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Synchronizing quantum clocks with classical one-way communication:
Bounds on the generated entropy
Dominik Janzing, Thomas Beth
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.
- oai_identifier:
- oai:arXiv.org:quant-ph/0306023
- categories:
- quant-ph
- comments:
- 23 pages, 2 figures
- arxiv_id:
- quant-ph/0306023
- created:
- 2003-06-03
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