Karol Życzkowski

scientific publications

(reverse chronological order - updated December 7, 2020)

Quantum Chaos

Foundations of Quantum Theory

Quantum Measurement & Entropy

Entanglement & Geometry of Quantum States

Theory of Quantum Information

Dynamical Systems & Fractals

Quantum Billiards & Wave Chaos

Random Matrices

Chaotic Scattering and statistical physics

Conductivity in Disordered Media

Quantum Optics

Mathematical theory of social choice

Financial Mathematics

some other Mathematics

Scientometrics

full list of publications and list of co-authors

The copyright for the PDF/PS files attached is owned by the publishers: American Institute of Physics, Elsevier Science, Institute of Physics Publishing, Plenum Publishing Corporation, The American Physical Society, Springer Verlag, World Scientific and other publishers

Quantum chaos

S. Denisov, T. Laptyeva, W. Tarnowski, D. Chruściński and K. Życzkowski, pdf "Universal spectra of random Lindblad operators", supplement Phys. Rev. Lett. 123, 140403 (2019); [arXiv:1811.12282 ]
W. Roga, M. Smaczynski and K. Życzkowski, pdf "Composition of quantum operations and products of random matrices", Acta Phys. Pol. B 42, 1123-1140 (2011), [arxiv:1105.3830]
W. Bruzda, M Smaczynski, V. Cappellini, H.-J. Sommers and K. Zyczkowski, pdf "Universality of spectra for interacting quantum chaotic systems", Phys. Rev. E 81, 066209 (2010), [arxiv:1003.2931]
A. Lozinski, K. Zyczkowski and W. Slomczynski, pdf "Quantum Iterated Function Systems", Phys. Rev. E 68, 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.Slomczynski, pdf "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, pdf "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)

Foundations of Quantum Theory

D. Goyeneche, W. Bruzda, O. Turek, D. Alsina, K. Życzkowski, "The powerfulness of classical correlations", preprint [arXiv:2004.00695]
D. Alsina, A. Cervera, D. Goyeneche, J. I. Latorre and K. Życzkowski, pdf "Operational approach to Bell inequalities: applications to qutrits", Phys. Rev. A94 , 032102 (2016), preprint [arXiv:1606.01991]
T. Durt, I. Bengtsson, B.-G. Englert and K. Życzkowski, pdf "On mutually unbiased bases", J.Int. J. Quant. Inform. 8, 535-640 (2010), [arxiv:1004.3348]
K. Zyczkowski, pdf "Quartic quantum theory: an extension of the standard quantum mechanics", J.Phys. A41, 0355302-23p (2008); [quant-ph/0804.1247]

Quantum Measurement & Entropy

J. Czartowski, D. Goyeneche, M. Grassl, K. Życzkowski, pdf "Iso-entangled mutually unbiased bases, symmetric quantum measurements and mixed-state designs", Phys. Rev. Lett. 124, 090503 (2020); [arXiv:1906.12291]
K. Szymański and K. Życzkowski, pdf "Geometric and algebraic origins of additive uncertainty relations", J.Phys. A 53, 015302 (2020); [arXiv:1804.06191]
J. Czartowski, D. Braun, K. Życzkowski, pdf "Trade--off relations for operation entropy of complementary quantum channels", IJ Quant. Inform. 17, 1950046--23p (2019); [arXiv:1908.03492]
J. Czartowski, D. Goyeneche and K. Życzkowski, pdf "Entanglement properties of multipartite informationally complete quantum measurements", J.Phys. A51, 305302-15 (2018), [arXiv:1801.07927]
Z. Puchała, Ł. Rudnicki, A. Krawiec and K. Życzkowski, pdf "Majorization uncertainty relations for mixed quantum states", J.Phys. A 51, 175306 (2018); [arXiv:1709.10294]
W. Bruzda, D. Goyeneche and K. Życzkowski, pdf Quantum measurements with prescribed symmetry, Phys. Rev. A 96, 022105 (2017), [arXiv:1704.04609]
A.E.Rastegin and K. Życzkowski, pdf "Majorization entropic uncertainty relations for quantum operations", J.Phys. A 49, 355301 (2016); [arxiv:1511.07099]
R. Adamczak, R. Latała, Z. Puchała and K. Życzkowski, pdf "Asymptotic entropic uncertainty relations", J. Math. Phys. 57, 032204 (2016); [arXiv:1412.7065]
Z. Puchala, L. Rudnicki, K. Chabuda, M. Paraniak and K. Zyczkowski, pdf "Certainty relations, mutual entanglement and non-displacable manifolds", Phys. Rev. A 92, 032109 (2015), [arXiv:1506.07709]
L. Rudnicki, Z. Puchala and K. Zyczkowski, pdf "Strong majorization entropic uncertainty relations", Phys. Rev. A 89, 052115 (2014), [arXiv: 1402.0129]
Z. Puchala, L. Rudnicki and K. Zyczkowski, pdf "Majorization entropic uncertainty relations", J.Phys. A 46, 272002-12pp (2013); [arxiv:1304.7755]
W. Roga, Z. Puchala, L. Rudnicki and K. Zyczkowski, pdf "Entropic trade-off relations for quantum operations", Phys. Rev. A 87, 032308-13pp (2013);[arxiv:1206.2536]
W. Roga, K. Zyczkowski and M. Fannes, pdf "Entropic characterization of quantum operations", Int. J. Quantum Information 9, 1031-1045 (2011), [arxiv:1101.4105]
W. Roga, M. Fannes and K. Zyczkowski, pdf "Composition of quantum states and dynamical subadditivity", J. Phys. A 41, 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. Pakoński 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. Kwapień, W.Slomczynski, and K. Zyczkowski, pdf "Coherent states measurement entropy", J.Phys A30, 3175-3200 (1997), [chao-dyn/9604010]
K. Zyczkowski and W.Slomczyński, pdf "Exponentional decay of relative entropies to the Kolmogorov - Sinai entropy for standard map"; Phys. Rev. E 52, 6879 (1995)
W.Slomczyński and K.Zyczkowski, pdf "Quantum chaos: an entropy approach"; J. Math. Phys 35, 5674 (1994)

Entanglement & Geometry of Quantum States

G. M. Quinta, R. Andre, A. Burchardt, and K. Życzkowski, pdf "Cut-resistant links and multipartite entanglement resistant to particle loss", Phys. Rev. A 100, 062329 (2019), [arXiv:1908.10390]
J. Czartowski, K. Szymański, B. Gardas, Y. Fyodorov and K. Życzkowski, pdf "Separability gap and large-deviation entanglement criterion", Phys. Rev. A 100, 042326 (2019), [arXiv:1812.09251]
W. Kłobus, A. Burchardt, A. Kołodziejski, M. Pandit, T. Vertesi, K. Życzkowski and W. Laskowski, pdf "On k-uniform mixed states", Phys. Rev. A 100, 032112 (2019), [arXiv:1906.01311]
M. Enriquez, F. Delgado and K. Życzkowski, pdf "Entanglement of three-qubit random pure states", Entropy 20, 745 (2018), [arxiv:1809.00642]
G. Rajchel, A. Gąsiorowski and K. Zyczkowski, pdf "Robust Hadamard matrices, unistochastic rays in Birkhoff polytope
and equi-entangled bases in composite spaces", Math. Comput.Sci. 12, 473-490 (2018), [arXiv:1804.10715]
L. Saveso, D. Goyeneche and K. Życzkowski, pdf "Coarse-grained entanglement classification through orthogonal arrays", J. Math. Phys.59, 072203 (2018), [arXiv:1709.05916]
D. Goyeneche, Z. Raissi, S. Di Martino and K. Zyczkowski, pdf "Entanglement and quantum combinatorial designs", Phys. Rev. A 97 , 062326-12 (2018), [arXiv:1708.05946]
D. Goyeneche, J. Bielawski and K. Zyczkowski, pdf "Multipartite entanglement in heterogeneous systems", Phys. Rev. A94 , 012346 (2016), [arXiv:1602.08064]
M. Enriquez, Z. Puchala and K. Zyczkowski, pdf "Minimal Renyi-Ingarden-Urbanik entropy of multipartite quantum states", Entropy 17, 5063-5084 (2015), [arXiv:1506.04788]
K. Bartkiewicz, P. Horodecki, K. Lemr, A. Miranowicz and K. Zyczkowski, pdf "Method for universal detection of two-photon polarization entanglement", Phys. Rev. A 91, 032315 (2015), [arXiv:1405.5560]
D. Goyeneche and K. Zyczkowski, pdf "Genuinely multipartite entangled states and orthogonal arrays", Phys. Rev. A 90, 022316 (2014), [arXiv:1404.3586]
L. Rudnicki, Z. Puchala, P. Horodecki, and K. Zyczkowski, pdf "A Natural Entanglement Test", J. Phys. A 47, 424035 (2014), [arXiv:1211.2306]
B. Collins, I. Nechita and K. Zyczkowski, pdf " Area law for random graph states", J. Phys. A 46, 305302 (2013), [arXiv:1302.0709]
L. Rudnicki, Z. Puchala, P. Horodecki, and K. Zyczkowski, pdf "Collectibility for Mixed Quantum States", Phys. Rev. A 86, 062329 (2012), [arXiv:1211.0573]
Z. Puchala, J.A. Miszczak, P. Gawron, C.F. Dunkl, J. A. Holbrook, K. Zyczkowski, pdf "Restricted numerical shadow and geometry of quantum entanglement", [arXiv:1201.2524]
I. Bentgsson, S. Weis and K. Zyczkowski, pdf "Geometry of the set of mixed quantum states: An apophatic approach", [arXiv:1112.2347], published in XXIX Workshop on Geometric Methods in Physics, Trends in Mathematics, pp. 175-197, ed P. Kielanowski et al. Springer, Basel 2013
W. Ganczarek, M. Kus and K. Zyczkowski,pdf "Barycentric measure of quantum entanglement", Phys. Rev. A 85, 032314 (2012) [arXiv:1112.0437]
L. Rudnicki, P. Horodecki, and K. Zyczkowski, pdf "Collective Uncertainty Entanglement Test", Phys. Rev. Lett. 107, 150502 (2011), [arXiv:1106.2018]
S. Szarek, E. Werner, and K. Zyczkowski, pdf "How often is a random quantum state k-entangled?" J. Phys. A 44, 045303 (2011), [arXiv:1010.1485]
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. Łozinski, 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. Sinołęcka, K. Zyczkowski and M. Kuś, 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],

Theory of Quantum Information

F. Shahbeigi, D. Amaro-Alcala, Z. Puchała and K. Życzkowski,
"Log-Convex set of Lindblad semigroups acting on N-level system",

preprint [arXiv:2003.12184]
K. Korzekwa, Z. Puchała, M. Tomamichel and K. Życzkowski; "Encoding classical information into quantum resources", [arXiv:1911.12373]
B. Jonnadula, P. Mandayam, K. Życzkowski and A. Lakshminarayan, "Thermalization of entangling power with arbitrarily weak interactions", [arXiv:1909.08139 ]
T. Linowski, G. Rajchel-Mieldzioć and K. Życzkowski, pdf, "Entangling power of multipartite unitary gates" J. Phys. A 53, 125303 (2020); [arXiv:1909.07709]
K. Korzekwa, S. Czachórski, Z. Puchała and K. Życzkowski, pdf "Distinguishing classically indistinguishable states and channels", J. Phys. A 52, 475303 (2019); [arXiv:1812.09083]
Z. Puchała, Ł. Rudnicki, and K. Życzkowski, pdf "Pauli semigroups and unistochastic quantum channels", Phys. Lett. A383, 2376-2381 (2019); [arxiv:1903.12448]
M. Białończyk, A. Jamiołkowski and K. Życzkowski, pdf "Application of Shemesh theorem to analysis of spectral properties of quantum channels", J. Math. Phys. 59, 102204 (2018); [arxiv:1711.02354]
A. Mandarino, T. Linowski and K. Życzkowski, pdf, "Bipartite unitary gates and billiard dynamics in the Weyl chamber", Phys. Rev. A 95, 040302(R) (2017), [arXiv:1710.10983]
Ł. Rudnicki, Z. Puchała and K. Życzkowski, pdf "Gauge invariant information concerning quantum channels", Quantum 2, 60 (2018); [arxiv:1707.06926]
K. Korzekwa, S. Czachórski, Z. Puchała and K. Życzkowski, pdf "Coherifying quantum channels", N.J.Phys. 20, 043028 (2018); [arXiv:710.04228]
B. Jonnadula, P. Mandayam, K. Życzkowski and A. Lakshminarayan, pdf, "Impact of local dynamics on entangling power", Phys. Rev. A 95, 040302(R) (2017), [arxiv:1611.00479]
P. Lipka-Bartosik and K. Zyczkowski, pdf, "Nuclear numerical range and quantum error correction codes for non-unitary noise models", Quant. Infor. Proc. 16:9 (2017), [arxiv:1610.00930]
M. Smaczynski, W. Roga and K. Zyczkowski, pdf "Selfcomplementary quantum channels", Open Syst. Inf. Dyn. 23, 1650001-26 (2016), [arxiv:1602.02140]
A.Lakshminarayan, Z. Puchala and K. Zyczkowski, pdf "Diagonal unitary entangling gates and contradiagonal quantum states", Phys. Rev. A 90, 0032303 (2014), [arxiv:1407.1169]
M. Demianowicz, P. Horodecki and K. Zyczkowski, pdf "Multiaccess quantum communication and product higher rank numerical range", Quantum Inform. Comput. 13, 0541-0566 (2013), [arxiv:1209.0119]
M. Fannes, F. de Melo, W. Roga, K. Zyczkowski, pdf "Matrices of fidelities for ensembles of quantum states and the Holevo quantity", Quantum Information & Computation 12, 472-489 (2012), [arxiv:1104.2271]
W. Roga, M. Fannes and K. Zyczkowski, pdf "Universal bounds for the Holevo quantity, coherent information and the Jensen-Shannon divergence", Phys. Rev. Lett. 105, 040505 (2010), [arxiv:1004.4782]
W. Roga, M. Fannes and K. Zyczkowski, pdf "Davies maps for qubits and qutrits", Rep. Math. Phys. 66, 311-329 (2010); [arxiv:0911.5607]
K. Majgier, H. Maasen and K. Zyczkowski, pdf "Protected Subspaces in Quantum Information", Quantum Inf. Process. 9 343-367 (2010) [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)

Random matrices

I. Nechita, Z. Puchała, Ł.Pawela, K. Życzkowski, pdf Almost all quantum channels are equidistant, J. Math. Phys. 59, 052201 (2018), preprint [arXiv:1612.00401]
M. Markiewicz, Z. Puchała, A. de Rosier, W. Laskowski, K. Życzkowski, pdf Quantum noise generated by local random Hamiltonians, Phys. Rev. A 95, 032333 (2017) [arXiv:1612.07826]
Z. Puchala, Ł. Pawela and K. Zyczkowski, pdf "Distinguishability of generic quantum states", Phys. Rev. A 93, 061221 (2016), [arXiv:1507.05123]
M. Mlotkowski, M. A. Nowak, K. A. Penson and K. Zyczkowski, pdf "Spectral density of generalized Wishart matrices and free multiplicative convolution", Phys. Rev. E87, 022121 (12pp) (2015) [arXiv:1407.1282]
P. Kondratiuk and K. Zyczkowski, pdf "Random unitary matrices associated to a graph", Acta. Phys. Pol. A 124, 1098 (2013), [arXiv:1311.3585]
M. Musz , M. Kus, and K. Zyczkowski, pdf "Unitary quantum gates, perfect entanglers, and unistochastic maps", Phys. Rev. A87, 022111(12pp) (2013) [arXiv:1211.3287]
S. Braunstein, S. Pirandola and K. Zyczkowski, pdf "Better Late than Never: Information Retrieval from Black Holes", Phys. Rev. Lett. 110, 101301 (2013)
M.Smaczynski, T. Tkocz, M. Kus, and K. Zyczkowski, pdf "Extremal spacings of random unitary matrices", Phys. Rev. E 88, 052902 (2013) [arXiv:1204.3023]
T. Tkocz, M. Smaczynski, M. Kus, O. Zeituni and K. Zyczkowski, pdf "Tensor products of random unitary matrices", Random Matrices: Theory and Applications 1, 1250009 (26 pp) (2012) [arXiv:1203.3818]
J. Fischmann, W. Bruzda, B. A. Khoruzhenko, H.-J. Sommers and K.Zyczkowski, pdf "Induced Ginibre ensemble of random matrices and quantum operations, J. Phys. A 45, 075203 (2012) [arXiv:1107.5019]
K. Zyczkowski, K. A. Penson, I. Nechita and B. Collins, pdf " Generating random density matrices", J. Math. Phys. 52, 062201 (2011) [arXiv:1010.3570]
K. A. Penson and K. Zyczkowski, pdf "Product of Ginibre matrices: Fuss-Catalan and Raney distribution", Phys. Rev. E 83, 061118 (2011) [arXiv:1103.3453]
B. A. Khoruzhenko, H.--J. Sommers, and K. Zyczkowski, pdf "Truncations of Random Orthogonal Matrices", Phys. Rev. E 82, 040106(R) (2010) [arXiv:1008.2075]
B. Collins, I. Nechita and K. Zyczkowski, pdf "Random graph states, maximal flow and Fuss-Catalan distributions", J. Phys. A 43, 275303 (2010) 39pp, [arXiv:1003.3075]
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, pdf "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, pdf "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, pdf "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)

Chaotic scattering and statistical physics

E. Aurell, J. Zakrzewski and K. Zyczkowski, pdf "Time reversals of irreversible quantum maps", J. Phys. A 48, 38FT01, (2015) [arXiv:1505.02259]
A.E. Rastegin and K. Zyczkowski, pdf "Jarzynski equality for quantum stochastic maps", Phys.Rev. E89, 012127, (2014) [arXiv:1307.5370]
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

Quantum Optics

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, pdf "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)

Mathematical theory of social choice

D. Boratyn, W. Kirsch, W.Slomczyński, D. Stolicki and K. Życzkowski; "Average Weights and Power in Weighted Voting Games", [arXiv:1905.04261]
W. Kirsch, W.Slomczyński, D. Stolicki and K. Życzkowski; "Double Majority and Generalized Brexit: Explaining Counterintuitive Results", [arXiv:1812.07048]
W.Slomczyński and K. Zyczkowski; pdf "Mathematical aspects of degressive proportionality", Mathem. Social Science 63, 94-101 (2012); arXiv:1110.1468
K. Zyczkowski and W. Slomczynski pdf "Square root voting system, optimal threshold and π", in Power, Voting, and Voting Power: 30 Years After, ed. M. J. Holler and H. Nurmi, Springer-Verlag, Berlin 2013, arXiv:1104.5213
W. Slomczynski and K. Zyczkowski pdf "Penrose voting system and optimal quota", Acta Physica Polonica B37, 3133 (2006); [arXiv: 0610271]

Financial Mathematics

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]

some other Mathematics

W. Bruzda, S. Friedland and K. Życzkowski; "Tensor rank and entanglement of pure quantum states", [arXiv:1912.06854 ]
K. Szymański, S. Weis and K. Życzkowski, pdf "Classification of joint numerical ranges of three hermitian matrices of size three", Lin. Alg. Appl. 545, 148-173 (2018) [arxiv:1603.06569]
K. Szymański, B. Collins, T. Szarek and K. Życzkowski, pdf " Convex set of quantum states with positive partial transpose analysed by hit and run algorithm", J. Phys.A 50, 255206-12 (2017), [arxiv:1611.01194]
C.F. Dunkl, P. Gawron, Ł Pawela, Z. Puchala, K. Życzkowski, pdf "Real numerical shadow and generalized B-splines", Lin. Alg. Appl. 479, 12-51 (2015) [arxiv:1409.4941]
B. Collins, T. Kousha, R. Kulik, T. Szarek and K. Zyczkowski, pdf "Exponentially convergent algorithm to generate random points in a d-dimensional body", [arXiv:1312.7061]
B. Collins, P. Gawron, A. Litvak and K. Zyczkowski, pdf "Numerical range for random matrices", J. Math. Anal. Appl. 418, 516-533 (2014) [arXiv:1309.6203]
W. Mlotkowski, K. Penson, and K. Zyczkowski, pdf "Densities of the Raney distributions", Documenta Math. 18, 1573--1596 (2013), [arXiv:1211.7259]
E.Gutkin and K. Zyczkowski, pdf "Joint numerical ranges, quantum maps, and joint numerical shadows", Linear Algebra Appl. 438, 2394–2404 (2013), [arXiv:1207.1227]
Z. Puchala, J. A. Miszczak, P. Gawron, C.F. Dunkl, J. A. Holbrook, K. Życzkowski, pdf "Restricted numerical shadow and geometry of quantum entanglement", J.Phys. A 45, 415309 (2012) [arxiv:1201.2524]
T. Banica, I. Nechita and K. Zyczkowski, pdf "Almost Hadamard matrices: general theory and examples", Open Systems Inform. Dynamics 19, 1250024 (26 pp)(2012), [arXiv:1202.2025]
C.F. Dunkl, P. Gawron, J. A. Holbrook, J. Miszczak, Z. Puchala, K. Zyczkowski, pdf "Numerical shadow and geometry of quantum states", J. Phys. A44, 335301 (19p) (2011) [arxiv:1104.2760]
C. Dunkl, P. Gawron, J. A. Holbrook, Z. Puchala, K. Zyczkowski, pdf "Numerical shadows: measures and densities on the numerical range", Linear Algebra Appl. 434, 2042-2080 (2011) [arxiv:1010.4189]
Z. Puchala, P. Gawron, J. A. Miszczak, L. Skowronek, M.-D. Choi, K. Zyczkowski, pdf "Product numerical range in a space with tensor product structure", Linear Algebra Appl. 434, 327-342 (2011) [arxiv:1008.3482]
P. Gawron, Z. Puchala, J. A. Miszczak, L. Skowronek, K. Zyczkowski, pdf "Restricted numerical range: a versatile tool in the theory of quantum information" J. Math. Phys 51, 102204 (2010) [arxiv.org/0905.3646]
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 (2009)" [arxiv.org/0909.0116]
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]

Scientometrics

K. Zyczkowski, pdf "Citation graph, weighted impact factors and performance indices", Scientometrics 85, 301-315 (2010); [arxiv:0904.2110]

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