dorsal/arxiv
View SchemaSynchronizing quantum clocks with classical one-way communication: Bounds on the generated entropy
| Authors | Dominik Janzing, Thomas Beth |
|---|---|
| Categories | |
| ArXiv ID | quant-ph/0306023 |
| URL | https://arxiv.org/abs/quant-ph/0306023 |
Abstract
We describe separable joint states on bipartite quantum systems that cannot be prepared by any thermodynamically reversible classical one-way communication protocol. We argue that the joint state of two synchronized microscopic clocks is always of this type when it is considered from the point of view of an ``ignorant'' observer who is not synchronized with the other two parties. We show that the entropy generation of a classical one-way synchronization protocol is at least \Delta S = \hbar^2/(4\Delta E \Delta t)^2 if \Delta t is the time accuracy of the synchronism and \Delta E is the energy bandwidth of the clocks. This dissipation can only be avoided if the common time of the microscopic clocks is stored by an additional classical clock. Furthermore, we give a similar bound on the entropy cost for resetting synchronized clocks by a classical one-way protocol. The proof relies on observations of Zurek on the thermodynamic relevance of quantum discord. We leave it as an open question whether classical multi-step protocols may perform better. We discuss to what extent our results imply problems for classical concepts of reversible computation when the energy of timing signals is close to the Heisenberg limit.
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"abstract": "We describe separable joint states on bipartite quantum systems that cannot\nbe prepared by any thermodynamically reversible classical one-way communication\nprotocol. We argue that the joint state of two synchronized microscopic clocks\nis always of this type when it is considered from the point of view of an\n``ignorant\u0027\u0027 observer who is not synchronized with the other two parties.\n We show that the entropy generation of a classical one-way synchronization\nprotocol is at least \\Delta S = \\hbar^2/(4\\Delta E \\Delta t)^2 if \\Delta t is\nthe time accuracy of the synchronism and \\Delta E is the energy bandwidth of\nthe clocks. This dissipation can only be avoided if the common time of the\nmicroscopic clocks is stored by an additional classical clock.\n Furthermore, we give a similar bound on the entropy cost for resetting\nsynchronized clocks by a classical one-way protocol. The proof relies on\nobservations of Zurek on the thermodynamic relevance of quantum discord. We\nleave it as an open question whether classical multi-step protocols may perform\nbetter.\n We discuss to what extent our results imply problems for classical concepts\nof reversible computation when the energy of timing signals is close to the\nHeisenberg limit.",
"arxiv_id": "quant-ph/0306023",
"authors": [
"Dominik Janzing",
"Thomas Beth"
],
"categories": [
"quant-ph"
],
"title": "Synchronizing quantum clocks with classical one-way communication: Bounds on the generated entropy",
"url": "https://arxiv.org/abs/quant-ph/0306023"
},
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