Synchronizing quantum clocks with classical one-way communication: Bounds on the generated entropy

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 ∆S = ~2/(4∆E∆t)2 if ∆t is the time accuracy of the synchronism and ∆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. 1 The thermodynamic advantage of quantum information transfer Among the most important properties of quantum channels is their ability to create entangled states in a bipartite or multipartite system. It is well-known that every nonentangled (i.e. separable) joint state can be prepared using local quantum operations on each subsystem and classical communication among them. However, although it is possible to prepare all separable joint states with classical communication it may ∗e-mail: [email protected]