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A quantum network of clocks


The development of precise atomic clocks plays an increasingly important role in modern society. Shared timing information constitutes a key resource for navigation with a direct correspondence between timing accuracy and precision in applications such as the Global Positioning System. By combining precision metrology and quantum networks, we propose a quantum, cooperative protocol for operating a network of geographically remote optical atomic clocks. Using nonlocal entangled states, we demonstrate an optimal utilization of global resources, and show that such a network can be operated near the fundamental precision limit set by quantum theory. Furthermore, the internal structure of the network, combined with quantum communication techniques, guarantees security both from internal and external threats. Realization of such a global quantum network of clocks may allow construction of a real-time single international time scale (world clock) with unprecedented stability and accuracy.

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Figure 1: The concept of world-wide quantum clock network.
Figure 2: Entangled state preparation between distant nodes.
Figure 3: Performance of different operation schemes. Comparison of the achievable (rescaled) Allan deviation using clock networks of different types and degrees of cooperation.
Figure 4: Schematics of security countermeasures.

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  1. Bloom, B. et al. An optical lattice clock with accuracy and stability at the 10−18 level. Nature 506, 71–75 (2014).

    Article  ADS  Google Scholar 

  2. Hinkley, N. et al. An atomic clock with 10−18 instability. Science 341, 1215–1218 (2013).

    Article  ADS  Google Scholar 

  3. Nicholson, T. L. et al. Comparison of two independent Sr optical clocks with 1 × 10−17 stability at 103 s. Phys. Rev. Lett. 109, 230801 (2012).

    Article  ADS  Google Scholar 

  4. Leroux, I. D., Schleier-Smith, M. H. & Vuletić, V. Implementation of cavity squeezing of a collective atomic spin. Phys. Rev. Lett. 104, 073602 (2010).

    Article  ADS  Google Scholar 

  5. Buzek, V., Derka, R. & Massar, S. Optimal quantum clocks. Phys. Rev. Lett. 82, 2207–2210 (1999).

    Article  ADS  Google Scholar 

  6. Ye, J. et al. Delivery of high-stability optical and microwave frequency standards over an optical fiber network. J. Opt. Soc. Am. B 20, 1459–1467 (2003).

    Article  ADS  Google Scholar 

  7. Droste, S. et al. Optical-frequency transfer over a single-span 1840 km fiber link. Phys. Rev. Lett. 111, 110801 (2013).

    Article  ADS  Google Scholar 

  8. Cirac, J., Zoller, P., Kimble, H. & Mabuchi, H. Quantum state transfer and entanglement distribution among distant nodes in a quantum network. Phys. Rev. Lett. 78, 3221–3224 (1997).

    Article  ADS  Google Scholar 

  9. Kimble, H. J. The quantum internet. Nature 453, 1023–1030 (2008).

    Article  ADS  Google Scholar 

  10. Perseguers, S., Lapeyre, G. J., Cavalcanti, D., Lewenstein, M. & Acín, A. Distribution of entanglement in large-scale quantum networks. Rep. Prog. Phys. 76, 096001 (2013).

    Article  ADS  MathSciNet  Google Scholar 

  11. Nielsen, M. A. & Chuang, I. L. Quantum Computation and Quantum Information (Cambridge Univ. Press, 2000).

    MATH  Google Scholar 

  12. Duan, L. M., Lukin, M. D., Cirac, J. I. & Zoller, P. Long-distance quantum communication with atomic ensembles and linear optics. Nature 414, 413–418 (2001).

    Article  ADS  Google Scholar 

  13. Bollinger, J., Itano, W., Wineland, D. & Heinzen, D. Optimal frequency measurements with maximally correlated states. Phys. Rev. A 54, R4649–R4652 (1996).

    Article  ADS  Google Scholar 

  14. Leibfried, D. et al. Toward Heisenberg-limited spectroscopy with multiparticle entangled states. Science 304, 1476–1478 (2004).

    Article  ADS  Google Scholar 

  15. Wineland, D. et al. Experimental issues in coherent quantum-state manipulation of trapped atomic ions. J. Res. Natl Inst. Stand. Technol. 103, 259–328 (1998).

    Article  Google Scholar 

  16. Kessler, E. M. et al. Heisenberg-limited atom clocks based on entangled qubits. Phys. Rev. Lett. 112, 190403 (2014).

    Article  ADS  Google Scholar 

  17. Giedke, G., Taylor, J., D Alessandro, D., Lukin, M. & Imamolu, A. Quantum measurement of a mesoscopic spin ensemble. Phys. Rev. A 74, 032316 (2006).

    Article  ADS  Google Scholar 

  18. Huelga, S. F. et al. Improvement of frequency standards with quantum entanglement. Phys. Rev. Lett. 79, 3865–3868 (1997).

    Article  ADS  Google Scholar 

  19. Rosenband, T. & Leibrandt, D. R. Exponential scaling of clock stability with atom number. Preprint at (2013).

  20. Borregaard, J. & Sørensen, A. S. Efficient atomic clocks operated with several atomic ensembles. Phys. Rev. Lett. 111, 090802 (2013).

    Article  ADS  Google Scholar 

  21. Escher, B. M., de Matos Filho, R. L. & Davidovich, L. General framework for estimating the ultimate precision limit in noisy quantum-enhanced metrology. Nature Phys. 7, 406–411 (2011).

    Article  ADS  Google Scholar 

  22. Borregaard, J. & Sørensen, A. S. Near-Heisenberg-limited atomic clocks in the presence of decoherence. Phys. Rev. Lett. 111, 090801 (2013).

    Article  ADS  Google Scholar 

  23. Chou, C. W., Hume, D. B., Koelemeij, J. C. J., Wineland, D. J. & Rosenband, T. Frequency comparison of two high-accuracy Al+ optical clocks. Phys. Rev. Lett. 104, 070802 (2010).

    Article  ADS  Google Scholar 

  24. Monz, T. et al. 14-qubit entanglement: Creation and coherence. Phys. Rev. Lett. 106, 130506 (2011).

    Article  ADS  Google Scholar 

  25. Maunz, P. et al. Quantum interference of photon pairs from two remote trapped atomic ions. Nature Phys. 3, 538–541 (2007).

    Article  ADS  Google Scholar 

  26. Schiller, S. et al. Einstein Gravity Explorer—A medium-class fundamental physics mission. Exp. Astron. 23, 573–610 (2008).

    Article  ADS  Google Scholar 

  27. Sørensen, A. & Mølmer, K. Entanglement and quantum computation with ions in thermal motion. Phys. Rev. A 62, 022311 (2000).

    Article  ADS  Google Scholar 

  28. Gisin, N., Ribordy, G., Tittel, W. & Zbinden, H. Quantum cryptography. Rev. Mod. Phys. 74, 145–195 (2002).

    Article  ADS  Google Scholar 

  29. Olmschenk, S. et al. Quantum teleportation between distant matter qubits. Science 323, 486–489 (2009).

    Article  ADS  Google Scholar 

  30. Chou, C-W. et al. Functional quantum nodes for entanglement distribution over scalable quantum networks. Science 316, 1316–1320 (2007).

    Article  ADS  Google Scholar 

  31. Togan, E. et al. Quantum entanglement between an optical photon and a solid-state spin qubit. Nature 466, 730–734 (2010).

    Article  ADS  Google Scholar 

  32. Bernien, H. et al. Heralded entanglement between solid-state qubits separated by three metres. Nature 497, 86–90 (2013).

    Article  ADS  Google Scholar 

  33. Ristè, D. et al. Deterministic entanglement of superconducting qubits by parity measurement and feedback. Nature 502, 350–354 (2013).

    Article  ADS  Google Scholar 

  34. Dür, W., Briegel, H-J., Cirac, J. & Zoller, P. Quantum repeaters based on entanglement purification. Phys. Rev. A 59, 169–181 (1999).

    Article  ADS  Google Scholar 

  35. Sherson, J. F. et al. Quantum teleportation between light and matter. Nature 443, 557–560 (2006).

    Article  ADS  Google Scholar 

  36. Ma, X-S. et al. Quantum teleportation over 143 kilometres using active feed-forward. Nature 489, 269–273 (2012).

    Article  ADS  Google Scholar 

  37. McConnell, R. et al. Generating entangled spin states for quantum metrology by single-photon detection. Phys. Rev. A 88, 063802 (2013).

    Article  ADS  Google Scholar 

  38. Andersen, U. L. & Ralph, T. C. High fidelity teleportation of continuous variable quantum states using delocalized single photons. Phys. Rev. Lett. 111, 050504 (2013).

    Article  ADS  Google Scholar 

  39. Djerroud, K. et al. Coherent optical link through the turbulent atmosphere. Opt. Lett. 35, 1479–1481 (2010).

    Article  ADS  Google Scholar 

  40. Tapley, B. et al. GGM02—An improved Earth gravity field model from GRACE. J. Geod. 79, 467–478 (2005).

    Article  ADS  Google Scholar 

  41. Abramovici, A. et al. LIGO: The laser interferometer gravitational-wave observatory. Science 256, 325–333 (1992).

    Article  ADS  Google Scholar 

  42. Seidel, A. et al. 2007 IEEE International Frequency Control Symposium Joint with the 21st European Frequency and Time Forum The aces microwave link: Instrument design and test results. 1295–1298 (IEEE, 2007).

    Chapter  Google Scholar 

  43. Wolf, P. et al. Quantum physics exploring gravity in the outer solar system: The SAGAS project. Exp. Astron. 23, 651–687 (2008).

    Article  ADS  Google Scholar 

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We are grateful to T. Rosenband, V. Vuletić, J. Borregaard and T. Nicholson for enlightening discussions. This work was supported by NSF, CUA, ITAMP, HQOC, JILA PFC, NIST, DARPA QuASAR and Quiness programs, the Alfred P. Sloan Foundation, the Packard Foundation, ARO MURI, and the ERC grant QIOS (grant no. 306576); M.B. acknowledges support from NDSEG and NSF GRFP. It is dedicated to R. Blatt and P. Zoller on the occasion of their 60th birthday, when initial ideas for this work were formed.

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Correspondence to M. D. Lukin.

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Kómár, P., Kessler, E., Bishof, M. et al. A quantum network of clocks. Nature Phys 10, 582–587 (2014).

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