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Every clock has two fundamental properties: a certain precision and a certain time resolution. The time resolution indicates how small the time intervals are that can be measured—i.e., how quickly the clock ticks. Precision tells you how much inaccuracy you have to expect with every single tick.
The research team was able to show that since no clock has an infinite amount of energy available (or generates an infinite amount of entropy), it can never have perfect resolution and perfect precision at the same time. This sets fundamental limits to the possibilities of quantum computers.
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Marcus Huber and his team investigated in general which laws must always apply to every conceivable clock. “Time measurement always has to do with entropy,” explains Marcus Huber. In every closed physical system, entropy increases and it becomes more and more disordered. It is precisely this development that determines the direction of time: the future is where the entropy is higher, and the past is where the entropy is even lower.
As can be shown, every measurement of time is inevitably associated with an increase in entropy: a clock, for example, needs a battery, the energy of which is ultimately converted into frictional heat and audible ticking via the clock’s mechanics—a process in which a fairly ordered state occurs the battery is converted into a rather disordered state of heat radiation and sound.
On this basis, the research team was able to create a mathematical model that basically every conceivable clock must obey. “For a given increase in entropy, there is a tradeoff between time resolution and precision,” says Florian Meier, first author of the second paper, now posted to the arXiv preprint server. “That means: Either the clock works quickly or it works precisely—both are not possible at the same time.”
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“Currently, the accuracy of quantum computers is still limited by other factors, for example, the precision of the components used or electromagnetic fields. But our calculations also show that today we are not far from the regime in which the fundamental limits of time measurement play the decisive role.”
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More information: Florian Meier et al, Fundamental accuracy-resolution trade-off for timekeeping devices, arXiv (2023). DOI: 10.48550/arxiv.2301.05173
Source: Limits for quantum computers: Perfect clocks are impossible, research finds
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