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Quantum metrology: dynamics vs. entang lement APS March Meeting Pittsburgh , 2009 March 16

Quantum metrology: dynamics vs. entang lement APS March Meeting Pittsburgh , 2009 March 16 Ramsey interferometry and cat states Quantum information perspective Beyond the Heisenberg limit Two-component BECs Appendix. Quantum metrology and resources Carlton M. Caves

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Quantum metrology: dynamics vs. entang lement APS March Meeting Pittsburgh , 2009 March 16

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  1. Quantum metrology: • dynamics vs. entanglement • APS March Meeting • Pittsburgh, 2009 March 16 • Ramsey interferometry and cat states • Quantum information perspective • Beyond the Heisenberg limit • Two-component BECs • Appendix. Quantum metrology and resources • Carlton M. Caves • University of New Mexico • http://info.phys.unm.edu/~caves • Quantum circuits in this presentation were set using the LaTeX package Qcircuit, developed at the University of New Mexico by Bryan Eastin and Steve Flammia. The package is available at http://info.phys.unm.edu/Qcircuit/ .

  2. I. Ramsey interferometry and cat states Herod’s Gate/King David’s Peak Walls of Jerusalem NP Tasmania

  3. N independent “atoms” Ramsey interferometry Frequency measurement Time measurement Clock synchronization Shot-noise limit

  4. N cat-state atoms Cat-state Ramsey interferometry Fringe pattern with period 2π/N J. J. Bollinger, W. M. Itano, D. J. Wineland, and D. J. Heinzen, Phys. Rev. A 54, R4649 (1996). Heisenberg limit It’s the entanglement, stupid.

  5. II. Quantum information perspective Cable Beach Western Australia

  6. cat state N = 3 Heisenberg limit Fringe pattern with period 2π/N Quantum information version of interferometry Shot-noise limit

  7. Cat-state interferometer State preparation Measurement Single-parameter estimation

  8. Separable inputs Generalized uncertainty principle (Cramér-Rao bound) Heisenberg limit S. L. Braunstein, C. M. Caves, and G. J. Milburn, Ann. Phys. 247, 135 (1996). V. Giovannetti, S. Lloyd, and L. Maccone, PRL 96, 041401 (2006).

  9. cat state Achieving the Heisenberg limit

  10. It’s the entanglement, stupid. Is it entanglement? But what about? We need a generalized notion of entanglement that includes information about the physical situation, particularly the relevant Hamiltonian.

  11. III. Beyond the Heisenberg limit Echidna Gorge Bungle Bungle Range Western Australia

  12. Beyond the Heisenberg limit The purpose of theorems in physics is to lay out the assumptions clearly so one can discover which assumptions have to be violated.

  13. Cat state does the job. Improving the scaling with N S. Boixo, S. T. Flammia, C. M. Caves, and JM Geremia, PRL 98, 090401 (2007). Nonlinear Ramsey interferometry Metrologically relevant k-body coupling

  14. Improving the scaling with N without entanglement Product input Product measurement S. Boixo, A. Datta, S. T. Flammia, A. Shaji, E. Bagan, and C. M. Caves, PRA 77, 012317 (2008).

  15. Improving the scaling with N without entanglement. Two-body couplings S. Boixo, A. Datta, S. T. Flammia, A. Shaji, E. Bagan, and C. M. Caves, PRA 77, 012317 (2008); M. J. Woolley, G. J. Milburn, and C. M. Caves, arXiv:0804.4540 [quant-ph].

  16. Improving the scaling with N without entanglement. Two-body couplings Super-Heisenberg scaling from nonlinear dynamics, without any particle entanglement Scaling robust against decoherence S. Boixo, A. Datta, M. J. Davis, S. T. Flammia, A. Shaji, and C. M. Caves, PRL 101, 040403 (2008).

  17. IV. Two-component BECs Pecos Wilderness Sangre de Cristo Range Northern New Mexico

  18. Two-component BECs

  19. Two-component BECs Different spatial wave functions J. E. Williams, PhD dissertation, University of Colorado, 1999.

  20. Two-component BECs Different spatial wave functions Renormalization of scattering strengths Let’s start over.

  21. Two-component BECs Different spatial wave functions Renormalization of scattering strengths

  22. Two-component BECs Two-body elastic losses Imprecise determination of N ? Perhaps ? With hard, low-dimensional trap

  23. Appendix. Quantum metrology and resources Cape Hauy Tasman Peninsula

  24. Making quantum limits relevant The serial resource, T, and the parallel resource, N, are equivalent and interchangeable, mathematically. The serial resource, T, and the parallel resource, N, are not equivalent and not interchangeable, physically. Physics perspective Distinctions between different physical systems Information science perspective Platform independence

  25. Making quantum limits relevant. One metrology story A. Shaji and C. M. Caves, PRA 76, 032111 (2007).

  26. One metrology story

  27. One metrology story

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