Karol Zyczkowski

  list of co-authors

• A. Lozinski, K. Zyczkowski and W. Slomczynski,  pdf "Quantum Iterated Function Systems",   Phys. Rev. E68, 046110 (2003)  [quant-ph/0210029]
• A. Ostruszka, Ch. Manderfeld, K. Zyczkowski, and F. Haake,   pdf "Quantization of Classical Maps with tunable Ruelle-Pollicott Resonances", Phys. Rev. E  68, 056201 (2003)  [nlin.CD/0301041]
• P. Pakonski, G. Tanner, K. Zyczkowski,  pdf "Families of line-graphs and their quantization",   J. Stat. Phys  111, 1331-1352 (2003)  [nlin.CD/0110043]
• A. Lozinski,  P. Pakonski, and K. Zyczkowski, pdf "Irreversible Quantum Baker Map",  Phys. Rev. E 66, 065201(R4)  (2002).  [quant-ph/0202153]
• P. Pakonski, K. Zyczkowski, M. Kuś, pdf  "Classical 1D maps, quantum graphs and ensembles of unitary matrices", J. Phys. A 34, 9303-9317 (2001) [nlin.CD/0011050]
• P. Braun, S. Gnutzmann, F.Haake, M. Kus and K. Zyczkowski,  pdf "Level Dynamics and Universality of Spectral Fluctuations",  Found. Phys. 31, 613-622 (2001) [nlin.CD/0006022]
• P. Pakonski, A. Ostruszka and K. Zyczkowski, pdf "Quantum baker map on the sphere",   Nonlinearity 12, 269 - 284 (1999),  [chao-dyn/9805020]
• D.Braun, M.Kus, and K. Zyczkowski, pdf "Time-reversal symmetry and random polynomials", J.Phys. A30, L117 (1997), [chao-dyn/9611003]
• P.Gerwinski, F.Haake, H.Wiedemann, M. Kuś and K.Zyczkowski, pdf "Semiclassical Spectra without Periodic Orbits for a Kicked Top"; Phys.Rev.Lett. 74, 1562 (1995)
• K.Zyczkowski, H.Wiedemann and W.Slomczyñski, "How to generalize Lapunov exponent for quantum mechanics"; Vistas in Astronomy 37, 153-156 (1993)
• G.Lenz and K. Zyczkowski, pdf "Time reversal symmetry breaking and the statistical properties of quantum systems"; J.Phys. A25, 5539-5551 (1992)
• F.Haake, H.Wiedemann and K.Zyczkowski, "Lapunov exponent for quantum mechanics"; Ann. Physik 1, 531-539 (1992)
• M. Kuś and K.Zyczkowski, pdf "Relative randomness of quantum observables"; Phys.Rev. A44, 956-959 (1991)
• M.Kus, J.Zakrzewski and K.Zyczkowski, pdf "Quantum scars on a sphere"; Phys.Rev. A43, 4244-4248 (1991)
• K. Zyczkowski, pdf  "Indicators of quantum chaos based on eigenvector statistics"; J.Phys. A23, 4427-4438, (1990)
• K. Zyczkowski, pdf  "Squeezed states in a quantum chaotic system"; J.Phys A22, L1147-L1151 (1989)
• K Zyczkowski and  J.Zakrzewski , pdf  "Modulated kicks approximation in non-integrable classical and quantum systems", J. Phys.  A 21, L371-L376 (1988).
• K. Zyczkowski,  pdf "Quantum chaotic system in generalised Husimi representation"; Phys. Rev. A35, 3546-49 (1987)

• W. Roga, M. Fannes and K. Zyczkowski, pdf "Composition of quantum states and dynamical subadditivity",  J.Phys. A41, 035305-15p (2008); [quant-ph/0706.2791]
• J. Emerson, R. Alicki and K. Zyczkowski,  pdf  "Scalable Noise Estimation with Random Unitary Operators";  J.Opt. B 7,  S347-S352 (2005); [quant-ph/0503243]
•  R. Alicki,  A. Lozinski, P. Pakonski and K. Zyczkowski,  pdf  "Quantum dynamical entropy and decoherence rate";  J.Phys. A37, 5157-5172 (2004); [quant-ph/0309194]
• F. Mintert and K. Zyczkowski,  pdf  "Wehrl entropy, Lieb conjecture and entanglement monotones";  Phys. Rev.  A69, 022317 (2004); [quant-ph/0307169]
• K. Zyczkowski,  pdf  "Renyi extrapolation of Shannon entropy";  Open Syst. Inf. Dyn. 10, 297-310 (2003); [quant-ph/0305062], with 2005  corrigendum 
• S. Gnutzmann and K. Zyczkowski, pdf, "Renyi-Wehrl entropies as measures of localization in phase space", J. Phys.  A 34,  10123-10139 (2001),  [quant-ph/0106016]
• K. Zyczkowski, "Localization of eigenstates and mean Wehrl entropy", pdf Physica E 9, 583-590 (2001),  [quant-ph/9910088]
• W. Slomczynski and K. Zyczkowski,  pdf  "Mean dynamical entropy of quantum maps on the sphere diverges in the semiclassical limit";  Phys. Rev. Lett. 80, 1880-1883 (1998); [chao-dyn/9707008]
• J. Kwapieñ, W.Slomczynski, and K. Zyczkowski, pdf  "Coherent states measurement entropy", J.Phys A30, 3175-3200 (1997), [chao-dyn/9604010]
• K. Zyczkowski and W.Slomczyñski,   pdf  "Exponentional decay of relative entropies to the Kolmogorov - Sinai entropy for standard map";   Phys. Rev. E 52, 6879 (1995)
• W.Slomczyñski and K.Zyczkowski,  pdf "Quantum chaos: an entropy approach";   J. Math. Phys 35, 5674 (1994)

Entanglement  & Geometry of Quantum States

• L Skowronek and K. Zyczkowski, pdf  "Positive maps, positive polynomials and entanglement witnesses", J. Phys.  A 42,  325302 (2009) 14pp,  [quant-ph/0903.3042]
• L Skowronek, E. Stormer and K. Zyczkowski,  pdf "Cones of positive maps and their duality relations", J. Math. Phys. 50, 062106 (2009) 18pp, [quant-ph/0902.4877]
• S. Szarek, E. Werner,  and K. Zyczkowski, pdf "Geometry of sets of quantum maps: a generic positive map acting on a high-dimensional system is not completely positive",  J. Math. Phys 49,  032113 (2008)  21pp, [arXiv:0710.1571]
• V. Cappellini, H.--J. Sommers, and K. Zyczkowski, pdf "Subnormalized states and trace-non-increasing maps",  J. Math. Phys 48, 052110 (2007) [quant-ph/0701143]
• V. Cappellini, H.--J. Sommers, and K. Zyczkowski, pdf  "Distribution of G-concurrence of random pure states",   Phys. Rev.  A 74, 062322 (2006) [quant-ph/0605251]
• S. Szarek, I. Bengtsson and  K. Zyczkowski pdf  "On the structure of the body of states with positive partial transpose", J. Phys.  A 39,  L119-L126 (2006),  [quant-ph/0509008]
• H.--J. Sommers, and K. Zyczkowski,  pdf, "Bures volume of the set of mixed quantum states", J. Phys.  A 36,  10083-10100 (2003),  [quant-ph/0304041]
• K. Zyczkowski and H.--J. Sommers, pdf, "Hilbert--Schmidt  volume of the set of mixed quantum states", J. Phys.  A 36,  10115-10130 (2003),  [quant-ph/0302197]
• A. Lozinski,  A. Buchleitner, K. Zyczkowski, and  T. Wellens, pdf,  "Entanglement of 2 x 3 quantum systems",  Europhys. Lett. 62, 168-174 (2003), [quant-ph/0302144]
• V.M. Kendon, K. Zyczkowski, and  W.J. Munro,  pdf, "Bounds on entanglement in qudit subsystems",  Phys. Rev. A 66, 062310 (2002), [quant-ph/0203037]
• M. Sinolecka,  K. Zyczkowski and M. Kus,  pdf, "Manifolds of equal entanglement for composite quantum systems", Acta Phys. Pol.  B 33, 2081-2095 (2002), [quant-ph/0110082]
• I. Bengtsson, J. Braennlund and  K. Zyczkowski pdf "CPⁿ, or, entanglement illustrated",  Int. J. Mod. Phys.  A17, 4675-4696 (2002)  [quant-ph/0108064]
• K. Zyczkowski, I. Bengtsson, pdf "Relativity of pure states entanglement", Ann. Phys. (N.Y.) 295, 115-135 (2002),  [quant-ph/0103027]
• K. Zyczkowski, P. Horodecki, M. Horodecki, and R. Horodecki, pdf, Dynamics of quantum entanglement",  Phys. Rev. A 65, 012101 (2002), [quant-ph/0008115]
• K. Zyczkowski and  W. Slomczynski,   pdf  "Monge Metric on the Sphere and Geometry of Quantum States",  J. Phys.  A 34, 6689-6722 (2001) [quant-ph/0008016]
• M. Kuś,  and K. Zyczkowski, pdf "Geometry of entangled states", Phys. Rev. A63, 032307 (2001); [quant-ph/0006068]
• K. Zyczkowski, pdf  "Volume of the set of separable  states II"; Phys. Rev. A60, 3496-3507 (1999); [quant-ph/9902050] .
• K. Zyczkowski and  W.Slomczynski, pdf  "Monge distance between quantum states", J.Phys.A 31, 9095-9104  (1998), [quant-ph/9711011]
• K. Zyczkowski, P. Horodecki, A. Sanpera and M.Lwenstein, pdf  "Volume of the set of separable  states";  Phys. Rev A  58, 883 (1998)     [quant-ph/9804024],

• W. Roga, M. Fannes and K. Zyczkowski, "Davies maps for qubits and qutrits",  [arxiv:0911.5607]
• K. Majgier, H. Maasen and K. Zyczkowski, pdf "Protected Subspaces in Quantum Information", Quantum Inf. Process.  (2009)  [quant-ph/0902.4126]
• D. W. Kribs, A. Pasieka and K. Zyczkowski, pdf  "Entropy of a Quantum Error Correction Code", Open Syst. Inf. Dyn. 15, 329-343 (2008); [quant-ph/0811.1621]
• J. A. Miszczak, Z. Puchala, P. Horodecki, A. Uhlmann,  K. Zyczkowski,  pdf "Sub-- and super--fidelity as bounds for quantum fidelity", Quantum Inf. Comp. 9, 0103-0130 (2009) [arXiv:0805.2037]
• D. Markham,  J. A. Miszczak, Z. Puchala,  K. Zyczkowski  pdf "Quantum state discrimination: a geometric approach", Phys. Rev. A 77, 042111 (2008) [arXiv:0711.4286]
• H. Carteret, D. R. Terno, and K. Zyczkowski,  pdf  "Physical accessibility of non-completely positive maps", Phys. Rev. A 77, 042113 (2008) [quant-ph/0512167]
• I. Bengtsson, W. Bruzda, A. Ericsson, J.-Å. Larsson, Wojciech Tadej, and K. Zyczkowski, pdf " MUBs and Hadamards of Order Six"; J. Math. Phys 48, 052106 (2007) [quant-ph/0610161]
• M.-D. Choi, D. W. Kribs and K. Zyczkowski, pdf  "Quantum Error Correction and Higher-Rank Numerical Range", Rep. Math. Phys. 58, 77-91 (2006). [quant-ph/0511101]
• K. Zyczkowski and I. Bengtsson,  pdf  "On duality between quantum states  and quantum maps";  Open Syst. Inf. Dyn. 11, 3-42 (2004); [quant-ph/0401119]
• K. Zyczkowski and H.--J. Sommers,  pdf "Average fidelity between random quantum states",  Phys. Rev. A 71, 032313 (2005), [quant-ph/0311117]

Dynamical Systems &  Fractals



• E.M. Bollt,  P. Gora  A. Ostruszka and  K. Zyczkowski,  pdf "Basis Markov Partitions and Transition Matrices for Stochastic Systems", SIAM Journal on Applied Dynamical Systems  7, 341-360 (2008).  [nlin.CD/0605017]
• D. Wojcik and   K. Zyczkowski;  "Fractality of certain quantum states",  [math-ph/0107030]
• A. Ostruszka and  K. Zyczkowski; pdf, "Spectrum of the Frobenius-Perron operator for systems with stochastic perturbation", Phys.  Lett.  A 289,  306-312 (2001),  [nlin.CD/0106003]
•   E.M. Bollt,  T. Stanford, Y.-C. Lai, and K. .Zyczkowski,  pdf  "What Symbolic Dynamics Do We Get With A Misplaced Partition?  On the Validity of Threshold Crossings Analysis of Chaotic Time-Series" Physica D 154, 259-286 (2001)
• D. Wojcik,  I. Bialynicki-Birula  and K. Zyczkowski, pdf  "Time Evolution of Quantum Fractals",  Phys. Rev. Lett. 85, 5022-5025 (2000),  [quant-ph/0005060]
• E.M. Bollt,  T. Stanford, Y.-C. Lai, and K. Zyczkowski,  pdf "Validity of threshold-crossing analysis of symbolic dynamics from chaotic time series",  Phys. Rev. Lett.  85, 3524-3527 (2000),  [nlin.CD/0005040]
• K Zyczkowski and  Y-C. Lai;  pdf  "Devil-staircase behaviour of dynamical invariants in chaotic scattering", Physica D 142, 197-216 (2000).
•  P.Ashwin, X.-C. Fu, T. Nishikawa, and K. Zyczkowski, pdf  "Invariant sets for discontinuous parabolic area-preserving torus maps" Nonlinearity, 13, 819-835 (2000)  [chao-dyn/9908017] .
• A. Ostruszka, P. Pakonski, W. Slomczynski, K. Zyczkowski;  pdf  "Dynamical entropy for systems with stochastic perturbation"; Phys.Rev. E 62, 2018-2029 (2000). [chao-dyn/9905041]
• T. Kapitaniak, K. Zyczkowski, U. Feudel  and C. Grebogi; pdf  "Analog to Digital Conversion in Physical Measurements";   Chaos, Solitons & Fractals 11, 1247-1251 (2000),  [chao-dyn/9901028]
• W.Slomczynski, J. Kwapien and K. Zyczkowski;  pdf "Entropy computing via integration over fractal measures", CHAOS 10, 180-188 (2000);[chao-dyn/9804006]
• K. Zyczkowski and E.M. Bollt;  pdf "On the entropy devil's staircase for the family of gap tent maps" Physica D 132, 393-411 (1999),  [chao-dyn/9807013]
• K. Zyczkowski and T. Nishikawa; pdf Linear parabolic maps on the torus", Phys. Lett. A259, 377-386 (1999), [chao-dyn/9903017]
• Y-C. Lai, K Zyczkowski and C. Grebogi; pdf  "Universal behavior in the parametric evolution of chaotic saddles", Phys.Rev. E 59, 5261-5265 (1999).

Quantum Billiards & Wave Chaos

 
• O. Hul,  S. Bauch,  P. Pakonski,  N. Savytskyy, K. Zyczkowski, and L. Sirko, pdf  "Experimental simulation of quantum graphs by microwave networks", Phys. Rev. E69,  056205 (2004)  [nlin.CD/0404006]
• A.Shudo, Y.Shimizu, P. Seba, J.Stein, H.-J.Stoeckmann and K.Zyczkowski, pdf  "Statistical properties of spectra of pseudointegrable systems", Phys. Rev. E49,  3748-3756 (1994)
• K. Zyczkowski, pdf  "Classical and quantum billiards: integrable, nonintegrable and pseudo-integrable"; Acta Phys. Pol. B23, 245-270 (1992)
• F.Haake, G. Lenz, P. Seba, J.Stein, H-J.Stoeckmann and K.Zyczkowski, pdf "Manifestation of wave chaos in pseudointegrable microwave resonators"; Phys.Rev. A44, R6161-R6164 (1991)
• P. Seba and K. Zyczkowski,  pdf  "Wave chaos in classically non chaotic system"; Phys. Rev. A44, 3457-3465 (1991)

• V.Al. Osipov,  H.--J. Sommers, and K. Zyczkowski, pdf "Random Bures mixed states and the distribution of their purity", J. Phys. A 43, 055302  (2010) 22pp, [arXiv:0909.5094]
• W. Bruzda, V. Cappellini, H.--J. Sommers, and K. Zyczkowski, pdf "Random Quantum Operations", Phys.  Lett.  A 373,  320-324 (2009) [arXiv:0804.2361]
• V. Cappellini,  H.--J. Sommers, W. Bruzda, and K. Zyczkowski, pdf "Random bistochastic matrices", J. Phys.  A 42,  365209 (2009) 23pp,  [arXiv:07011.3345]
• H.--J. Sommers and K. Zyczkowski pdf  "Statistical properties of random density matrices",  J. Phys. A37  8457-8466  (2004), [quant-ph/0405031]
• K. Zyczkowski,  M. Kus, W. Slomczynski and H.-J. Sommers,  pdf    "Random unistochastic matrices",   J. Phys. A36  3425-3450  (2003),  [nlin.CD/0112036]
• K. Zyczkowski and H.-J. Sommers,  pdf  "Induced measures in the space of mixed quantum states",  J. Phys. A  34, 7111-7125 (2001)  [quant-ph/0012101]
• K. Zyczkowski and H.-J. Sommers, pdf  "Truncations of random unitary matrices; J. Phys. A33, 2045-2057 (2000); [chao-dyn/9910032]
• M. Pozniak, K. Zyczkowski, and M. Kus,  pdf  "Composed ensembles of random unitary matrices"; J.Phys.A 31, 1059-1071 (1998), [chao-dyn/9707006]
• P. Kunstman, K. Zyczkowski, and J. Zakrzewski,  pdf  "Nonuniversality of level dynamics", Phys. Rev. E55, 2446-2454 (1997), [chao-dyn/9611019]
• F. Haake, M. Kus, H.--J. Sommers, H.Schomerus, and K. Zyczkowski, pdf  "Secular determinants of random unitary matrices",  J. Phys. A 29, 3641-3658 (1996),  [chao-dyn/9603006]
• K. Zyczkowski and M. Kus, pdf  "Interpolating ensembles of random unitary matrices";   Phys. Rev.  E 53, 319 (1996)
• F. Izrailev, L. Molinari, and K. Zyczkowski, pdf "Periodic and non-periodic band random matrices: structure of eigenstates",  J.Physique I (France) 6, 455 (1996)
• K. Zyczkowski and R.Serwicki, pdf "Scaling laws of complex band random matrices"; Z. Phys. B 99, 449-455 (1996)
• K. Zyczkowski - "Random matrices of circular symplectic ensemble"; in Chaos - The Interplay between Stochastic and Deterministic Behaviour, Proceedings, Karpacz,  Poland 1995, ed. P. Garbaczewski, M.Wolf and A.Weron, Springer 1995, pp 565-571.
• K. Zyczkowski and M. Kus,  pdf "Random unitary matrices"; J.Phys. A 27, 4235-4245 (1994)
• K. Zyczkowski, "Relatively random unitary operators"; Operator Theory: Advances & Applications 70 277-280 (1994)
• K. Zyczkowski,pdf "Parametric dynamics of quantum systems and transitions between ensembles of random matrices";  Acta Phys. Pol. B24, 967-1025 (1993)
• K. Zyczkowski, M. Lewenstein, M. Kus and F. Izrailev,  pdf  "Eigenvectors statistics of random band matrices"; Phys.Rev. A45, 811-815 (1992)
• G.Lenz, K. Zyczkowski and D. Saher,   pdf  "Scaling laws of additive random-matrix model"; Phys.Rev. A44, 8043-8050 (1991)
• B. Dietz and K. Zyczkowski, "Level spacing distribution beyond Wigner surmise"; Z.Phys. B84, 157-158 (1991)
• K. Zyczkowski and G. Lenz, "Eigenvector statistics for the transition from the orthogonal to the unitary ensemble";   Z.Phys. B82, 299-303 (1991)
• F. Haake and K. Zyczkowski,  pdf  "Random--matrix theory and eigenmodes of dynamical systems"; Phys.Rev. A42, 1013-1016, (1990)

• R. Gebarowski, P. Seba, K. Zyczkowski, and J. Zakrzewski, pdf  "Quantum scattering in the strip: from ballistic to localized regimes", Europhys.  J.  B 6, 399-409 (1998), [cond-mat/9801314]
• K. Zyczkowski,  pdf "Scattering matrices with block symmetries", Phys. Rev. E56, 2257-2260 (1997), [chao-dyn/9703001]
• P. Seba, K. Zyczkowski, and J. Zakrzewski,   pdf "Statistical properties of random scattering matrices", Phys. Rev. E 54, 2438-2446 (1996), [chao-dyn/9603005]

Conductivity in disordered media



• P. Seba, K. Zyczkowski, J.Zakrzewski; "Random matrix approach to `nonuniversal' conductance"; Acta Physica Polonica B 30, 2797-2810 (1999); [cond-mat/9712048]
• I.Guarneri, K. Zyczkowski, J.Zakrzewski, L. Molinari and G. Casati, pdf  "Parametric spectral correlations of disordered systems in the Fourier domain"; Phys. Rev. E52, 2220-2234 (1995), [chao-dyn/9501019]
• K. Zyczkowski, L. Molinari and F. Izrailev, pdf "Level curvature and metal--insulator transition in 3D Anderson model", J.Physique I (France) 4, 1469 (1994)
• G. Casati, I. Guarneri, F. Izrailev, L. Molinari and K. Zyczkowski,  pdf  "Periodic band random matrices, curvature and conductance in disordered media"; Phys. Rev. Lett. 72, 2697-2700

• A. Kenfack and  K. Zyczkowski,  pdf  "Negativity of the Wigner function as an indicator of nonclassicality";  J.Opt. B 6,  396-404 (2004); [quant-ph/0406015]
• K.Zyczkowski and F.Haake,  pdf "Line width of a sub-poissonian laser"; J. Quant. Opt. 4, 79-83 (1992)
• K.Zyczkowski, J.Zakrzewski, "Diffusive ionization in the Rosen-Morse potential"; Acta Phys.Pol. A75, 743-769 (1989)
• J.Zakrzewski, K.Zyczkowski,  pdf  "A simple model for strong field ionization"; Phys. Rev. A36, 4311-20 (1987)
• J.Mostowski, K.Zyczkowski, "Phase space approach to above threshold ionisation"; Z. Physik D5, 293-98 (1987)
• T.Dohnalik, J. Koperski, M. Stankiewicz, J. Zakrzewski K.Zyczkowski, "Quantum beats in forward scattering of resonance radiation"; Acta Phys. Pol. A66, 493-501 (1984)

• E. Aurell  and K. Zyczkowski: "Option pricing & partial hedging: theory of Polish Options", -  preprint
• E. Aurell, J-P. Bouchaud, M.Potters, and K. Zyczkowski, "Option pricing and hedging beyond Black-Scholes",  preprint
• E. Aurell  and K.Zyczkowski,  "Risk-return arguments applied to options with trading costs", J.Phys. IV France 8, Pr6-3 (1998), [cond-mat/9803238]

•  C. Dunkl and K. Zyczkowski, pdf "Volume of the set of unistochastic matrices of order 3 and the mean Jarlskog invariant",  J. Math. Phys 50, 123521 (2000)"  [arxiv.org/0909.0116]
• P.  Gawron, Z.  Puchala, J. A. Miszczak, L. Skowronek, M.-D. Choi, K. Zyczkowski, "Local numerical range: a versatile tool in the theory of quantum information".  [arxiv.org/0905.3646]
• W. Tadej, K. Zyczkowski,  pdf "Defect of a unitary matrix",  Lin. Alg. Appl. 429 447-481 (2008),  [math.RA/0702510]
• M.-D. Choi, J.A. Holbrook, D. W. Kribs and K. Zyczkowski, pdf "Higher-Rank Numerical Ranges of unitary and normal matrices", Operators  and Matrices 1, 409-426 (2007) [quant-ph/0608244] 
• W. Tadej and K. Zyczkowski,  pdf  "A concise guide to complex Hadamard matrices", Open Syst. Inf. Dyn. 13, 133-177 (2006); [quant-ph/0512154]
• M.-D. Choi, D. W. Kribs and K. Zyczkowski, pdf "Higher-Rank Numerical Ranges and Compression Problems", Lin. Alg. Appl. 418, 828-839 (2006).  [math.FA/0511278]
• I. Bengtsson, A. Ericsson, M. Kus, W. Tadej, and K. Zyczkowski, pdf   "Birkhoff's polytope and unistochastic matrices, N=3 and N=4", Comm. Math. Phys. 259,  307-324 (2005).    [math.CO/0402325]

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