A. Schuch N. Cirac I. How long can a quantum memory withstand depolarizing noise?. Phys. Rev. Lett. 2009, 103(8):080501. 10.1103/PhysRevLett.103.080501.
    • (2009) Phys. Rev. Lett. , vol.103 , Issue.8 , pp. 080501
    • Pastawski, F.1    Kay, A.2    Schuch, N.3    Cirac, I.4
  • 43
    • 33749002225 scopus 로고    scopus 로고
    • Expander graphs and their applications
    • 10.1090/S0273-0979-06-01126-8
    • Hoory S. Linial N. Wigderson A. Expander graphs and their applications. Bull. Am. Math. Soc. 2006, 43(4):439-562. 10.1090/S0273-0979-06-01126-8.
    • (2006) Bull. Am. Math. Soc. , vol.43 , Issue.4 , pp. 439-562
    • Hoory, S.1    Linial, N.2    Wigderson, A.3
  • 44
    • 65649117114 scopus 로고    scopus 로고
    • An explicit construction of quantum expanders
    • preprint arXiv:0709.0911 .
    • Ben-Aroya A. Schwartz O. Ta-Shma A. An explicit construction of quantum expanders. 2007, and preprint arXiv:0709.0911.
    • (2007)
    • Ben-Aroya, A.1    Schwartz, O.2    Ta-Shma, A.3
  • 45
    • 34548811944 scopus 로고    scopus 로고
    • Random unitaries give quantum expanders
    • 10.1103/PhysRevA.76.032315
    • Hastings M.B. Random unitaries give quantum expanders. Phys. Rev. A 2007, 76:032315. 10.1103/PhysRevA.76.032315.
    • (2007) Phys. Rev. A , vol.76 , pp. 032315
    • Hastings, M.B.1
  • 46
    • 65649116848 scopus 로고    scopus 로고
    • Quantum margulis expanders
    • Gross D. Eisert J. Quantum margulis expanders. Quantum Inf. Comput. 2008, 8(8):722-733.
    • (2008) Quantum Inf. Comput. , vol.8 , Issue.8 , pp. 722-733
    • Gross, D.1    Eisert, J.2
  • 47
    • 14844321925 scopus 로고    scopus 로고
    • Notes on super-operator norms induced by schatten norms
    • Watrous J. Notes on super-operator norms induced by schatten norms. Quantum Inf. Comput. 2005, 5(1):058-068.
    • (2005) Quantum Inf. Comput. , vol.5 , Issue.1 , pp. 058-068
    • Watrous, J.1


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