Research

Slides and a video clip

1. Additivity questions of quantum channels
2. A proof of additivity violation of minimum output entropy of quantum channels
3. Output entropy of tensor products of random quantum channels
4. Partial transpose of random quantum states and meander polynomials
5. Probabilistic Methods in Quantum Information Theory (Japanese)
6. Additivity problems and tensor powers of quantumm channels→ YouTube video clip

Publication list

• Published
• M. Fukuda, R. Koenig, "Typical entanglement for Gaussian states", J. Math. Phys., 60, 112203 (2019); arXiv:1903.04126 [quant-ph].
• M. Fukuda, I. Nechita, "Enumerating meandric systems with large number of loops", Annales de l'Institut Henri Poincaré D, 6, 4, 607-640 (2019); arXiv:1609.02756 [math.CO].
• M. Fukuda, R. Koenig, I.Nechita, "RTNI - A symbolic integrator for Haar-random tensor networks", J. Phys. A: Math. Theor. 52 425303 (2019); arXiv:1902.08539 [quant-ph].
• M. Fukuda, I. Nechita, "On the minimum output entropy of random orthogonal quantum channels", IEEE Trans. Info. Theo., Vol. 64, Iss. 2, 1374 - 1384 (2018); arXiv:1703.08979 [quant-ph].
• M. Fukuda, G. Gour, "Additive bounds of minimum output entropies for unital channels and an exact qubit formula", IEEE Trans. Info. Theo., Vol. 63, Iss. 3, 1818-1828 (2017); arXiv: 1502.06411 [quant-ph].
• M. Fukuda, I. Nechita, "Additivity rates and PPT property for random quantum channels", Annales Mathematiques Blaise Pascal, 22, 1, 1-72 (2015); arXiv: 1411.6881 [math-ph].
• M. Fukuda, I. Nechita, M. M. Wolf, "Quantum channels with polytopic images and image additivity", IEEE Trans. Info. Theo., Vol. 61, Iss. 4, 1851-1859 (2015); arXiv: 1408.2340[quant-ph].
• B. Collins, M. Fukuda, P. Zhong, "Estimates for compression norms and additivity violation in quantum information", Inter. J. Math., 26, 1, 1550002 (2015); arXiv:1408.3957 [math.OA].
• B. Collinns, M. Fukuda, I. Nechita, "On the convergence of output sets of quantum channels", J. Oper. Theo. 73:2, 333-360 (2015); arXiv: 1311.7571 [math-ph].
• M. Fukuda, "Revisiting additivity violation of quantum channels", Comm. Math. Phys., 332, 2, 713-728 (2014); arXiv: 1307.0707 [math-ph].
• M. Fukuda, I. Nechita, "Asymptotically well-behaved input states do not violate additivity for conjugate pairs of random quantum channels", Comm. Math. Phys., 328, 3, 995-1021 (2014); arXiv: 1212.1630 [math-ph].
• M. Fukuda, P. Sniady, "Partial transpose of random quantum states: Exact formulas and meanders", J. Math. Phys., 54, 042202 (2013); arXiv:1211.1525 [math-ph].
• B. Collins, M. Fukuda, I. Nechita, "Low entropy output states for products of random unitary channels", Random Matrices: Theory Appl., 02, 1250018 (2013); arXiv:1208.1449 [math-ph]. Slide 3
• B. Collins, M. Fukuda, I. Nechita, "Towards a state minimizing the output entropy of a tensor product of random quantum channels", J. Math. Phys., 53, 032203 (2012); arXiv: 1111.6269 [math-ph].
• M. Fukuda, C. King, "Entanglement of random subspaces via the Hastings bound", J. Math. Phys., 51, 042201 (2010); arXiv: 0907.5446 [quant-ph].
• M. Fukuda, "An application of decomposable maps in proving multiplicativity of low dimensional maps", J. Math. Phys., 51, 022201 (2010); arXiv: 0906.3355 [quant-ph].
• M. Fukuda, C. King, D. Moser, "Comments on Hastings' Additivity Counterexamples", Comm. Math. Phys., 296, 1, 111-143 (2010); arXiv: 0905.3697 [quant-ph].
• M. Fukuda, M. M. Wolf, "Simplifying additivity problems using direct sum constructions", J. Math. Phys., 48, 072101 (2007); arXiv: 0704.1092 [quant-ph].
• M. Fukuda, "Simplification of additivity conjecture in quantum information theory", Quant. Info. Proc., 6, 179-186 (2007); arXiv: quant-ph/0608010.
• N. Datta, M. Fukuda, A. S. Holevo, "Complementarity and additivity for covariant channels", Quant. Info. Proc., 5, 179-207 (2006); arXiv: quant-ph/0510148.
• M. Fukuda, "Extending additivity from symmetric to asymmetric channels", J. Phys. A: Math. Gen., 38, L753-L758 (2005); arXiv: quant-ph/0505022.
• Not published yet
• M. Fukuda, I. Nechita "Generating series and matrix models for meandric systems with one shallow side", arXiv:2103.03615[math.CO]
• M. Fukuda, T. Hasebe, S. Sato, "Additivity violation of quantum channels via strong convergence to semi-circular and circular elements", arXiv:2101.00424[math-ph]
Applied research:
• Motohisa Fukuda, Takashi Okuno, Shinya Yuki, "Central object segmentation by deep learning for fruits and other roundish objects", arXiv:2008.01251 [cs.CV].