dorsal/arxiv
View SchemaBounds on the entropy generated when timing information is extracted from microscopic systems
| Authors | Dominik Janzing, Thomas Beth |
|---|---|
| Categories | |
| ArXiv ID | quant-ph/0301125 |
| URL | https://arxiv.org/abs/quant-ph/0301125 |
Abstract
We consider Hamiltonian quantum systems with energy bandwidth \Delta E and show that each measurement that determines the time up to an error \Delta t generates at least the entropy (\hbar/(\Delta t \Delta E))^2/2. Our result describes quantitatively to what extent all timing information is quantum information in systems with limited energy. It provides a lower bound on the dissipated energy when timing information of microscopic systems is converted to classical information. This is relevant for low power computation since it shows the amount of heat generated whenever a band limited signal controls a classical bit switch. Our result provides a general bound on the information-disturbance trade-off for von-Neumann measurements that distinguish states on the orbits of continuous unitary one-parameter groups with bounded spectrum. In contrast, information gain without disturbance is possible for some completely positive semi-groups. This shows that readout of timing information can be possible without entropy generation if the autonomous dynamical evolution of the clock is dissipative itself.
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"abstract": "We consider Hamiltonian quantum systems with energy bandwidth \\Delta E and\nshow that each measurement that determines the time up to an error \\Delta t\ngenerates at least the entropy (\\hbar/(\\Delta t \\Delta E))^2/2. Our result\ndescribes quantitatively to what extent all timing information is quantum\ninformation in systems with limited energy. It provides a lower bound on the\ndissipated energy when timing information of microscopic systems is converted\nto classical information. This is relevant for low power computation since it\nshows the amount of heat generated whenever a band limited signal controls a\nclassical bit switch.\n Our result provides a general bound on the information-disturbance trade-off\nfor von-Neumann measurements that distinguish states on the orbits of\ncontinuous unitary one-parameter groups with bounded spectrum. In contrast,\ninformation gain without disturbance is possible for some completely positive\nsemi-groups. This shows that readout of timing information can be possible\nwithout entropy generation if the autonomous dynamical evolution of the clock\nis dissipative itself.",
"arxiv_id": "quant-ph/0301125",
"authors": [
"Dominik Janzing",
"Thomas Beth"
],
"categories": [
"quant-ph"
],
"title": "Bounds on the entropy generated when timing information is extracted from microscopic systems",
"url": "https://arxiv.org/abs/quant-ph/0301125"
},
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"execution_id": "f77dbade-1ab8-48a7-b583-fe1292189fbc",
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