Efficient high-dimensional entanglement imaging with a compressive-sensing double-pixel camera

Physical Review X

Volumn 3, Issue 1, 2013, Pages

  Howland, Gregory A ^a   Howell, John C ^a  

^a UNIVERSITY OF ROCHESTER   (United States)

Author keywords

[No Author keywords available]

Indexed keywords

COMPRESSIVE SENSING; CORRELATED SYSTEMS; EINSTEIN-PODOLSKY-ROSEN; ENTANGLED PHOTONS; MUTUAL INFORMATIONS; SEPARABILITY CRITERION; SPATIAL CORRELATIONS; SPONTANEOUS PARAMETRIC DOWN-CONVERSION;

PHOTONS; PIXELS;

CAMERAS;

EID: 84877939152     PISSN: None     EISSN: 21603308     Source Type: Journal    
DOI: 10.1103/PhysRevX.3.011013     Document Type: Article

References (54)

1. A. Einstein, B. Podolsky, and N. Rosen, Can Quantum-Mechanical Description of Physical Reality Be Considered Complete?, Phys. Rev. 47, 777 (1935).
2. J. C. Howell, R. S. Bennink, S. J. Bentley, and R.W. Boyd, Realization of the Einstein-Podolsky-Rosen Paradox Using Momentum- and Position-Entangled Photons from Spontaneous Parametric Down Conversion, Phys. Rev. Lett. 92, 210403 (2004).
3. J. B. Pors, Ph.D. thesis, Leiden University, 2011.
4. A. K. Ekert, Quantum Cryptography Based on Bell's Theorem, Phys. Rev. Lett. 67, 661 (1991).
5. S. P. Walborn, D. S. Lemelle, M. P. Almeida, and P. H. Souto Ribeiro, Quantum Key Distribution with Higher-Order Alphabets Using Spatially Encoded Qudits, Phys. Rev. Lett. 96, 090501 (2006).
6. S. P. Walborn, D. S. Lemelle, D. S. Tasca, and P. H. Souto Ribeiro, Schemes for Quantum Key Distribution with Higher-Order Alphabets Using Single-Photon Fractional Fourier Optics, Phys. Rev. A 77, 062323 (2008).
7. C. H. Bennett and S. J. Wiesner, Communication via Oneand Two-Particle Operators on Einstein-Podolsky-Rosen States, Phys. Rev. Lett. 69, 2881 (1992).
8. S. L. Braunstein and H. J. Kimble, Dense Coding for Continuous Variables, Phys. Rev. A 61, 042302 (2000).
9. T. B. Pittman, Y. H. Shih, D.V. Strekalov, and A.V. Sergienko, Optical Imaging by Means of Two-Photon Quantum Entanglement, Phys. Rev. A 52, R3429 (1995).
10. A. F. Abouraddy, B. E.A. Saleh, A.V. Sergienko, and M. C. Teich, Role of Entanglement in Two-Photon Imaging, Phys. Rev. Lett. 87, 123602 (2001).
11. D. S. Tasca, R. M. Gomes, F. Toscano, P. H. Souto Ribeiro, and S. P. Walborn, Continuous-Variable Quantum Computation with Spatial Degrees of Freedom of Photons, Phys. Rev. A 83, 052325 (2011).
12. S. P. Walborn, D. S. Ether, R. L. de Matos Filho, and N. Zagury, Quantum Teleportation of the Angular Spectrum of a Single-Photon Field, Phys. Rev. A 76, 033801 (2007).
13. H. Di Lorenzo Pires, C. H. Monken, and M. P. van Exter, Direct Measurement of Transverse-Mode Entanglement in Two-Photon States, Phys. Rev. A 80, 022307 (2009).
14. V. C. Coffey, Seeing in the Dark: Defense Applications of IR Imaging, Opt. Photonics News 22, 26 (2011).
15. M. A. Albota et al. Three-Dimensional Imaging Laser Radars with Geiger-Mode Avalanche Photodiode Arrays, Lincoln Laboratory Journal 13, 351 (2002).
16. M. A. Itzler, M. Entwistle, M. Owens, K. Patel, X. Jiang, K. Slomkowski, S. Rangwala, P. F. Zalud, T. Senko, J. Tower, and J. Ferraro, in Infrared Remote Sensing and Instrumentation XVIII, SPIE Proceedings Vol. 7808 (SPIE-International Society for Optical Engineering, Bellingham, WA, 2010), p. 78080C.
17. M. P. Edgar, D. S. Tasca, F. Izdebski, R. E. Warburton, J. Leach, M. Agnew, G. S. Buller, R.W. Boyd, and M. J. Padgett, Imaging High-Dimensional Spatial Entanglement with a Camera, Nat. Commun. 3, 984 (2012).
18. P. B. Dixon, G. A. Howland, J. Schneeloch, and J. C. Howell, Quantum Mutual Information Capacity for High-Dimensional Entangled States, Phys. Rev. Lett. 108, 143603 (2012).
19. R. Bellman, Dynamic Programming (Dover, New York, 2003).
20. J. Schneeloch, P. B. Dixon, G. A. Howland, C. J. Broadbent, and J. C. Howell, Witnessing Continuous Variable Entanglement with Discrete Measurements, arXiv:1210.4234.
21. D. L. Donoho, Compressed Sensing, IEEE Trans. Inf. Theory 52, 1289 (2006).
22. E. J. Cande's and J. Romberg, Sparsity and Incoherence in Compressive Sampling, Inverse Probl. 23, 969 (2007).
23. R. G. Baraniuk, Compressive Sensing [Lecture Notes], IEEE Signal Process. Mag. 24, 118 (2007).
24. E. J. Candes and M. B. Wakin, An Introduction to Compressive Sampling, IEEE Signal Process. Mag. 25, 21 (2008).
25. E. J. Cande's and J. Romberg, l1-Magic: Recovery of Sparse Signals via Convex Programming (unpublished).
26. E. J. Candes, J. Romberg, and T. Tao, Robust Uncertainty Principles: Exact Signal Reconstruction from Highly Incomplete Frequency Information, IEEE Trans. Inf. Theory 52, 489 (2006).
27. D. Gross, Y.-K. Liu, S. T. Flammia, S. Becker, and J. Eisert, Quantum State Tomography via Compressed Sensing, Phys. Rev. Lett. 105, 150401 (2010).
28. A. Shabani, R. L. Kosut, M. Mohseni, H. Rabitz, M. A. Broome, M. P. Almeida, A. Fedrizzi, and A. G. White, Efficient Measurement of Quantum Dynamics via Compressive Sensing, Phys. Rev. Lett. 106, 100401 (2011).
29. O. Katz, Y. Bromberg, and Y. Silberberg, Compressive Ghost Imaging, Appl. Phys. Lett. 95, 131110 (2009).
30. P. Zerom, K.W. C. Chan, J. C. Howell, and R.W. Boyd, Entangled-Photon Compressive Ghost Imaging, Phys. Rev. A 84, 061804(R) (2011).
31. M. B. Wakin, J. N. Laska, M. F. Duarte, D. Baron, S. Sarvotham, D. Takhar, K. F. Kelly, and R. G. Baraniuk, in IEEE International Conference on Image Processing, 2006 (IEEE, New York, 2006), p. 1273-1276.
32. M. F. Duarte, M. A. Davenport, D. Takhar, J.N. Laska, T. Sun, K. F. Kelly, and R. G. Baraniuk, Single-Pixel Imaging via Compressive Sampling, IEEE Signal Process. Mag. 25, 83 (2008).
33. M. F. Duarte and R. G. Baraniuk, in IEEE International Conference on Acoustics, Speech, and Signal Processing (ICASSP), 2010 (IEEE, New York, 2010), p. 3650-3653.
34. M. F. Duarte and R. G. Baraniuk, Kronecker Compressive Sensing, IEEE Trans. Image Process. 21, 494 (2012).
35. C. Li,W. Yin, and Y. Zhang, TVAL3: TV Minimization by Augmented Lagrangian and ALternating Direction ALgorithms (unpublished).
36. R. A. Horn and C. R. Johnson, Topics in Matrix Analysis (Cambridge University Press, Cambridge, England, 1994).
37. Rebecca M.Willett, Roummel F. Marcia, and Jonathan M. Nichols, Compressed Sensing for Practical Optical Imaging Systems: A Tutorial, Opt. Eng. (Bellingham, Wash.) 50, 072601 (2011).
38. D. L. Donoho, A. Maleki, and A. Montanari, The Noise-Sensitivity Phase Transition in Compressed Sensing, IEEE Trans. Inf. Theory 57, 6920 (2011).
39. Yihong Wu and S. Verdu, Optimal Phase Transitions in Compressed Sensing, IEEE Trans. Inf. Theory 58, 6241 (2012).
40. G. Reeves and M. Gastpar, in 46th Annual Conference on Information Sciences and Systems (CISS), 2012 (Curran, Red Hook, NY, 2012), p. 1-6.
41. R. M. Willett and M. Raginsky, in IEEE International Symposium on Information Theory (ISIT), 2009 (IEEE, New York, 2009), p. 174-178.
42. Z. T. Harmany, R. F. Marcia, and R. M. Willett, in IEEE/ SP 15th Workshop on Statistical Signal Processing (SSP), 2009 (IEEE, New York, 2009), p. 634-637.
43. Surya Ganguli and Haim Sompolinsky, Statistical Mechanics of Compressed Sensing, Phys. Rev. Lett. 104, 188701 (2010).
44. M. A. T. Figueiredo, R. D. Nowak, and S. J. Wright, Gradient Projection for Sparse Reconstruction: Application to Compressed Sensing and Other Inverse Problems, IEEE J. Sel. Top. Signal Process. 1, 586 (2007).
45. P. R. Gill, A. Wang, and A. Molnar, The In-Crowd Algorithm for Fast Basis Pursuit Denoising, IEEE Trans. Signal Process. 59, 4595 (2011).
46. S. M. Barnett and S. J. D. Phoenix, Entropy as a Measure of Quantum Optical Correlation, Phys. Rev. A 40, 2404 (1989).
47. S. P. Walborn, B. G. Taketani, A. Salles, F. Toscano, and R. L. de Matos Filho, Entropic Entanglement Criteria for Continuous Variables, Phys. Rev. Lett. 103, 160505 (2009).
48. S. P. Walborn, A. Salles, R. M. Gomes, F. Toscano, and P. H. Souto Ribeiro, Revealing Hidden Einstein-Podolsky-Rosen Nonlocality, Phys. Rev. Lett. 106, 130402 (2011).
49. M.V. Fedorov, Yu.M. Mikhailova, and P. A. Volkov, Gaussian Modelling and Schmidt Modes of SPDC Biphoton States, J. Phys. B 42, 175503 (2009).
50. M. D. Reid, Demonstration of the Einstein-Podolsky-Rosen Paradox Using Nondegenerate Parametric Amplification, Phys. Rev. A 40, 913 (1989).
51. Lu-Ming Duan, G. Giedke, J. I. Cirac, and P. Zoller, Inseparability Criterion for Continuous Variable Systems, Phys. Rev. Lett. 84, 2722 (2000).
52. R. Simon, Peres-Horodecki Separability Criterion for Continuous Variable Systems, Phys. Rev. Lett. 84, 2726 (2000).
53. I. Ali-Khan, C. J. Broadbent, and J. C. Howell, Large-Alphabet Quantum Key Distribution Using Energy-Time Entangled Bipartite States, Phys. Rev. Lett. 98, 060503 (2007).
54. W. Gong and S. Han, Correlated Imaging in Scattering Media, Opt. Lett. 36, 394 (2011).