SAMOP 2021 – wissenschaftliches Programm
Bereiche | Tage | Auswahl | Suche | Aktualisierungen | Downloads | Hilfe
QI: Fachverband Quanteninformation
QI 4: Quantum Thermodynamics and Open Quantum Systems
QI 4.3: Vortrag
Dienstag, 21. September 2021, 14:45–15:00, H3
Thermodynamic information erasure with computational limitations — •Naga B. T. Kothakonda1,2, Jonas Haferkamp2,3, Nicole Yunger Halpern4, Jens Eisert2,3, and Philippe Faist2 — 1University of Cologne — 2Freie Univ. Berlin — 3HZB Berlin — 4Harvard Univ., MIT, Univ. of Maryland
The role of information entropy in thermodynamics is epitomized by the example of Landauer erasure: To reset a quantum state ρ to a standard pure state, there is a minimum dissipation of kT ln(2) H(ρ), where H(ρ) is the information entropy of the quantum state. Here, we determine the energy cost of resetting a quantum state on a memory register to a standard state under an additional computational restriction: The agent cannot apply more than a given number of unitary gates from a given gate set. The cost is given by a new entropy measure, the complexity-effective entropy, which accounts for the complexity of the state. The effective entropy is consistent with known results in the regime where the agent can perform arbitrarily many gates. The effective entropy provides a direct link between complexity and entropy, by quantifying the trade-off between complexity cost and work cost for Landauer erasure. On a conceptual level, the effective entropy generalizes the approach in statistical mechanics whereby a system is studied via the properties of its local observables. Along with our recent results on the linear growth of complexity in random circuits, we believe that the effective entropy can be a powerful tool to understand the physical properties of quantum systems that are chaotic, as well as in quantum gravity, where complexity is believed to play a major role.