Aeyels, D.: Generic observability of differentiable systems. SIAM J. Control. Optim. 19(5), 595–603 (1981)
Article MathSciNet Google Scholar
Bachiller, A.Y.: Quantum tomography enabled by homogeneous Markovian evolutions. Master’s thesis, Department of Physics, Technical University of Munich (2023)
Burgarth, D., Maruyama, K., Nori, F.: Coupling strength estimation for spin chains despite restricted access. Phys. Rev. A 79, 020305 (2009)
Carmeli, C., Heinosaari, T., Kech, M., Schultz, J., Toigo, A.: Stable pure state quantum tomography from five orthonormal bases. Europhys. Lett. 115(3), 30001 (2016)
Czerwinski, A.: Quantum state tomography with informationally complete POVMs generated in the time domain. Quantum Inf. Process. 20(3), 105 (2021)
Article ADS MathSciNet Google Scholar
de Almeida, J.O., Kleinmann, M., Sentis, G.: Comparison of confidence regions for quantum state tomography (2023). arXiv:2303.07136
Elben, A., Flammia, S.T., Huang, H.-Y., Kueng, R., Preskill, J., Vermersch, B., Zoller, P.: The randomized measurement toolbox. Nat. Rev. Phys. 5(1), 9–24 (2023)
Evans, D.E.: Conditionally completely positive maps on operator algebras. Q. J. Math. 28(3), 271–283 (1977)
Article MathSciNet Google Scholar
Flammia, S.T., Gross, D., Liu, Y., Eisert, J.: Quantum tomography via compressed sensing: error bounds, sample complexity and efficient estimators. New J. Phys. 14(9), 095022 (2012)
Guta, M., Kahn, J., Kueng, R., Tropp, J.A.: Fast state tomography with optimal error bounds. J. Phys. A: Math. Theor. 53(20), 204001 (2020)
Article ADS MathSciNet Google Scholar
Grabowski, J., Kus, M., Marmo, G.: Geometry of quantum systems: density states and entanglement. J. Phys. A: Math. Gen. 38(47), 10217 (2005)
Article ADS MathSciNet Google Scholar
Hatcher, A.: Algebraic Topology. Cambridge University Press, Cambridge (2015)
Hedemann, S.R.: Explicit inverse confluent Vandermonde matrices with applications to exponential quantum operators (2017). arXiv:1709.05257
Horn, R.A., Johnson, C.R.: Matrix Analysis, 2nd edn. Cambridge University Press, Cambridge (2013)
Heinosaari, T., Mazzarella, L., Wolf, M.M.: Quantum tomography under prior information. Commun. Math. Phys. 318(2), 355–374 (2013)
Article ADS MathSciNet Google Scholar
Jamiolkowski, A.: On complete and incomplete sets of observables, the principle of maximum entropy revisited. Rep. Math. Phys. 46(3), 469–482 (2000)
Article ADS MathSciNet Google Scholar
Kalman, R.E.: On the general theory of control systems. IFAC Proceedings Volumes, 1(1), 491–502; 1st International IFAC Congress on Automatic and Remote Control, p. 1960. USSR, Moscow (1960)
Kech, M.: Dynamical quantum tomography. J. Math. Phys. 57(12), 122201 (2016)
Article ADS MathSciNet Google Scholar
Kukulski, R., Nechita, I., Pawela, L., Puchala, Z., Zyczkowski, K.: Generating random quantum channels. J. Math. Phys. 62(6), 062201 (2021)
Article ADS MathSciNet Google Scholar
López Gutiérrez, I., Dietrich, F., Mendl, C.B.: Quantum process tomography of unitary maps from time-delayed measurements. Quantum Inf. Process. 22(6), 251 (2023)
Article ADS MathSciNet Google Scholar
Luther, U., Rost, K.: Matrix exponentials and inversion of confluent Vandermonde matrices. Electron. Trans. Numer. Anal. 18, 91–100 (2004)
Milnor, J.: Topology from the Differentiable Viewpoint. University Press of Virginia, Charlottesville (1965)
Mityagin, B.S.: The zero set of a real analytic function. Math. Notes 107(3), 529–530 (2020)
Article MathSciNet Google Scholar
Merkel, S.T., Riofrío, C.A., Flammia, S.T., Deutsch, I.H.: Random unitary maps for quantum state reconstruction. Phys. Rev. A 81, 032126 (2010)
O’Donnell, R., Wright, J.: Efficient quantum tomography. In: Proceedings of the Forty-Eighth Annual ACM Symposium on Theory of Computing, STOC ’16, New York, NY, USA. Association for Computing Machinery, pp. 899–912 (2016)
Peruzzo, M., Grigoletto, T., Ticozzi, F.: Reconstructing quantum states from local observation: a dynamical viewpoint (2025). arXiv:2501.13668
Pinkus, A.: Totally Positive Matrices. Cambridge Tracts in Mathematics. Cambridge University Press, Cambridge (2009)
Robinson, J.C.: Dimensions, Embeddings, and Attractors. Cambridge Tracts in Mathematics. Cambridge University Press, Cambridge (2010)
Sone, A., Cappellaro, P.: Hamiltonian identifiability assisted by a single-probe measurement. Phys. Rev. A 95, 022335 (2017)
Skelton, R.E.: Dynamic Systems Control: Linear Systems Analysis and Synthesis. Wiley, Hoboken (1988)
Sussmann, H.J.: Generic single-input observability of continuous-time polynomial systems. In: 1978 IEEE Conference on Decision and Control including the 17th Symposium on Adaptive Processes, pp. 566–571 (1978)
Sauer, T., Yorke, J.A., Casdagli, M.: Embedology. J. Stat. Phys. 65(3), 579–616 (1991)
Article ADS MathSciNet Google Scholar
Sinolecka, M.M., Zyczkowski, K., Kus, M.: Manifolds of equal entanglement for composite quantum systems. Acta Phys. Pol., B 33, 2081 (2002)
Takens, F.: Detecting strange attractors in turbulence. In: Rand, D., Young, L.-S. (eds.) Dynamical Systems and Turbulence, Warwick 1980, pp. 366–381. Springer, Berlin (1981)
Tu, L.W.: An Introduction to Manifolds. Universitext, Springer, New York (2010)
vom Ende, F.: Almost all quantum channels are diagonalizable. Open. Syst. Inf. Dyn. 31(03), 2450012 (2024)
Article MathSciNet Google Scholar
Wolf, M.M., Perez-Garcia, D.: Assessing quantum dimensionality from observable dynamics. Phys. Rev. Lett. 102, 190504 (2009)
Article ADS MathSciNet Google Scholar
Yang, S.-J., Hua-Zhang, W., Zhang, Q.-B.: Generalization of Vandermonde determinants. Linear Algebra Appl. 336(1), 201–204 (2001)
Article MathSciNet Google Scholar
Yang, P., Min, Yu., Betzholz, R., Arenz, C., Cai, J.: Complete quantum-state tomography with a local random field. Phys. Rev. Lett. 124, 010405 (2020)
Comments (0)