Publications

2018

[BGT18] A. Barchielli, M. Gregoratti, A. Toigo: Measurement uncertainty relations for discrete observables: Relative entropy formulation. Commun. Math. Phys. 357 (2018) 1253-1304. DOI: 10.10.1007/s00220-017-3075-7

[CHT18] C. Carmeli, T. Heinosaari, A. Toigo: State discrimination with post-measurement information and incompatibility of quantum measurements. (2018). arXiv:1804.09693

[BG18] A. Barchielli, M. Gregoratti: Uncertainty relations and information loss for spin 1/2 measurements. (2018). arXiv:1805.03919

2017

[CST17] C. Carmeli, J. Schultz, A. Toigo: Maximally symmetric stabilizer MUBs in even prime-power dimensions. J. Math. Phys. 58 (2017) 032201. DOI: 10.1063/1.4977830

[CHST17] C. Carmeli, T. Heinosaari, J. Schultz, A. Toigo: Probing quantum state space: does one have to learn everything to learn something?. P. R. Soc. A 473 No. 2201 (2017) 20160866. DOI: 10.1098/rspa.2016.0866

[BGT17] A. Barchielli, M. Gregoratti, A. Toigo: Measurement Uncertainty Relations for Position and Momentum: Relative Entropy Formulation. Entropy 19 (2017) 301. DOI:10.3390/e19070301

[CHMST17] C. Carmeli, T. Heinosaari, S. Maniscalco, J. Schultz, A. Toigo: Determining quantum coherence with minimal resources (2017). arXiv:1708.05597

[FSU17] F. Fagnola, E. Sasso, V. Umanità: Structure of Uniformly Continuous Quantum Markov Semigroups with Atomic Decoherence-free Subalgebra. Open Sys. Inf. Dyn. 24 (2017) 1740005-1740023. DOI:10.1142/S1230161217400054

[AF17] J. Agredo, F. Fagnola: On quantum versions of the classical Wasserstein distance. Stochastic 89 (2017) 910-922. DOI:10.1080/17442508.2016.1276914

[BF17] J.R. Bolanos-Servin, F. Fagnola: On the structure of quantum Markov semigroups of weak coupling limit type. J. Phys. Conference series 819 (2017) 012003-012012. DOI:10.1088/1742-6596/819/1/012003

[CS17] F. Cipriani, J.L. Sauvageot: Amenability and subexponential spectral growth rate of Dirichlet forms on von Neumann algebras. Adv. Math. 322 (2017) 308-340. DOI:10.1016/j.aim.2017.10.017

[C17] F. Cipriani: Logarithmic Sobolev inequalities for an ideal Bose gas. Advances in Quantum Mechanics, 121-133, Springer INdAM Ser. 18, Springer, Cham (2017). DOI:10.1007/978-3-319-58904-6_7

[CSU17] R. Carbone, E. Sasso, V. Umanità: Structure of generic quantum Markov semigroup. Infin. Dimens. Anal. Quantum. Probab. Relat. Top. 20, 1750012 (2017) [19 pages] DOI:10.1142/S0219025717500126

2016

[AFQ16] L. Accardi, F. Fagnola and R. Quezada: On three new principles in non-equilibrium statistical mechanics and Markov semigroups of weak coupling limit type. Infin. Dimens. Anal. Quantum Probab. Relat. Top. 19 (2) (2016) 1650009 (37 pages) DOI: 10.1142/S0219025716500090

[FR16] F. Fagnola, R. Rebolledo: Entropy production and detailed balance for a class of quantum Markov semigroups. Open Syst. Inf. Dyn. 22 (3) (2015) 1550013-1 -- 1550013-14

[DFSU16] J. Deschamps, F. Fagnola, E. Sasso and V. Umanità: Structure of Uniformly Continuous Quantum Markov Semigroups. Rev. Math. Phys. 28 (2016), 1650003-1 -- 1650003-32. DOI:10.1142/S0129055X16500033

[BGT16] A. Barchielli, M. Gregoratti, A. Toigo: Measurement uncertainty relations for discrete observables: Relative entropy formulation, (2016) arXiv:1608.01986

[B16] A. Barchielli: Quantum stochastic equations for an opto-mechanical oscillator with radiation pressure interaction and non-Markovian effects, Rep. Math. Phys. 77 (2016) 315-333; doi:10.1016/S0034-4877(16)30033-7

[CHKaST16] C. Carmeli, T. Heinosaari, A. Karlsson, J. Schultz, A. Toigo, Verifying the Quantumness of Bipartite Correlations, Phys. Rev. Lett. 116 No.23 (2016) 230403

[CHKeST16] C. Carmeli, T. Heinosaari, M. Kech, J. Schultz, A. Toigo, Stable pure state quantum tomography from five orthonormal bases, Europhys. Lett. 115 No.3 (2016) 30001

[CHRST16] C. Carmeli, T. Heinosaari, D. Reitzner, J. Schultz, A. Toigo, Quantum incompatibility in collective measurements, Mathematics 4 No.3 (2016) 54

[CST16] C. Carmeli, J. Schultz, A. Toigo, Covariant mutually unbiased bases, Rev. Math. Phys. 28 No.4 (2016) 1650009

[C16] F. Cipriani: Noncommutative potential theory: a survey. J. Geom. Phys. 105 (2016), 25-59

2015

[BSF15] J. Bolanos-Servin, F. Fagnola: On the range of the generator of a quantum Markov semigroup, Infin. Dimens. Anal. Quantum Probab. Relat. Top. 18 (4) Dec 2015 1550027-1--1550027-10

[FM15] F. Fagnola, C.M. Mora: On the relationship between a quantum Markov semigroup and its representation via linear stochastic Schroedinger equations. Indian J. Pure Appl. Math. 46, 399-414 (2015)

[FR15] F. Fagnola, R. Rebolledo: Entropy Production for Quantum Markov Semigroups. Commun. Math. Phys. 335, 547–570 (2015) (DOI) 10.1007/s00220-015-2320-1 arxiv1212.1366

[BV15] A. Barchielli, B. Vacchini: Quantum Langevin equations for optomechanical systems, New J. Phys. 17 (2015) 083004 (30 pgs); doi:10.1088/1367-2630/17/8/083004

[G15] M. Gregoratti: The Hamiltonian Generating Quantum Stochastic Evolutions in the Limit from Repeated to Continuous Interactions. Open Syst. Inf. Dyn. 22 (2015), no. 4, 1550022, 15 pp., DOI: 10.1142/S1230161215500225

[CHST15c] C. Carmeli, T. Heinosaari, J. Schultz, A. Toigo, How many orthonormal bases are needed to distinguish all pure quantum states?, Eur. J. Phys. D 69 No.7 (2015) 179

[CHST15b] C. Carmeli, T. Heinosaari, J. Schultz, A. Toigo, Expanding the principle of local distinguishability, Phys. Rev. A 91 No.4 (2015) 042121

[CHST15a] C. Carmeli, T. Heinosaari, J. Schultz, A. Toigo, Nonuniqueness of phase retrieval for three fractional Fourier transforms, Appl. Comput. Harmon. Anal. 39 No.2 (2015) 339-346

[KHRS15] J. Kiukas, T. Heinosaari, D. Reitzner, J. Schultz, Incompatibility breaking quantum channels, J. Phys. A Math. Theor. 48 No.43 (2015) 435301

[HKS15] T. Heinosaari, J. Kiukas, J. Schultz, Breaking Gaussian incompatibility on continuous variable quantum systems, J. Math. Phys. 56 No.8 (2015) 082202

[CS15] F. Cipriani, J.-L. Sauvageot: Variations in noncommutative potential theory: finite-energy states, potentials and multipliers. Trans. Amer. Math. Soc. 367 (2015), no. 7, 4837-4871

2014

[AFR14] J. Agredo, F. Fagnola and R. Rebolledo: Decoherence free subspaces of a quantum Markov semigroup, J. Math. Phys. 55 112201 (2014) http://dx.doi.org/10.1063/1.4901009

[SSPB14] I. Semina, V. Semin, F. Petruccione, A. Barchielli, Stochastic Schroedinger equations for Markovian and non-Markovian cases; Open Systems & Information Dynamics, Vol. 21, Nos. 1 & 2 (2014) 1440008 (31 pages), DOI:10.1142/S1230161214400083

[HSTZ14] T. Heinosaari, J. Schultz, A. Toigo, M. Ziman, Maximally incompatible quantum observables, Phys. Lett. A 378 No.24-25 (2014) 1695-1699

[DVRT14] E. De Vito, L. Rosasco, A. Toigo, Learning sets with separating kernels, Appl. Comput. Harmon. Anal. 37 No.2 (2014) 185--217

[CHST14] C. Carmeli, T. Heinosaari, J. Schultz, A. Toigo, Tasks and premises in quantum state determination, J. Phys. A Math. Theor. 47 No.7 (2014) 075302

[CGIS14] F. Cipriani, D. Guido, T. Isola, J.-L. Sauvageot: Spectral triples for the Sierpinski gasket. J. Funct. Anal. 266 (2014), no. 8, 4809-4869

[CFK14] F. Cipriani, U. Franz, A. Kula: Symmetries of Lévy processes on compact quantum groups, their Markov semigroups and potential theory. J. Funct. Anal. 266 (2014), no. 5, 2789-2844

2013

[FM13] F. Fagnola, C.M. Mora: Stochastic Schroedinger Equations with Unbounded Coefficients and Applications to Ehrenfest-type theorems. ALEA, Lat. Am. J. Probab. Math. Stat. 10 (1), 191--223 (2013). arxiv1207.2939

[AF13] L. Accardi, F. Fagnola: "Quantum Probability and Related Topics. Proceedings of the 32nd conference", Levico Terme (Italy), May 29 - June 4, 2011. QP-PQ: Quantum Probability and White Noise Analysis - Vol. 29. 280pp. World Scientific, January 2013. ISBN: 978-981-4447-53-9

[FP13] F. Fagnola, L. Pantaleon Martinez: Generation of Semigroups by Degenerate Elliptic Operators Arising in Open Quantum Systems. In L. Accardi and F. Fagnola (eds.) ``Quantum Probability and Related Topics. Proceedings of the 32nd conference'', Levico Terme (Italy), May 29 - June 4, 2011. QP-PQ: Quantum Probability and White Noise Analysis - Vol. 29 p. 84--97. World Scientific, January 2013. ISBN: 978-981-4447-53-9

[BG13b] A. Barchielli, M. Gregoratti, Quantum continuous measurements: The stochastic Schroedinger equations and the spectrum of the output, Quantum Measurements and Quantum Metrology. Volume 1, Pages 34-56, ISSN (Online) 2299-114X, DOI: 10.2478/qmetro-2013-0005, August 2013

[BG13a] A. Barchielli, M. Gregoratti, Entanglement Protection and Generation Under Continuous Monitoring. In L. Accardi and F. Fagnola (eds.) ``Quantum Probability and Related Topics. Proceedings of the 32nd conference'', Levico Terme (Italy), May 29 - June 4, 2011. QP-PQ: Quantum Probability and White Noise Analysis - Vol. 29 p. 17-42. World Scientific, January 2013. ISBN: 978-981-4447-53-9; arXiv:1202.2041v1 [quant-ph]

[BBBCHT13] R. Beneduci, T.J. Bullock, P. Busch, C. Carmeli, T. Heinosaari, A. Toigo, Operational link between mutually unbiased bases and symmetric informationally complete positive operator-valued measures, Phys. Rev. A 88 No.3 (2013) 032312

[CHT13] C. Carmeli, T. Heinosaari, A. Toigo, Minimal covariant observables identifying all pure states, Phys. Lett. A 377 No.21-22 (2013) 1407-1415

[CTU13] G. Chiribella, A. Toigo, V. Umanità, Normal completely positive maps on the space of quantum operations, Open Syst. Inf. Dyn. 20 No.1 (2013) 1350003

[SP13] J. Schultz, J.-P. Pellonpää, Measuring the canonical phase with phase space measurements, Phys. Rev. A 88 No.1 (2013) 012121

[KS13] J. Kiukas, J. Schultz, Informationally complete sets of Gaussian measurements, J. Phys. A Math. Theor. 46 No.48 (2013) 485303

[BHSS13] P. Busch, T. Heinosaari, J. Schultz, N. Stevens, Comparing the degrees of incompatibility inherent in probabilistic physical theories, Europhys. Lett. 103 No.1 (2013) 10002

[CGIS13] F. Cipriani, D. Guido, T. Isola, J.-L. Sauvageot: Integrals and potentials of differential 1-forms on the Sierpinski gasket. Adv. Math. 239 (2013), 128-163

2012

[FM12] F. Fagnola, C.M. Mora, Stochastic Schroedinger Equations with Unbounded Coefficients; arxiv1207.2939 [quant-ph]

[FR12] F. Fagnola, R. Rebolledo, Entropy Production for Quantum Markov Semigroups; arxiv1212.1366 [math-ph]

[FH12] F. Fagnola, S. Hachicha: Decomposition and Classification of Generic Quantum Markov Semigroups: the Gaussian Gauge Invariant Case. Open Syst. Inf. Dyn., 19, n.2 (2012), 1250010 (15 pages). ISSN 1230-1612 DOI: 10.1142/S1230161212500102

[FU12c] F. Fagnola, V. Umanità: Generic Quantum Markov Semigroups, Cycle Decomposition and Deviation From Equilibrium, Infin. Dimens. Anal. Quantum Probab. Relat. Top., 15, No. 3 (2012) 1250016 (17 pages) DOI: 10.1142/S0219025712500166

[FU12b] F. Fagnola, V. Umanità: Quantum detailed balance conditions with time reversal: three-level systems, Stochastics, 84 (2-3), 273-293 2012. DOI: 10.1080/17442508.2010.518707

[FU12a] F. Fagnola, V. Umanità: Quantum detailed balance conditions with time reversal: the finite-dimensional case. Proceedings of the ``13th WORKSHOP: NON-COMMUTATIVE HARMONIC ANALYSIS'' Banach Center Publications, 96 (2012) 159--174. ISSN: 0137-6934 DOI:10.4064/bc96-0-10

[FP12] F. Fagnola, L. Pantaleon Martinez: Are sufficient conditions for conservativitity of minimal quantum semigroups necessary? Math. Notes, 91, n.6 (2012), 851--856. ISSN 0001-4346 DOI: 10.1134/S000143461205032X

[FG12] F. Fagnola, M. Gregoratti, Bell's Inequality Violations: Relation with de Finetti's Coherence Principle and Inferential Analysis of Experimental Data, Communications on Stochastic Analysis, vol. 6, no. 1 (March 2012)

[BG12] A. Barchielli, M. Gregoratti, Quantum measurements in continuous time, non-Markovian evolutions and feedback, Philosophical Transactions A, 370, 5364-5385 (2012)

[BPP12] A. Barchielli, C. Pellegrini, F. Petruccione, Quantum trajectories: Memory and continuous observation, Phys. Rev. A 86, 063814 (2012); DOI: 10.1103/PhysRevA.86.063814; arXiv:1207.16010v1 [quant-ph]

[CHT12] C. Carmeli, T. Heinosaari, A. Toigo: Informationally complete joint measurements on finite quantum systems, Phys. Rev. A 85 No.1 (2012) 012109

2011

[AFQ11] L. Accardi, F. Fagnola, R. Quezada: Weighted Detailed Balance and Local KMS Condition for Non-Equilibrium Stationary States. Bussei Kenkyu 97 (3) (2011), 318-356.

[DFR11] A. Dhahri, F. Fagnola, R. Rebolledo: The decoherence-free subalgebra of a quantum Markov semigroup on B(h). In R. Rebolledo and M. Orszag (eds.) ``Quantum Probability and Related Topics Proceedings of the 30th conference'', Santiago (Cile), November 23-28, 2009. QP-PQ: Quantum Probability and White Noise Analysis - Vol.27 p.131-147. World Scientific, January 2011. ISBN: 978-981-4338-73-8 981-4338-73-7

[CSU11] R. Carbone, E. Sasso, V. Umanità: Decoherence for positive semigroups on M2(C). J. Math. Phys. 52 (2011), no. 3, 17 pp

[BDPP11] A. Barchielli, P. Di Tella, C. Pellegrini, F. Petruccione: Stochastic Schrödinger equations and memory. In R. Rebolledo, M. Orszag (eds.), Quantum Probability and Related Topics, QP-PQ: Quantum Probability and White Noise Analysis (ISSN: 1793-5121) Vol.27, (World Scientific, Singapore, 2011) pp.52-67. arXiv:1006.3647v1 [quant-ph]

[BC11] A. Barchielli, R. Castro Santis: Quantum stochastic differential equations and continuous measurements: unbounded coefficients. Rep. Math. Phys. 67 (2011) 229-254. cdoi:10.1016/S0034-4877(11)80014-5; arXiv:1001.2826v1 [math.PR]

[CHT11] C. Carmeli, T. Heinosaari, A. Toigo: Sequential measurements of conjugate observables. J. Phys. A-Math. Theor. 44 no.28 (2011) DOI: 10.1088/1751-8113/44/28/285304

2010

[DFR10] A. Dhahri, F. Fagnola, R. Rebolledo: The decoherence-free subalgebra of a quantum Markov semigroup with unbounded generator. Infin. Dimens. Anal. Quantum Probab. Relat. Top., Vol.13, No.3 (2010) 413-433, DOI: 10.1142/S0219025710004176

[F10] F. Fagnola: Quantum Fokker-Planck models: an Open System Approach.. Oberwolfach Reports, 7 no.4 (2010), 3819--3191. ISSN: 1660-8933, online ISSN: 1660-8941 DOI: 10.4171/OWR/2010/54

[FU10b] F. Fagnola, V. Umanità: Generators of KMS Symmetric Markov Semigroups on B(h) Symmetry and Quantum Detailed Balance. Commun. Math. Phys., Volume 298, Number 2, (2010) 523-547, DOI 10.1007/s00220-010-1011-1

[FU10a] F. Fagnola, V. Umanità: On two quantum versions of the detailed balance condition. In: Noncommutative harmonic analysis with applications to probability II (M. Bozejko, A. Krystek, L.Wojakowski, eds.), Banach Center Publications, Polish Academy of Sciences, Institute of Mathematics, 89 (2010), 105-119. ISBN: 978-83-86806-08-9, doi:10.4064/bc89

[FR10] F. Fagnola, R. Rebolledo: From classical to quantum entropy production. In H. Ouerdiane, A. Barhoumi (eds.) Quantum Probability and Infinite Dimensional Analysis, Proceedings of the 29-th Conference on Quantum Probability and Infinite Dimensional Analysis, Hammamet (Tunisia), October 13-18, 2008, QP-PQ: Quantum Probability and White Noise Analysis - Vol. 25 p. 245-261. World Scientific, February 2010. ISBN: 978-981-4295-42-0 981-4295-42-6

[FN10] F. Fagnola, L. Neumann: Quantum Fokker-Planck models: Limiting case in the Lindblad Condition. In H. Ouerdiane, A. Barhoumi (eds.) Quantum Probability and Infinite Dimensional Analysis, Proceedings of the 29-th Conference on Quantum Probability and Infinite Dimensional Analysis, Hammamet (Tunisia), October 13-18, 2008, QP-PQ: Quantum Probability and White Noise Analysis - Vol. 25 p. 245-261. World Scientific, February 2010. ISBN: 978-981-4295-42-0 981-4295-42-6

[BPP10] A. Barchielli, C. Pellegrini, F. Petruccione: Stochastic Schroedinger equations with coloured noise, EPL 91 (2010) 24001; DOI: 10.1209/0295-5075/91/24001; arXiv:0911.2554v1 [quant-ph]

[Gr10] M. Gregoratti, Dilations à la Quantum Probability of Markov evolutions in discrete time, Theory of Probability and Its Applications (TVP) 54, no.1, 140-150 (2010)

[CDTU10] C. Carmeli, E. De Vito, A. Toigo and V. Umanità: Vector valued reproducing kernel Hilbert spaces and Universality, Analysis and Applications (Singap.) 8, no.1, 19-61 (2010) DOI: 10.1142/S0219530510001503

[DRT10] E. De Vito, L. Rosasco, A. Toigo: Spectral Regularization for Support Estimation, Advances in Neural Information Processing Systems 23 (J. Lafferty, C.K.I. Williams, J. Shawe-Taylor, R.S. Zemel, A. Culotta eds.) 487-495 (2010)

2009

[FP09] F. Fagnola, R. Pellicer Bidot: Irreducible and periodic positive maps. Commun. Stoch. Anal. 3 (2009), 407--418. ISSN 0973-9599

[F09] F. Fagnola: Quantum Markov Semigroups and Flows Arising from Form Generators on B(h). Oberwolfach Reports, 6 (2009), 526--527. ISSN: 1660-8933, online ISSN: 1660-8941

[FU09] F. Fagnola and V. Umanità, Generators of KMS Symmetric Quantum Markov Semigroups and Detailed Balance, arXiv:0908.0967

[BG09b] A. Barchielli, M. Gregoratti, Feedback control of the squeezing of the fluorescence light, International Physics and Control Society (IPACS) Library, http://lib.physcon.ru/?item=2090

[BG09a] A. Barchielli, M. Gregoratti: Quantum Trajectories and Measurements in Continuous Time - The Diffusive Case. Lecture Notes in Physics, Vol. 782, 2009, Springer Berlin / Heidelberg.
ISBN: 978-3-642-01297-6, DOI
10.1007/978-3-642-01298-3, Versione elettronica disponibile in rete

[BGL09] A. Barchielli, M. Gregoratti, M. Licciardo: Feedback control of the fluorescence light squeezing, EPL 85 (2009) 14006  arXiv:0804.0085v1

[Gr09] M. Gregoratti, Dilations à la Quantum Probability of Markov evolutions in discrete time, Teoriya Veroyatnostei i ee Primeneniya 54, no.1, 185-196 (2009)

[CGI09] F. Cipriani, D. Guido, T. Isola: A C∗-algebra of geometric operators on self-similar CW-complexes. Novikov-Shubin and L2-Betti numbers. J. Funct. Anal. 256 (2009), no. 3, 603-634

[CG09] F. Cipriani, G. Grillo: Hypercontractivity, Nash inequalities and subordination for classes of nonlinear semigroups. Semigroup Forum 78 (2009), no. 1, 77-98

[CS09] F. Cipriani, J.-L. Sauvageot: Fredholm modules on P.C.F. self-similar fractals and their conformal geometry. Comm. Math. Phys. 286 (2009), no. 2, 541-558

2008

[AFN08] A. Arnold, F. Fagnola, L. Neumann: Quantum Fokker-Planck models: the Lindblad and Wigner approaches. In: ``Quantum Probability and Related Topics'' Proceedings of the 28-th Conference CIMAT-Guanajuato, México, September 2-8, 2007. World Scientific 2008, pp. 23-48. arXiv:0806.2984

[FU08] F. Fagnola and V. Umanità, Detailed balance, time reversal and generators of Quantum Markov Semigroups, Mathematical Notes, MAIK Nauka/Interperiodica, vol.84, no.1, 108-115 (2008)

[FR08] F. Fagnola, R. Rebolledo: Algebraic conditions for convergence of a quantum Markov semigroup to a steady state. Infin. Dimens. Anal. Quantum Probab. Relat. Top., 11 no.3 (2008) 1--8.

[CFGQ08] R. Carbone, F. Fagnola, J.C. García, R. Quezada: Spectral properties of the two-photon absorption and emission process, J. Math. Phys. 49 (3) 2008, p. 32106.

[CarS08] R. Carbone, E. Sasso, Hypercontractivity for Quantum Ornstein-Uhlenbeck Semigroup, Probab. Theory Related Fields 140 (2008), no. 3-4, 505-522.

[BL08] A. Barchielli, G. Lupieri, Information gain in quantum continual measurements, in V.P. Belavkin and M. Guta, Quantum Stochastic and Information (World Scientific, Singapore, 2008) pp. 325--345. arXiv:quant-ph/0612010v1.

[BG08] A. Barchielli, M. Gregoratti: Quantum continuous measurements: the spectrum of the output. In: J C García, R Quezada, S B Sontz (eds.) Quantum Probability and Related Topics, QP-PQ XXIII, World Scientific, Singapore 2008, pp. 63--76. arXiv:0802.1877

[BGL08] A. Barchielli, M. Gregoratti, M. Licciardo: Quantum trajectories, feedback and squeezing, International Journal of Quantum Information 6 (2008) 581-587, arXiv:0801.4710

[Gr08] M. Gregoratti, Dilations à la Hudson-Parthasarathy of Markov semigroups in Classical Probability, Stochastic Analysis and Applications 26 (2008) no.5 1025-1052

[ATU08] P. Albini, A. Toigo and V. Umanità, Relations between convergence rates in Schatten p-norms, Journal of Mathematical Physics, 49, 01354, 2008

[C08] F. Cipriani: Dirichlet forms on noncommutative spaces. Quantum potential theory, 161-276, Lecture Notes in Math., 1954, Springer, Berlin, 2008

[C08] P. Biane, L. Bouten, F. Cipriani, N. Konno, N. Privault, Q. Xu: Quantum potential theory. Lectures presented at the School ``Quantum Potential Theory: Structure and Applications to Physics'' held at the Alfried Krupp Wissenschaftskolleg, Greifswald, February 26-March 9, 2007. Edited by Michael Schürmann and Uwe Franz. Lecture Notes in Mathematics, 1954. Springer-Verlag, Berlin, 2008. xii+457 pp. ISBN: 978-3-540-69364-2

2007

[BL07] A. Barchielli, G. Lupieri, Entropic bounds and continual measurements; in L.Accardi, W.Freudenberg, M.Schurmann (eds.), Quantum Probability and Infinite Dimensional Analysis,  Quantum Probability Series QP-PQ Vol.XX (World Scientific, Singapore, 2007); quant-ph/0511090.

[BF07] A. Ben Ghorbal, F. Fagnola: Boson cocycle as the second quantization of Boolean cocycle. In: L.Accardi, W.Freudengerg, M.Schurmann (eds.) Quantum Probability and Infinite Dimensional Analysis, QP-PQ XX, Proceedings of the 26th Conference, pp. 134-144, World Scientific, Singapore 2007. ISBN-13 978-981-270-851-9 ISBN-10 981-270-851-0

[CFH07] R. Carbone, F. Fagnola, S. Hachicha. Generic quantum Markov semigroups: the Gaussian gauge invariant case. Open Syst. Inf. Dyn. 14 (2007), 425-444.

[FU07] F. Fagnola, V. Umanità: Generators of detailed balance quantum Markov semigroups. Infin. Dimens. Anal. Quantum Probab. Relat. Top. 10 no.3, 335 - 363 (2007).

[FS07] F. Fagnola, M. Skeide: Restrictions of CP-Semigroups to Maximal Commutative Subalgebras. Noncommutative harmonic analysis with applications to probability (M. Bozej\-ko, A. Krystek, W. Mlotkowski, and J. Wysoczanski, eds.), Banach Center Publications, vol.78, Polish Academy of Sciences --- Institute of Mathematics, 2007, (arXiv: math.OA/0703001), pp.121--132. ISSN: 0137-6934(p) 1730-6299(e)

[CG07] F. Cipriani, G. Grillo, From Hypercontractivity of Nonlinear Semigroups to Gagliardo-Nirenberg Inequalities for Their Generators, ArXiv:0704.3527

2006

[BL06b] A. Barchielli, G. Lupieri, Quantum measurements and entropic bounds on information transmission, Quantum Information and Computation 6 (2006) 16-45; quant-ph/0505090.

[BL06a] A. Barchielli, G. Lupieri, Instruments and mutual entropies in quantum information theory, in M. Bozejko, W. Mlotkowski, J. Wysoczanski (eds.), Quantum Probability, Banach Center Publications, Vol. 73 (2006), pp. 65-80; quant-ph/0412116.

[Ba06a] A. Barchielli, Continual Measurements in Quantum Mechanics and Quantum Stochastic Calculus. In S. Attal, A. Joye, C.-A. Pillet (eds.), Open Quantum Systems III, Lecture Notes in Mathematics 1882 (Springer, Berlin, 2006), pp. 207-291.

[AFR06] L. Accardi, F. Fagnola, M. Roeckner: Weak, strong, and four semigroup solutions of classical stochastic differential equations: an example. In: Stochastic partial differential equations and applications---VII, 1--6, Lect. Notes Pure Appl. Math., 245, Chapman & Hall CRC, Boca Raton, FL, 2006. ISBN: 0824700279

[F06] F. Fagnola: Quantum Stochastic Differential Equations and Dilations of Completely Positive Semigroups. In: S. Attal, A. Joye, C.-A. Pillet (eds.) Open Quantum Systems II - The Markovian Approach. Lecture Notes in Mathematics 1881 p. 183--220. Springer Berlin, Heidelberg (2006). ISBN 978-3-540-30992-5

[FR06] F. Fagnola, R. Rebolledo: Notes on the Qualitative Behaviour of Quantum Markov Semigroups. In: S. Attal, A. Joye, C.-A. Pillet (eds.) Open Quantum Systems III - Recent Developments. Lecture Notes in Mathematics 1882 p. 161-206. Springer Berlin, Heidelberg (2006). ISBN 978-3-540-30993-2

[AFH06] L. Accardi, F. Fagnola, S. Hachicha: Generic q-Markov semigroups and speed of convergence of q-algorithms. Infin. Dimens. Anal. Quantum Probab. Relat. Top. 9, n. 4 (2006) pp. 567-594. ISSN: 0219-0257

[C06b] F. Cipriani, Positive maps in $C^*$-algebras, Encyclopedia of Mathematical Physics, Article 00454, (2006) Elsevier Ltd, Amsterdam The Netherlands.

[C06a] F. Cipriani, Dirichlet forms as Banach algebras and applications, Pacific. J. Math., 223 n.2 (2006), 229-249.

[Gr06b] M. Gregoratti, Erratum: "The Hamiltonian operator associated with some quantum stochastic evolutions", [Comm. Math. Phys. 222 (2001), no. 1, 181--200], Comm. Math. Phys. 264 (2006), no 2, 563-564.

[Gr06a] M. Gregoratti: Traces of Sobolev functions with one square integrable directional derivative, Math. Meth. Appl. Sci. 29, 2 (2006) 157-171. Published Online: 29 Sep 2005, DOI: 10.1002/mma.669]

2005

[BL05] A. Barchielli, G. Lupieri, Instruments and channels in quantum information theory, Optics and Spectroscopy 99 (2005) 425-432; quant-ph/0409019.

[FQ05] F. Fagnola, R. Quezada: Two-photon absorption and emission process, Infin. Dimens. Anal. Quantum Probab. Relat. Top. 8, n. 4 (2005) pp. 573-591 ISSN: 0219-0257 (doi:10.1142/S0219025705002116).

[Gr05] M. Gregoratti: A universal dilation of discrete Markov evolutions; Quaderno di Dipartimento n.649/P; math.PR/0512393.

2004

[Ba04] A. Barchielli, Appunti su Equazioni differenziali stocastiche ed equazione di Fokker-Planck, lezioni per la Scuola Estiva: Campi vettoriali di Hörmander, equazioni differenziali ipoellittiche e applicazioni, Politecnico di Milano, 12-16 luglio 2004.

[BL04c] A. Barchielli, G. Lupieri, Instrumental processes, entropies, information in quantum continual measurements, in O. Hirota (ed.), Quantum information, Statistics, Probability (Rinton, Princeton, 2004) pp. 30-43; Quantum Information and Computation 4 (2004) 437-449 - quant-ph/0401114.

[Fa04] F. Fagnola: Quantum Markov semigroups: structure and asymptotics. Rend. Circ. Mat. Palermo serie II Suppl. No. 73 (2004), 35-51.

[CF04] H. Comman, F. Fagnola: $C^*$-algebras of quadratures. J. Operator Theory 52 (2004), 259-266.

[C04] R. Carbone, Optimal log-Sobolev inequality and hypercontractivity for semigroups on $M_2(C)$, Infinite Dimensional Analysis Quantum Probability and Related Topics 7 (2004), no.3, 317--335.

[GW04] M. Gregoratti, R. F. Werner: On quantum error-correction by classical feedback in discrete time.  J. Math. Phys.  45  (2004), no. 7, 2600-2612.

2003

[BP03] A. Barchielli, A. M. Paganoni, On the asymptotic behaviour of some stochastic differential equations for quantum states, Infinite Dimensional Analysis, Quantum Probability and Related Topics 6 (2003) 223-243.

[FR03] F. Fagnola, R. Rebolledo: Transience and Recurrence of Quantum Markov Semigroups. Probab. Theory Related Fields 126 (2003) n.2, 289-306.

[CF03]  R. Carbone, F. Fagnola: The Feller property of a class of Quantum Markov Semigroups II. Quantum probability and infinite dimensional analysis (Burg, 2001), 57-76, QP-PQ: Quantum Probab. White Noise Anal., 15, World Sci. Publishing, River Edge, NJ, 2003.

[FR03] F. Fagnola, R. Rebolledo: Quantum Markov Semigroups and their Stationary States. In R. Rebolledo (ed.): Stochastic analysis and mathematical physics. Birkhäuser Verlag, Basel 2003.

[Fa03a] F. Fagnola: H-P Quantum Stochastic Differential Equations. Invited paper in A. Hora, T. Matsui and N. Obata (eds): Non-Commutativity, Infinite-Dimensionality and Probability at the Crossroads. World Scientific, Singapore, (2003). ISBN 981-238-297-6.

[Fa03b] F. Fagnola: Quantum stochastic differential equations. Quantum probability communications, Vol. XI (Grenoble, 1998), 123-170, QP-PQ, XI, World Sci. Publishing, River Edge, NJ, 2003.

[FW03] F. Fagnola, S. J. Wills: Solving quantum stochastic differential equations with unbounded coefficients. J. Funct. Anal. 198 (2003), no. 2, 279-310.

[CS03c] F. Cipriani, J.-L. Sauvageot, Strong solutions to the Dirichlet problem for differential forms: a quantum dynamical semigroup approach, Contemp. Math., 335, 109-117, Amer. Math. Soc., Providence RI, 2003

[CG03b] F. Cipriani, G. Grillo, Nonlinear Markov semigroups, nonlinear Dirichlet forms and applications to minimal  surfaces, J. Reine Angew. Math. 562 (2003), 201--235

[CS03b] F. Cipriani, J.-L. Sauvageot, Noncommutative potential theory andthe sign of the curvature operator in Riemannian geometry, Geom. Funct. Anal., 13, (2003), no. 3, 521-545

[CG03a] F. Cipriani, G. Grillo, Ultracontractivity and convergence to equilibrium for supercritical quasilinear parabolic equations on Riemannian manifolds, Adv. Differential Equations, 8 (2003), no. 7, 843--872

[CS03a] F. Cipriani, J.-L. Sauvageot, Derivations as square roots of Dirichlet forms, J. Funct. Anal., 201 (2003), no. 1, 78--120

[C03] F. Cipriani, Perron theory for positive maps and semigroups on von Neumann algebras, CMS Conf. Proc,, 335, (2003), 115--123, Amer. Math. Soc., Providence RI

[GW03] M. Gregoratti, R. F. Werner: Quantum lost and found. International Conference on Quantum Information, Conceptual Foundations, Developments and Perspectives (Oviedo, 2002).  J. Modern Opt.  50 (2003),  no. 6-7, 915-933.

2002

[BPe02] A. Barchielli, N. Pero, A quantum stochastic approach to the spectrum of a two-level atom, J. Opt. B: Quantum Semiclass. Opt. 4 (2002) 272-282. - quant-ph/0202166.

[BP02] A. Barchielli, A. M. Paganoni, Stochastic differential equations for trace-class operators and quantum continual measurements. In G. Da Prato, L. Tubaro (eds.), Stochastic Partial Differential Equations and Applications (Marcel Dekker, New York, 2002), pp. 53-67; math.PR/0012226.

[AF02] L. Accardi, F. Fagnola (eds): Quantum Interacting Particle Systems. QP - PQ Quantum Probability and White Noise Analysis XIV, World Scientific 2002.

[FR02a] F. Fagnola, R. Rebolledo: Some results on invariant states of quantum Markov semigroups. In: G. Da Prato and L. Tubaro (eds.) Stochastic partial differential equations and applications (Trento, 2002), 197-208, Lecture Notes in Pure and Appl. Math., 227, Dekker, New York, 2002.

[FR02b] F. Fagnola, R. Rebolledo: Subharmonic projections for a quantum Markov semigroup. J. Math. Phys. 43 (2002), no. 2, 1074-1082.

2001

[Ba01] A. Barchielli, Entropy and information gain in quantum continual measurements, in P. Tombesi, O. Hirota (eds.), Quantum Communication, Computing, and Measurement 3 (Kluwer, New York, 2001) pp. 49-57; quant-ph/0012115.

[FR01] F. Fagnola, R. Rebolledo: On the existence of invariant states for quantum dynamical semigroups. J. Math. Phys. 42 (2001), no. 3, 1296-1308.

[CF01] R. Carbone, F. Fagnola: The Feller property of a class of Quantum Markov Semigroups. In: D. Hernández, J.A. López-Mimbela, R. Quezada (eds.) Modelos Estocásticos II Guanajuato (Mexico) 23-27 Maggio 2000 VI Simposiode Probabilidad y Procesos Estocásticos. Aportaciones Matemáticas 16Sociedad Matemática Mexicana (Mexico) 2001, 143-158.

[CG01] F. Cipriani, G. Grillo, Uniform bounds for solutions to quasilinear parabolic equations, J. Differential Equations 177 (2001), no. 1, 209--234

[Gr01] M. Gregoratti: The Hamiltonian operator associated with some quantum stochastic evolutions.  Comm. Math. Phys.  222  (2001),  no. 1, 181-200.

2000

[BL00] A. Barchielli, G. Lupieri, Quantum stochastic models of two-level atoms and electromagnetic cross sections, J. Math. Phys. 41 (2000) 7181-7205; quant-ph/9904065.

[FR00] F. Fagnola, R. Rebolledo: Lectures on the Qualitative Analysis of Quantum Markov Semigroups. CIRM - Volterra International School “Quantum Interacting Particle Systems” Levico Terme, September 2000. In L. Accardi, F. Fagnola (eds): Quantum Interacting Particle Systems. QP - PQ Quantum Probability and White Noise Analysis XIV, World Scientific (2002), p. 197-239.

[CF00] R. Carbone, F. Fagnola: Exponential $L^2$-convergence of quantum Markov semigroups on B(H). Mat. Zametki 68 (2000), no. 4, 523-538, translation in Math. Notes 68 (2000), no. 3-4, 452-463.

[FW00] F. Fagnola, S. J. Wills: Mild solutions of quantum stochastic differential equations. Electron. Comm. Probab. 5 (2000), 158-171.

[CFL00] F. Cipriani, F. Fagnola, J. M. Lindsay: Spectral Analysis and Feller Property for Quantum Ornstein-Uhlenbeck Semigroups. Comm. Math. Phys. 210 (2000) 1, 85-105.

[C00b] F. Cipriani, Sobolev-Orlicz imbeddings, weak compactness, and spectrum, J. Funct. Anal., 177 (2000), no. 1, 89--106

[C00a] F. Cipriani, Estimates for capacities of nodal sets and polarity criteria in recurrent Dirichlet spaces, Forum. Math., 12 (2000), no. 1, 1--21

[Gr00] M. Gregoratti, On the Hamiltonian operator associated to some quantum stochastic differential equations.  Infin. Dimens. Anal. Quantum Probab. Relat. Top.  3  (2000),  no. 4, 483-503.

1999

[Ba99] A. Barchielli, Quantum stochastic models of two-level atoms and electromagnetic cross sections. In Mini-proceedings: Workshop on Stochastic and Quantum Physics, MaPhySto, University of Aarhus, Miscellanea no. 16, December 1999, pp. 8-16.

[Fa99] F. Fagnola: Quantum Markov Semigroups and Quantum Markov Flows. Proyecciones 18, n.3 (1999) 1-144.

1998

[BZ98] A. Barchielli, F. Zucca, On a class of stochastic differential equations used in quantum optics. Rendiconti del Seminario Matematico e Fisico di Milano, Vol. LXVI (1996) (Due Erre Grafica, Milano, 1998) pp. 355-376; funct-an/9711002.

[BL98] A. Barchielli, G. Lupieri, Photoemissive sources and quantum stochastic calculus. In R. Alicki, M. Bozejko, W. A. Majewski (eds.), Quantum Probability, (Polish Academy of Sciences, Inst. of Math., Warsavia, 1998) pp. 53-62; quant-ph/9711050.

[BPZ98] A. Barchielli, A. M. Paganoni, F. Zucca, On stochastic differential equations and semigroups of probability operators in quantum probability, Stochastic Process. Appl. 73 (1998) 69-86.

[FR98a] F. Fagnola, R. Rebolledo: A view on stochastic differential equations derived from quantum optics. Fifth Mexican Symposium on Probability Theory. Guanajuato, March 1998. Aportaciones Matemáticas. Modelos Estocásticos. 14 (1998) 193-214.

[FRS98] F. Fagnola, R. Rebolledo, C. Saavedra: Reduction of Noise by Squeezed Vacuum. Proceedings of the Second International Workshop Stochastic Analysis and Mathematical Physics ANESTOC ’96 World Scientific 1998. p. 61-71.

[CF98] A. M. Chebotarev, F. Fagnola: Sufficient conditions for conservativity of quantum dynamical semigroups. Preprint n.308. Genova, Maggio 1996. J. Funct. Anal. 153, n. 2, p. 382-404 (1998).

[FR98b] F. Fagnola, R. Rebolledo: The approach to equilibrium of a class of quantum dynamical semigroups. Infinite Dimensional Analysis, Quantum Probability and Related Topics. 1 n. 4 (1998), 561-572.

[C98] F. Cipriani, The variational approach to the Dirichlet problem in $C^*$-algebras, Banach Center Publ., 43, (1998), 135--146, Polish Acad. Sci., Warsaw

[CG98b] F. Cipriani, G. Grillo, Pointwise properties of eigenfunctions and heat kernels of Dirichlet-Schrödinger operators, Potential Anal., 8 (1998), no. 2, 101-126

[CG98a] F. Cipriani, G. Grillo, $L^p$-exponential decay for solutions to functional equations in local Dirichlet paces, J. Reine Angew. Math., 496 (1998), 63--179

1997

[Ba97] A. Barchielli, On the quantum theory of direct detection. In O. Hirota, A. S. Holevo, C. M. Caves (eds.), Quantum Communication, Computing, and Measurement (Plenum Press, New York, 1997) pp. 243-252. 

[FM97] F. Fagnola, R. Monte:  Quantum extensions of semigroups generated by Bessel processes. (Russian) Mat. Zametki 60 (1996), no. 4, 519--537, 639; translation in Math. Notes 60 (1996), no. 3-4, 389--401 (1997).

[C97] F. Cipriani, Dirichlet forms and Markovian emigroups on standard forms of von Neumann algebras, J. Funct. Anal., 147 (1997), no. 2, 259--300

1996

[Ba96] A. Barchielli: Some stochastic differential equations in quantum optics and measurement theory: the case of diffusive processes, in C. Cecchini (ed.), Contributions in Probability - In memory of Alberto Frigerio (Forum, Udine, 1996), pp. 43-55.

[BP96a] A. Barchielli, A. M. Paganoni: Detection theory in quantum optics: Stochastic representation, Quantum Semiclass. Opt. 8 (1996) 133-156.

[BP96b] A. Barchielli, A. M. Paganoni: A note on a formula of Lévy-Khinchin type in quantum probability, Nagoya Math. J. 141 (1996) 29-43.

[BFS96] R. B. V. Bhat, F. Fagnola, K. B. Sinha: On quantum extensions of semigroups of Brownian motion on a halfline. Russian J. Math. Phys. 4 (1996), no. 1, 13-28.

[CGS96] F. Cipriani, D. Guido, S. Scarlatti, A remark on trace properties of  $K$-cycles J. Operator Theory, 35 (1996), no. 1, 179-189

1995

[BH95] A. Barchielli, A. S. Holevo, Constructing quantum measurement processes via classical stochastic calculus, Stoch. Proc. Appl. 58 (1995) 293-317.

[CF95] A. M. Chebotarev,  F. Fagnola: On quantum extensions of the Azéma martingale semigroup. Séminaire de Probabilités, XXIX, 1-16, Lecture Notes in Math., 1613, Springer, Berlin, 1995.

[FR95] F. Fagnola, R. Rebolledo: Sur l'approche de l'équilibre au moyen des flots quantiques. (French) [Approach to equilibrium by means of quantum flows] C. R. Acad. Sci. Paris Sér. I Math. 321 (1995), no. 4, 473-476.

[CG95] F. Cipriani, G. Grillo, Contractivity properties of Schrödinger semigroups on bounded domains, J. London Math. Soc., 52 (1995), no. 3, 583--593

1994

[Ba94] A. Barchielli, Some stochastic differential equations in quantum optics and measurement theory: the case of counting processes. In L. Diòsi, B. Lukàcs (eds.), Stochastic Evolution of Quantum States in Open Systems and in Measurement Processes (World Scientific, Singapore, 1994), pp. 1-14.

[Fa94] F. Fagnola: On the realization of classical Markov processes as quantum flows in Fock space. Probability theory and mathematical statistics (Vilnius, 1993), 253-275, TEV, Vilnius, 1994.

[FRS94] F. Fagnola, R. Rebolledo, C. Saavedra: Quantum flows associated to master equations in quantum optics. J. Math. Phys. 35 (1994), no. 1, 1-12.

[C94b] F. Cipriani, Intrinsic ultracontractivity of Schrödinger operators with deep wells potentials, Bollettino U.M.I., 8-B (1994), no.2, 355--370

[C94a] F. Cipriani, Intrinsic ultracontractivity of  Dirichlet Laplacians in nonsmooth domains Potential Anal., 3 (1994), no. 2, 203--218