学术报告：Exponential Sensitivity and its Cost in Quantum Physics

报告人：Prof. Tamás Kiss（the Institute for Solid State Physics and Optics of the Wigner Research Centre for Physics, a leading national institution supported by the Hungarian Academy of Sciences）

邀请人：薛鹏

时间：11月10号（周五）下午2:00

地点：田家炳南楼205

摘要：State selective protocols, like entanglement purification, lead to an essentially non- linear quantum evolution, unusual in naturally occurring quantum processes. Entanglement itself can evolve truly chaotically [1]. Sensitivity to initial states in quantum systems, stemming from such non-linear dynamics, is a promising perspective for applications.  We demonstrate that chaotic behavior is a rather generic feature in state selective protocols: exponential sensitivity can exist for all initial states in some protocols. Moreover, any complex rational polynomial map, including the example of the Mandelbrot set, can be directly realized. In state selective protocols, one needs an ensemble of initial states, the size of which decreases with each iteration. We prove that exponential sensitivity to initial states in any quantum system has to be related to downsizing the initial ensemble also exponentially. Our results show that magnifying initial differences of quantum states (a Schrodinger's microscope) is possible, however, there is a bound on the number of copies needed [2]. We discuss the possibility of realizing a non-linear protocol by a Tavis-Cummings model [3]. A class of protocols can be applied for quantum state discrimination [4].

参考文献：

[1] T. Kiss, S. Vymetal, L. D. Toth, A. Gabris, I. Jex, G. Alber, Phys. Rev. Lett. 107, 100501 (2011)

[2] Andras Gilyen, Tamas Kiss, Igor Jex, Sci. Rep. 6, 20076 (2016)

[3] Torres, J.M., Bernád, J.Z., Alber, G., Kálmán, O. and Kiss, T., Physical Review A, 95(2), 023828 (2017)

[4] Kálmán, O. and Kiss, T., arXiv preprint arXiv:1708.0361