Inicjatywa Doskonałości - Uczelnia Badawcza

Uniwersyteckie Centrum Doskonałości „Dynamika, analiza matematyczna i sztuczna inteligencja”

Kontaktul. Gagarina 11, 87-100 Toruń
e-mail: damsi@umk.pl

Stany splątane i dynamika otwartych układów kwantowych

Published

2020

  1. E.O. Kiktenko, A.O. Malyshev, A.S. Mastiukova, V.I. Man’ko, A.K. Fedorov, and D. Chruściński: Probability representation of quantum dynamics using pseudostochastic maps, Phys. Rev. A 101, 052320 (2020). https://link.aps.org/doi/10.1103/PhysRevA.101.052320
  2. Joonwoo Bae, Dariusz Chruściński & Beatrix C. Hiesmayr: Mirrored entanglement witnesses,
    npj Quantum Information 6, 15 (2020). https://doi.org/10.1038/s41534-020-0242-z
  3. Gniewomir Sarbicki, Giovanni Scala, Dariusz Chruściński: A family of multipartite separability criteria based on correlation tensor, Phys. Rev. A 101, 012341 (2020). https://journals.aps.org/pra/abstract/10.1103/PhysRevA.101.012341
  4. Alberto Riccardi, Dariusz Chruściński, and Chiara Macchiavello: Optimal entanglement witnesses from limited local measurements, Phys. Rev. A 101, 062319 (2020). https://journals.aps.org/pra/abstract/10.1103/PhysRevA.101.062319
  5. Katarzyna Siudzińska, Dariusz Chruściński: Quantum evolution with a large number of negative decoherence rates, J. Phys. A: Math. Theor.  53, 375305 (2020). https://doi.org/10.1088/1751-8121/aba7f2, arXiv:2006.02793 [quant-ph]
  6. Dariusz Chruściński, Takashi Matsuoka: Quantum conditional probability and measurement induced disturbance of a quantum channel, Rep. Math. Phys. 86, 115 (2020). https://doi.org/10.1016/S0034-4877(20)30060-4
  7. Katarzyna Siudzińska: Geometry of generalized Pauli channels, Phys. Rev. A. 101, 062323 (2020). https://journals.aps.org/pra/abstract/10.1103/PhysRevA.101.062323,  arXiv:2002.04657v2 [quant-ph], 2020.
  8. Katarzyna Siudzińska: Generalization of Pauli channels through mutually unbiased measurements, Phys. Rev. A. 102 , 032603 (2020). https://journals.aps.org/pra/abstract/10.1103/PhysRevA.102.032603,  arXiv:2003.12570 [quant-ph]
  9. W. Jaskólski, G. Sarbicki: Topologically protected gap states and resonances in gated trilayer graphene, Phys. Rev. B. 102, 035424-1 (2020). https://journals.aps.org/prb/abstract/10.1103/PhysRevB.102.035424,  arXiv:2005.11473 [cond-mat.mes-hall]
  10. Gniewomir Sarbicki, Giovanni Scala, Dariusz Chruściński, Enhanced realignment criterion vs. linear entanglement witnesses,  J. Phys. A: Math. Theor. 53, 455302 (2020). https://doi.org/10.1088/1751-8121/abba46
  11. Sagnik Chakraborty, Dariusz Chruściński, Gniewomir Sarbicki, Frederik vom Ende: On the Alberti-Uhlmann Condition for Unital Channels, Quantum 4, 360 (2020). https://doi.org/10.22331/q-2020-11-08-360
  12. Katarzyna Siudzińska: Classical capacity of the generalized Pauli channels, J. Phys. A: Math. Theor. 53, 445301 (2020). https://doi.org/10.1088/1751-8121/abb276,  arXiv:1908.03917 [quant-ph]
  13. Dariusz Chruściński, Farrukh Mukhamedov: On Kadison-Schwarz Approximation to Positive Maps, Open Sys. Inf. Dyn. vol 27-3, 2050016 (2020). (DOI to be supplied)
  14. Katarzyna Siudzińska: Geometry of symmetric and non-invertible Pauli channels, Phys. Rev. A 102, 062615 (2020).  arXiv:2010.01128 [quant-ph], https://doi.org/10.1103/PhysRevA.102.062615

2021

  1. K. Siudzińska, Markovian semigroup from mixing noninvertible dynamical maps, Phys. Rev. A 103, 022605 (2021).  https://doi.org/10.1103/PhysRevA.103.022605
  2. D. Chruściński, R. Fujii, G. Kimura, H. Ohno, Constraints for the spectra of generators of quantum dynamical semigroups, Linear Alg. Appl. 63 (2021), 293.  https://doi.org/10.1016/j.laa.2021.08.012
  3. U. Chakraborty, D. Chruściński, Construction of propagators for divisible dynamical maps, New J. Phys. 23 (2021), 013009.  https://doi.org/10.1088/1367-2630/abd43b
  4. B. C. Hiesmayr, D. McNulty, S. Baek, S. Singha Roy, J. Bae, D. Chruściński, Detecting entanglement can be more effective with inequivalent mutually unbiased bases, New J. Phys. 23 (2021), 093018.  https://doi.org/10.1088/1367-2630/ac20ea
  5. D. Chruściński, On the hybrid Davies like generator for quantum dissipation, Chaos 31 (2021), 023110.  https://doi.org/10.1063/5.0036620  [Q1]
  6. W. Tarnowski, I. Yusipov, T. Laptyeva, S. Denisov, D. Chruściński, K. Życzkowski, Random generators of Markovian evolution: A quantum-classical transition by superdecoherence, Phys. Rev. E. 104 (2021), 034118.  https://doi.org/10.1103/PhysRevE.104.034118  [Q1]
  7. D. Chruściński, G. Kimura, A. Kossakowski, Y. Shishido, Universal Constraint for Relaxation Rates for Quantum Dynamical Semigroup, Phys. Rev. Lett. 127 (2021), 050401.  https://doi.org/10.1103/PhysRevLett.127.050401
  8. K. Siudzińska, S. Chakraborty, and D. Chruściński, Interpolating between Positive and Completely Positive Maps: A New Hierarchy of Entangled States, Entropy 23, 625 (2021).  https://doi.org/10.3390/e23050625
  9. A. Das, A. Bera, S. Chakraborty, D. Chruściński, Thermodynamics and the quantum speed limit in the non-Markovian regime, Phys. Rev. A. 104 (2021), 042202.  https://doi.org/10.1103/PhysRevA.104.042202
  10. K. Siudzińska, A. Das, and A. Bera, Engineering classical capacity of generalized Pauli channels with admissible memory kernels, Entropy 23, 1382 (2021).   https://doi.org/10.3390/e23111382
  11. K. Siudzińska and D. Chruściński, Entanglement witnesses from mutually unbiased measurements, Sci. Rep. 11, 22988 (2021).  https://doi.org/10.1038/s41598-021-02356-2
  12. G. Sarbicki, G. Scala, D. Chruściński, Detection Power of Separability Criteria Based on a Correlation Tensor: A Case Study, Open Syst. Inf. Dyn. 28, 2150010 (2021).  https://doi.org/10.1142/S1230161221500104
  13. A. Dąbrowska, D. Chruściński, S. Chakraborty, G. Sarbicki, Eternally non-Markovian dynamics of a qubit interacting with a single-photon wavepacket, New J. Phys. 23, 123019 (2021).  https://doi.org/10.1088/1367-2630/ac3c60

2022

  1. K. Siudzińska, Non-Markovianity criteria for mixtures of noninvertible Pauli dynamical maps, J. Phys. A: Math. Theor. 55, 215201 (2022). https://doi.org/10.1088/1751-8121/ac65c0 [Q1]
  2. K. Siudzińska, All classes of symmetric measurements in finite dimensions, Phys. Rev. A 105, 042209 (2022). https://doi.org/10.1103/PhysRevA.105.042209
  3. D. Chruściński, G. Kimura, H. Ohno, T. Singal, Bounding the Frobenius norm of a q-deformed commutator, Linear Algebra Appl. 646 (2022) 95–106, https://doi.org/10.1016/j.laa.2022.03.021
  4. Anindita Bera, Filip A. Wudarski, Gniewomir Sarbicki, and Dariusz Chruściński, Class of Bell-diagonal entanglement witnesses in C4⊗C4: Optimization and the spanning property, Phys. Rev. A 105, 052401 (2022).
    https://doi.org/10.1103/PhysRevA.105.052401
  5. Sudipto Singha Roy, Anindita Bera, and Germán Sierra, Simulating violation of causality using a topological phase transition, Phys. Rev. A 105, 032432 (2022).   https://doi.org/10.1103/PhysRevA.105.032432
  6. D. Lonigro and D. Chruściński, Quantum regression in dephasing phenomena, J. Phys. A: Math. Theor. 55, 225308 (2022). https://doi.org/10.1088/1751-8121/ac6a2d  [Q1]
  7. D. Lonigro and D. Chruściński, Quantum regression beyond the Born-Markov approximation for generalized spin-boson models, Phys. Rev. A 105, 052435 (2022).  https://link.aps.org/doi/10.1103/PhysRevA.105.052435
  8. K. Siudzińska, Indecomposability of entanglement witnesses constructed from symmetric measurements, Sci. Rep. 12, 10785 (2022),   https://doi.org/10.1038/s41598-022-14920-5
  9. K. Siudzińska, Phase-covariant mixtures of non-unital qubit maps, J. Phys. A: Math. Theor. 55, 405303 (2022),  https://doi.org/10.1088/1751-8121/ac909b  [Q1]
  10. D. Chruściński, K. Luoma, J. Piilo, A. Smirne, How to design quantum-jump trajectories via distinct master equation representations, Quantum 6, 835 (2022). https://doi.org/10.22331/q-2022-10-13-835
  11. D. Chruściński, G. Kimura, H. Ohno, T. Singal, One parameter generalization of the Böttcher-Wenzel inequality and its application to open quantum dynamics, Linear Algebra and its Applications 656, 158–166 (2022). https://doi.org/10.1016/j.laa.2022.09.022
  12. F. Benatti, D. Chruściński, R. Floreanini, Local generation of entanglement with Redfield dynamics, Open Syst. Inf. Dyn. 29:1, 2250001 (2022). https://doi.org/10.1142/S1230161222500019
  13. T. Matsuoka, D. Chruściński, Compound State, Its Conditionality and Quantum Mutual Information, [In:] Accardi, L., Mukhamedov, F., Al Rawashdeh, A. (eds.) Infinite Dimensional Analysis, Quantum Probability and Applications. ICQPRT 2021. Springer Proceedings in Mathematics & Statistics, vol 390. Springer, Cham, 2022. https://doi.org/10.1007/978-3-031-06170-7_7
  14. D. Chruściński, Dynamical maps beyond Markovian regime, Physics Reports 992, 1–85 (2022). https://doi.org/10.1016/j.physrep.2022.09.003
  15. D. Chruściński, The legacy of Andrzej Kossakowski, Open Syst. Inf. Dyn. 28:4, 2150015 (2022). https://doi.org/10.1142/S1230161221500153
  16. Yujun Choi, Tanmay Singal, Young-Wook Cho, Sang-Wook Han, Kyunghwan Oh, Sung Moon, Yong-Su Kim, and Joonwoo Bae, Single-copy certification of two-qubit gates without entanglement, Phys. Rev. Applied 18, 044046 (2022), DOI: https://doi.org/10.1103/PhysRevApplied.18.044046
  17. G. Sarbicki, M. Ghosh Dastidar, Detecting entanglement between modes of light, Phys. Rev. A 105, 062459 (2022). https://doi.org/10.1103/PhysRevA.105.062459
  18. Joonwoo Bae, Anindita Bera, Dariusz Chruscinski, Beatrix C. Hiesmayr, and Daniel McNulty, How many measurements are needed to detect bound entangled states?, Journal of Physics A: Mathematical and Theoretical 55, 505303 (December 2022), https://iopscience.iop.org/article/10.1088/1751-8121/acaa16
  19. Sagnik Chakraborty, Arpan Das, Dariusz Chruściński, Strongly coupled quantum Otto cycle with single qubit bath, Phys. Rev. E 106, 064133, pp. 1-11 (2022), https://doi.org/10.1103/PhysRevE.106.064133
  20. Chruściński Dariusz, Time inhomogeneous quantum dynamical maps, Scientific Reports  12:1, 21223, pp. 1-10 (2022), https://doi.org/10.1038/s41598-022-25694-1
  21. Davide Lonigro, Dariusz Chruściński, On the classicality of quantum dephasing processes, Frontiers in Quantum Science and Technology 1, 1090022, pp.1-13 (2022), https://doi.org/10.3389/frqst.2022.1090022

2023

  1. K. Siudzińska, Improving classical capacity of qubit dynamical maps through stationary state manipulation, J. Phys. A: Math. Theor. 56, 235301 (2023) [Q1], https://doi.org/10.1088/1751-8121/acd1c7
  2. K. Siudzińska and M. Studziński, Adjusting phase-covariant qubit channel performance with non-unitality, J. Phys. A: Math. Theor. 56, 205301 (2023) [Q1], https://doi.org/10.1088/1751-8121/acccbf
  3. K. Siudzińska, Geometry of phase-covariant qubit channels, J. Phys. Commun. 7, 075002 (2023),  https://doi.org/10.1088/2399-6528/ace0f4,   arXiv:2210.17448 [quant-ph] (2022).
  4. Madhura Ghosh Dastidar, Gniewomir Sarbicki, and Vidya Praveen Bhallamudi, Synchronized Bell protocol for detecting nonlocality between modes of light, Phys. Rev. A 108, 032410 (2023),  https://doi.org/10.1103/PhysRevA.108.032410
  5. Anindita Bera, Gniewomir Sarbicki, Dariusz Chruściński, A class of optimal positive maps in $M_n$, Linear Algebra and its Applications 668, 131-148 (2023), https://doi.org/10.1016/j.laa.2023.03.015
  6. Dariusz Chruściński, Samaneh Hesabi, Davide Lonigro, On Markovianity and classicality in multilevel spin–boson models, Scientific Reports 13:1, 1518, pp. 1-16 (2023), https://doi.org/10.1038/s41598-023-28606-z
  7. Dariusz Chruściński, Gen Kimura, Hiromichi Ohno (et al.), One-parameter generalization of the Böttcher-Wenzel inequality and its application to open quantum dynamics, Linear Algebra and Its Applications  656, pp. 158-166 (2023),  https://doi.org/10.1016/j.laa.2022.09.022
  8. Anindita Bera, Joonwoo Bae, Beatrix C. Hiesmayr, Dariusz Chruściński, On the structure of mirrored operators obtained from optimal entanglement witnesses, Scientific Reports 13:1, 10733, pp.1-15 (2023),  https://doi.org/10.1038/s41598-023-37771-0
  9. W. Tarnowski, D. Chruściński, S. Denisov, and K. Życzkowski, Random Lindblad Operators Obeying Detailed Balance, Open Systems & Information Dynamics 30:2, 2350007 (2023),  https://doi.org/10.1142/S1230161223500075
  10. Davide Lonigro, Dariusz Chruściński, Excitation-damping quantum channels, J. Phys. A: Math. and Theor. 56:25, 255301, pp. 1-22 (2023) [Q1], https://doi.org/10.1088/1751-8121/acd734
  11. Samaneh Hesabi, Anindita Bera, and Dariusz Chruscinski, Memory effects displayed in the evolution of continuous variable system, Physics Letters A 478, 128894 (May 2023),  https://doi.org/10.1016/j.physleta.2023.128894
  12. Krzysztof Szczygielski, D-divisible quantum evolution families, J. Phys. A: Math. Theor. 56, 485202 (2023) [Q1], https://doi.org/10.1088/1751-8121/ad07c8

2024

  1. K. Siudzińska, How much symmetry do symmetric measurements need for efficient operational applications? J. Phys. A: Math. Theor. 57, 355301 (2024).  https://doi.org/10.1088/1751-8121/ad6cb8
  2. K. Siudzińska, Informationally overcomplete measurements from generalized equiangular tight frames, J. Phys. A: Math. Theor. 57, 335302 (2024).   https://doi.org/10.1088/1751-8121/ad6722
  3. K. Siudzińska, Non-Markovian quantum dynamics from symmetric measurements, Phys. Rev. A 110, 012440 (2024).   https://doi.org/10.1103/PhysRevA.110.012440
  4. Chruściński Dariusz, Bhattacharya Bihalan, A class of Schwarz qubit maps with diagonal unitary and orthogonal symmetries, J. Phys. A: Math. and Theor. 57, 395202 (2024) [Q1], DOI:10.1088/1751-8121/ad75d6 
  5. Chruściński Dariusz, Kimura Gen, Mukhamedov Farrukh, Universal constraint for relaxation rates of semigroups of qubit Schwarz maps, J. Phys. A: Math. and Theor. 57, 185302 (2024) [Q1], DOI:10.1088/1751-8121/ad3c82
  6. Lonigro Davide, Sakuldee Fattah, Cywiński Łukasz, Chruściński Dariusz, Szańkowski Piotr, Double or nothing: a Kolmogorov extension theorem for multitime (bi)probabilities in quantum mechanics, Quantum 8, 1447-1475 (2024), DOI:10.22331/q-2024-08-27-1447
  7. Scala Giovanni, Bera Anindita, Sarbicki Gniewomir, Chruściński Dariusz,  Optimality of generalized Choi maps in M3, J. Phys. A: Math. and Theor. 57, 195301 (2024) [Q1], DOI:10.1088/1751-8121/ad3ca6
  8. Anindita Bera, Giovanni Scala, Gniewomir Sarbicki, Dariusz Chruściński, Generalizing Choi map in M3 beyond circulant scenario, Linear and Multilinear Algebra 72, 1-16 (2024), DOI:10.1080/03081087.2024.2326249
  9. Settimo Federico, Luoma Kimmo, Chruściński Dariusz, Vacchini Bassano, Smirne Andrea, Piilo Jyrki, Generalized-rate-operator quantum jumps via realization-dependent transformations, Phys. Rev. A 109, 062201 (2024), DOI:10.1103/physreva.109.062201
  10. A. Mayumi, G. Kimura, H. Ohno, D. Chruściński, Boettcher-Wenzel inequality for weighted Frobenius norms and its application to quantum physics, Lin. Alg. Appl. 700, 35 (2024), https://doi.org/10.1016/j.laa.2024.07.013
  11. Abhay Srivastav, Vivek Pandey, Arun Pati, Effect of measurements on quantum speed limit, Europhysics Letters 146, 60001 (2024), https://doi.org/10.1209/0295-5075/ad56c2
  12. F. Benatti, G. Nichele, D. Chruściński, Quantum vs. classical-divisibility, Phys. Rev. A 110, 052212 (2024), https://doi.org/10.1103/PhysRevA.110.052212

2025

  1. A. Rutkowski and K. Siudzińska, Controlling nonlocality of bipartite qubit states via quantum channels, Phys. Lett. A 536, 130313 (2025). https://doi.org/10.1016/j.physleta.2025.130313
  2. K. Siudzińska and K. Szczygielski, Decomposable dynamics on matrix algebras, Phys. Lett. A 532, 130185 (2025). https://doi.org/10.1016/j.physleta.2024.130185

 

Edited volumes

2022

  1. D. Chruściński, M. Michalski, J. Jurkowski,  “Andrzej Kossakowski Memorial Volume”, Open Systems and Information Dynamics, vol. 28:4 and 29:1-4 (2022), 26 contributed papers, 570 pages.

2023

  1. D. Chruściński, M. Michalski, J. Jurkowski,  “Göran Lindblad Memorial Volume”, Open Systems and Information Dynamics, vol. 30:2-3  (2023), 14 contributed papers, 386 pages.

 

Accepted

2024

  1. Vivek Pandey, Swapnil Bhowmick, Brij Mohan, Sohail, Ujjwal Sen, Fundamental speed limits on entanglement dynamics of bipartite quantum systems, arxiv:2303.07415 [quant-ph],  accepted in Physical Review A
  2. Krzysztof Szczygielski, Dariusz Chruściński, Eventually entanglement breaking quantum dynamics and eventual EB-divisibility, arXiv:2407.16583 [math-ph], accepted in J. Phys. A
  3. A. Mayumi, G. Kimura, H. Ohno, and D. Chruściński, Uncertainty relations based on state-dependent norm of commutator, arXiv:2406.12280 [quant-ph], accepted in Physical Review A

 

Submitted

2021

  1. Dariusz Chruściński, Kimmo Luoma, Jyrki Piilo, Andrea Smirne, Open system dynamics and quantum jumps: Divisibility vs. dissipativity, arXiv:2009.11312 [quant-ph], 2020.
  2. Sudipto Singha Roy, Anindita Bera, Germán Sierra, No causal order and topological phases, arXiv:2105.09795 [quant-ph], 2021.
  3. T. Singal, M.-H. Hsiu, Approximate 3-designs and partial decomposition of the Clifford group representation using transvections,  arXiv:2111.13678  [quant-ph], 2021-22

2022

  1. A. Das, B. K. Agarwalla, and V. Mukherjee, Precision bound in periodically modulated continuous quantum thermal machines, arXiv: 2204.14005 (2022).
  2. T. Saha, A. Das, and S. Ghosh, Quantum homogenization in non-Markovian collisional model, arXiv: 2201.08412 [quant-ph] (2022).
  3. D. Chruściński, Time inhomogeneous quantum dynamical maps, arXiv:2210.02770 [quant.ph] (2022)
  4. D. Chruściński, S. Hesabi, D. Lonigro, On Markovianity and classicality in multilevel spin-boson models, arXiv:2210.06199 [quant.ph] (2022)
  5. D. Lonigro, D. Chruściński, Excitation-damping quantum channels, arXiv:2206.04623 [quant.ph] (2022)
  6. Tanmay Singal, Che Chiang, Eugene Hsu, Eunsang Kim, Hsi-Sheng Goan and Min-Hsiu Hsieh, Counting stabiliser codes for arbitrary dimension, arXiv:2209.01449 [quant-ph] (2022)
  7. G.Sarbicki, M. Ghosh Dastidar, Generalization of the CHSH inequality for detecting entanglement between two-mode light states, submitted to: Phys. Rev. A, arXiv:2210.05341 [quant-ph]
  8. S. Chakraborty, A. Das and D. Chruściński, Strongly coupled quantum Otto cycle with single qubit bath, arXiv:2206.14751 [quant-ph] (2022).

2023

  1. Anindita Bera, Gniewomir Sarbicki, and Dariusz Chruściński, Optimizing positive maps in the matrix algebra Mn, arXiv:2309.09621 [quant-ph] (2023)
  2. Jaemin Kim, Anindita Bera, Joonwoo Bae, and Dariusz Chruściński, Detecting Entanglement by State Preparation and a Fixed Measurement, arXiv:2303.16368 [quant-ph] (2023)
  3. Anindita Bera, Giovanni Scala, Gniewomir Sarbicki, and Dariusz Chruściński, Generalizing Choi map in beyond circulant scenario, arXiv:2212.03807 [quant-ph] (December 2022)
  4. Giovanni Scala, Anindita Bera, Gniewomir Sarbicki, Dariusz Chruściński, Optimality of generalized Choi maps in $M_3$, https://doi.org/10.48550/arXiv.2312.02814

2024

  1. A. Rutkowski and K. Siudzińska, Controlling nonlocality of bipartite qubit states via quantum channels,
    arXiv:2407.16035 [quant-ph] (2024), submitted to Phys. Lett. A.
  2. P. Szańkowski, D. Lonigro, F. Sakuldee, Ł. Cywiński, D. Chruściński, Phenomenological quantum mechanics: deducing the formalism from experimental observations, arXiv:2410.14410 [quant-ph].
  3. P. Muratore-Ginanneschi, G. Kimura, D. Chruściński, Universal bound on the relaxation rates for quantum Markovian dynamics, arXiv:2409.00436 [quant-ph].
  4. K. Szczygielski, D. Chruściński, Eventually entanglement breaking quantum dynamics and eventual EB-divisibility, arXiv:2407.16583 [quant-ph].
  5. Bihalan Bhattacharya, Uwe Franz, Saikat Patra and Ritabrata Sengupta, Infinite dimensional dynamical maps, arXiv: 2406.19176 [quant-ph].
  6. Abhay Srivastav, Vivek Pandey, Brij Mohan, Arun Pati, Family of Exact and Inexact Quantum Speed Limits for Completely Positive and Trace-Preserving Dynamics, arXiv:2406.08584 [quant-ph], June 2024, under review in Physical Review A.
  7. Sohail, Vivek Pandey, Uttam Singh, Siddhartha Das, Fundamental limitations on the recoverability of quantum processes, arxiv:2403.12947, under review in Annales Henri Poincaré.
  8. K. Siudzińska and K. Szczygielski, Decomposable dynamics on matrix algebras, arXiv:2411.01712 [quant-ph] (2024), submitted to Phys. Lett. A.
  9. K. Siudzińska, Entanglement witnesses and separability criteria based on generalized equiangular tight frames, arXiv:2411.07065 [quant-ph] (2024).