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Mapping coherence in measurement via full quantum tomography of a hybrid optical detector

Abstract

Quantum states and measurements exhibit wave-like (continuous) or particle-like (discrete) character. Hybrid discrete–continuous photonic systems are key to investigating fundamental quantum phenomena1,2,3, generating superpositions of macroscopic states4, and form essential resources for quantum-enhanced applications5 such as entanglement distillation6,7 and quantum computation8, as well as highly efficient optical telecommunications9,10. Realizing the full potential of these hybrid systems requires quantum-optical measurements sensitive to non-commuting observables such as field quadrature amplitude and photon number11,12,13. However, a thorough understanding of the practical performance of an optical detector interpolating between these two regions is absent. Here, we report the implementation of full quantum detector tomography, enabling the characterization of the simultaneous wave and photon-number sensitivities of quantum-optical detectors. This yields the largest parameterization to date in quantum tomography experiments, requiring the development of novel theoretical tools. Our results reveal the role of coherence in quantum measurements and demonstrate the tunability of hybrid quantum-optical detectors.

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Figure 1: Experimental set-up.
Figure 2: Experimentally reconstructed one-click POVM elements of a weak-homodyne APD.
Figure 3: Reconstructed POVM elements.

References

  1. Kuzmich, A., Walmsley, I. A. & Mandel, L. Violation of Bell's inequality by a generalized Einstein–Podolsky–Rosen state using homodyne detection. Phys. Rev. Lett. 85, 1349–1353 (2000).

    Article  ADS  MathSciNet  Google Scholar 

  2. Shchukin, E. & Vogel, W. Universal measurement of quantum correlations of radiation. Phys. Rev. Lett. 96, 200403 (2006).

    Article  ADS  Google Scholar 

  3. Parigi, V., Zavatta, A., Kim, M. & Bellini, M. Probing quantum commutation rules by addition and subtraction of single photons to/from a light field. Science 317, 1890–1893 (2007).

    Article  ADS  Google Scholar 

  4. Ourjoumtsev, A., Jeong, H., Tualle-Brouri, R. & Grangier, P. Generation of optical ‘Schrödinger cats’ from photon number states. Nature 448, 784–786 (2007).

    Article  ADS  Google Scholar 

  5. Braunstein, S. L. & van Loock, P. Quantum information with continuous variables. Rev. Mod. Phys. 77, 513–577 (2005).

    Article  ADS  MathSciNet  Google Scholar 

  6. Ourjoumtsev, A., Dantan, A., Tualle-Brouri, R. & Grangier, P. Increasing entanglement between Gaussian states by coherent photon subtraction. Phys. Rev. Lett. 98, 030502 (2007).

    Article  ADS  Google Scholar 

  7. Takahashi, H. et al. Entanglement distillation from Gaussian input states. Nature Photon. 4, 178–181 (2010).

    Article  ADS  Google Scholar 

  8. Neergaard-Nielsen, J. S. et al. Optical continuous-variable qubit. Phys. Rev. Lett. 105, 053602 (2010).

    Article  ADS  Google Scholar 

  9. Guha, S. Structured optical receivers to attain superadditive capacity and the Holevo limit. Phys. Rev. Lett. 106, 240502 (2011).

    Article  ADS  Google Scholar 

  10. Tsujino, K. et al. Quantum receiver beyond the standard quantum limit of coherent optical communication. Phys. Rev. Lett. 106, 250503 (2011).

    Article  ADS  Google Scholar 

  11. Puentes, G. et al. Bridging particle and wave sensitivity in a configurable detector of positive operator-valued measures. Phys. Rev. Lett. 102, 080404 (2009).

    Article  ADS  Google Scholar 

  12. Bimbard, E., Jain, N., MacRae, A. & Lvovsky, A. I. Quantum-optical state engineering up to the two-photon level. Nature Photon. 4, 243–247 (2010).

    Article  ADS  Google Scholar 

  13. Laiho, K., Cassemiro, K. N., Gross, D. & Silberhorn, C. Probing the negative Wigner function of a pulsed single photon point by point. Phys. Rev. Lett. 105, 253603 (2010).

    Article  ADS  Google Scholar 

  14. Boyd, R. Radiometry and the Detection of Optical Radiation (Wiley, 1983).

    Google Scholar 

  15. Luis, A. & Sanchez-Soto, L. L. Complete characterization of arbitrary quantum measurement processes. Phys. Rev. Lett. 83, 3573–3576 (1999).

    Article  ADS  MathSciNet  Google Scholar 

  16. Fiurášek, J. Maximum-likelihood estimation of quantum measurement. Phys. Rev. A 64, 024102 (2001).

    Article  ADS  Google Scholar 

  17. D'Ariano, G. M., Maccone, L. & Presti, P. L. Quantum calibration of measurement instrumentation. Phys. Rev. Lett. 93, 250407 (2004).

    Article  ADS  Google Scholar 

  18. Lundeen, J. S. et al. Tomography of quantum detectors. Nature Phys. 5, 27–30 (2009).

    Article  ADS  Google Scholar 

  19. D'Auria, V., Lee, N., Amri, T., Fabre, C. & Laurat, J. Quantum decoherence of single-photon counters. Phys. Rev. Lett. 107, 050504 (2011).

    Article  ADS  Google Scholar 

  20. Feito, A. et al. Measuring measurement: theory and practice. New J. Phys. 11, 093038 (2009).

    Article  ADS  Google Scholar 

  21. Coldenstrodt-Ronge, H. B. et al. A proposed testbed for detector tomography. J. Mod. Opt. 56, 432–441 (2009).

    Article  ADS  Google Scholar 

  22. Brida, G. et al. Full quantum characterization of superconducting photon counters. Preprint at http://arXiv.org/abs/1103.2991 (2011).

  23. Akhlaghi, M. K., Majedi, A. H. & Lundeen, J. S. Nonlinearity in single photon detection: modeling and quantum tomography. Opt. Express 19, 21305–21312 (2011).

    Article  ADS  Google Scholar 

  24. Řeháěk, J., Hradil, Z. & Ježek, M. Iterative algorithm for reconstruction of entangled states. Phys. Rev. A 63, 040303 (2001).

    Article  ADS  MathSciNet  Google Scholar 

  25. Nunn, J., Smith, B. J., Puentes, G., Walmsley, I. A. & Lundeen, J. S. Optimal experiment design for quantum state tomography: fair, precise, and minimal tomography. Phys. Rev. A 81, 042109 (2010).

    Article  ADS  Google Scholar 

  26. Haeffner, H. et al. Scalable multi-particle entanglement of trapped ions. Nature 438, 643–646 (2005).

    Article  ADS  Google Scholar 

  27. Sanders, B. C. Quantum dynamics of the nonlinear rotator and the effects of continual spin measurement. Phys. Rev. A 40, 2417–2427 (1989).

    Article  ADS  Google Scholar 

  28. Datta, A. et al. Quantum metrology with imperfect states and detectors. Phys. Rev. A 83, 063836 (2011).

    Article  ADS  Google Scholar 

  29. Laiho, K., Avenhaus, M., Cassemiro, K. N. & Silberhorn, C. Direct probing of the Wigner function by time-multiplexed detection of photon statistics. New J. Phys. 11, 043012 (2009).

    Article  ADS  Google Scholar 

  30. Gerrits, T. et al. Generation of optical coherent-state superpositions by number-resolved photon subtraction from the squeezed vacuum. Phys. Rev. A 82, 031802 (2010).

    Article  ADS  Google Scholar 

  31. Namekata, N. et al. Non-Gaussian operation based on photon subtraction using a photon-number-resolving detector at a telecommunications wavelength. Nature Photon. 4, 655–660 (2010).

    Article  ADS  Google Scholar 

  32. Achilles, D., Silberhorn, C., Sliwa, C., Banaszek, K. & Walmsley, I. A. Fiber-assisted photon-number resolving detector. Opt. Lett. 28, 2387–2389 (2003).

    Article  ADS  Google Scholar 

  33. Achilles, D., Silberhorn, C. & Walmsley, I. A. Direct, loss-tolerant characterization of nonclassical photon statistics. Phys. Rev. Lett. 97, 043602 (2006).

    Article  ADS  Google Scholar 

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Acknowledgements

The authors thank G. Donati, T. J. Bartley, J. Eisert, X. Yang and A. Feito for assistance and fruitful discussions. This work was funded in part by the Engineering and Physical Sciences Research Council of the UK (EPSRC, project EP/H03031X/1), the US European Office of Aerospace Research & Development (EOARD, project 093020), the European Commission (under Integrated Project Quantum Interfaces, Sensors, and Communication based on Entanglement (QESSENCE) and Specific Targeted Research Project (STREP) Hybrid Information Processing (HIP)) and the Alexander von Humboldt Foundation. I.A.W. acknowledges support from the Royal Society.

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L.Z., H.B.C.-R. and A.D. contributed equally to this work. L.Z., H.B.C.-R., X.-M.J. and I.A.W. conceived the project and contributed to the design of the experiment and to laboratory measurements and data analysis. L.Z., A.D. and M.B.P contributed modelling and data analysis. G.P., J.S.L. and B.J.S. contributed to the initial conception of the project. All authors contributed to writing the manuscript.

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Correspondence to Lijian Zhang.

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The authors declare no competing financial interests.

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Zhang, L., Coldenstrodt-Ronge, H., Datta, A. et al. Mapping coherence in measurement via full quantum tomography of a hybrid optical detector. Nature Photon 6, 364–368 (2012). https://doi.org/10.1038/nphoton.2012.107

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