Bulletin of the American Physical Society
APS March Meeting 2018
Monday–Friday, March 5–9, 2018; Los Angeles, California
Session V15: Non-Equilibrium Quantum Thermodynamics
2:30 PM–5:06 PM,
Thursday, March 8, 2018
LACC Room: 304C
Sponsoring Units: DQI GSNP
Chair: Jens Eisert, Dahlem Center for Complex Quantum Systems, Freie Universität Berlin
Abstract: V15.00011 : Uncertainty Relations in Implementation of Unitary Control*
4:30 PM–4:42 PM
We study the underlying mechanism in the implementation of unitary control on a system with an experimental apparatus. We regard the unitary time evolution in the system as a physical phenomenon that results from the interaction between the system and the external system. We consider the conditions required to approximate the dynamics of the reduced density matrix of the system by the desired unitary time evolution US. Then, we derive fundamental trade-off relations to implement the unitary dynamics: δUδE≧‖[US,HS]‖/40. Here, HS is the Hamiltonian of the system, δU is the implementation error of the desired unitary US, and δE is the energy fluctuation of the external system. We also show that the energy fluctuation δE should be caused by a quantum superposition. Namely, precise unitary control in the system requires large quantum fluctuation of energy in the external system.
Because of the generality of our results, we can apply them to many objects, e.g., quantum heat engines. Our uncertainty relation says that when the dynamics of the heat engine and baths becomes close to unitary, the energy fluctuation of the work storage diverges.
*The present work was supported by JSPS Grants-in-Aid for Scientific Research No. JP14J07602 (NS), No. JP25103003 (KS), and No. JP16H02211 (KS).
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