Hi all,

Tomorrow we will have two talks. Marc Sanz Drudis will tell us about his semester project with Lidia del Rio. Florian Meier will tell us about his master thesis he conducted in Vienna, entitled 'Performance limits of decay clocks'. See below for the abstracts. The talks will take place at 2pm in E 41.1 or on Zoom: https://ethz.zoom.us/j/362994444.

Best, Ladina

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Contextuality in quantum mechanics is one of the main features that set it aside from "classical" theories. Before making such an assumption one wants to be convinced that a non-contextual model would not be able to replicate the same results. Pre- and Post- Selection Paradoxes (PPS Paradoxes) are a good candidate to prove contextuality. In 2014 it was proven that the existence of anomalous weak values in quantum mechanics makes it incompatible with any non-contextual model. A year after that it was proven that a non-contextual model would not be able to replicate "Logical" PPS Paradoxes. We try to relax the assumption that our PPS Paradoxes need to be logical by exploring the relationship between weak values and PPS paradoxes. We show that we can relax the assumption for binary measurements and establish a methodology to generalize the result to an arbitrary number of possible outcomes.

%%%% Performance limits of decay clocks

Clocks are among the most precise measurement devices ever built, but like anything else, they are bound by the laws of thermodynamics. As a consequence, all clocks are inherently subject to noise and thus cannot be infinitely precise. We examine these limitations and the thermodynamic cost of running a clock. From minimal assumptions, we derive that processes driving a clock must be irreversible. In the simplest memory-less thermodynamic setting, this leads to exponential decay. Under the assumption of a fixed decay rate \Gamma Γ, we explore what types of quantum clocks can be built using an exponentially decaying process to generate the ticks of the clock, but with a clockwork that is otherwise unconstrained. Using the average number of ticks N N until a clock is off by one tick as the measure for its accuracy, and the inverse average tick time as the measure for its resolution R R, we show that any increase in accuracy ultimately comes at the cost of resolution, subject to the bound N\leq \Gamma^2/R^2 N≤Γ 2 /R 2 . With a periodic process in the clockwork to concentrate the decay event probability to specific times, we can build clocks that approach this optimal accuracy-resolution trade-off. Based on a quantum clock from Schwarzhans et al. [1], that uses as its only resource out of equilibrium heat baths, we design a clock that we conjecture to reach the scaling N\sim \text{const.}/R^2 N∼const./R 2 asymptotically. In this example, the entropy production grows linearly with the accuracy, confirming the thermodynamic limitation of the clock performance.

[1] Emanuel Schwarzhans, Maximilian P. E. Lock, Paul Erker, Nicolai Friis, and Marcus Huber. Autonomous Temporal Probability Concentration: Clockworks and the Second Law of Thermodynamics. RX, 11(1):011046, 2021. doi: 10.1103/PhysRevX.11.011046. URL https://link.aps.org/doi/10.1103/PhysRevX.11.011046 https://link.aps.org/doi/10.1103/PhysRevX.11.011046.