Speciality:
01.01.03 (Mathematical physics)
Birth date:
5.07.1983
Phone: +7 (495) 984 81 41 * 36 62
E-mail: Keywords: mathematical theory of open quantum systems, quantum master equations, quantum key distribution, quantum networks, mathematical foundations of statistical mechanics, quantum information
UDC: 517.958, 530.145
Subject:
1. Mathematical foundations of theory of open quantum systems: derivation of quantum master equations, asymptotic properties of solutions of the Gorini–Kosssakowski–Sudarshan–Lindblad (GKSL) equation, applications to quantum biology and quantum thermodynamics. The general focus is on mathematically rigorous results on challenging problems in theoretical physics.
2. Quantum key distribution: security proofs of quantum key distribution with imperfect devices (i.e., for the practical case), quantum networks.
The most important results:
In the field of mathematical foundations of statistical mechanics and irreversibility:
The existence of microscopic (singular) solutions of the nonlinear integro-differential Boltzmann–Enskog kinetic equation has been proved (with M. Pulvirenti and S. Simonella). These solutions were discovered by N. N. Bogolyubov on the physical level of rigour and are important for understanding the correspondence between the reversible microscopic dynamics and irreversible macroscopic dynamics.
In the field of quantum key distribution:
Security of the most widely used BB84 protocol with detection-efficiency mismatch has been proved. This case is practical and significantly more mathematically challenging. The main mathematical difficulty was to obtain estimates for quantum entropic quantities in an infinite-dimensional space. This result is included in the list of the most important achievements of the Russian scientists in the field of mathematics in 2020.
In the field of mathematical foundations of the theory of open quantum systems:
Based on the perturbation theory, the local approach to quantum master equations has been rigorously justified (with I. V. Volovich). This result is important because the local approach is simple and widely used in theoretical physics, but had not rigorous justification.
The unified quantum master equation for the weak system-bath coupling regime beyond the secular approximation has been rigorously derived. This was a known fundamental problem in this field.
Main publications:
A. S. Trushechkin, M. Merkli, J. D. Cresser, J. Anders, “Open quantum system dynamics and the mean force Gibbs state”, AVS Quantum Sci., 4 (2022), 012301 , 23 pp., arXiv: 2110.01671;
A. Trushechkin, “Security of quantum key distribution with detection-efficiency mismatch in the multiphoton case”, Quantum, 6 (2022), 771 , 29 pp., arXiv: 2004.07809;
A. Trushechkin, “Unified Gorini–Kossakowski–Lindblad–Sudarshan quantum master equation beyond the secular approximation”, Phys. Rev. A, 103:6 (2021), 062226 , 12 pp., arXiv: 2103.12042
M. Pulvirenti, S. Simonella, A. Trushechkin, “Microscopic solutions of the Boltzmann-Enskog equation in the series representation”, Kinet. Relat. Models, 11:4 (2018), 911–931 , arXiv: 1802.05926
A. S. Trushechkin, I. V. Volovich, “Perturbative treatment of inter-site couplings in the local description of open quantum networks”, EPL, 113:3 (2016), 30005 , 6 pp., arXiv: 1509.05754
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