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

We implement a double-pixel, compressive sensing camera to efficiently characterize, at high resolution, the spatially entangled fields produced by spontaneous parametric downconversion. This technique leverages sparsity in spatial correlations between entangled photons to improve acquisition times over raster-scanning by a scaling factor up to n^2/log(n) for n-dimensional images. We image at resolutions up to 1024 dimensions per detector and demonstrate a channel capacity of 8.4 bits per photon. By comparing the classical mutual information in conjugate bases, we violate an entropic Einstein-Podolsky-Rosen separability criterion for all measured resolutions. More broadly, our result indicates compressive sensing can be especially effective for higher-order measurements on correlated systems.

[1]  E. Candes,et al.  11-magic : Recovery of sparse signals via convex programming , 2005 .

[2]  Simón.  Peres-horodecki separability criterion for continuous variable systems , 1999, Physical review letters.

[3]  Robert W. Boyd,et al.  Entangled-photon compressive ghost imaging , 2011 .

[4]  S. Walborn,et al.  Schemes for quantum key distribution with higher-order alphabets using single-photon fractional Fourier optics , 2008 .

[5]  R. Kosut,et al.  Efficient measurement of quantum dynamics via compressive sensing. , 2009, Physical review letters.

[6]  Reid,et al.  Demonstration of the Einstein-Podolsky-Rosen paradox using nondegenerate parametric amplification. , 1989, Physical review. A, General physics.

[7]  R. M. Willett,et al.  Compressed sensing for practical optical imaging systems: A tutorial , 2011, IEEE Photonics Conference 2012.

[8]  E.J. Candes,et al.  An Introduction To Compressive Sampling , 2008, IEEE Signal Processing Magazine.

[9]  Cirac,et al.  Inseparability criterion for continuous variable systems , 1999, Physical review letters.

[10]  S. Walborn,et al.  Quantum teleportation of the angular spectrum of a single-photon field , 2007 .

[11]  Richard G. Baraniuk,et al.  Kronecker product matrices for compressive sensing , 2010, 2010 IEEE International Conference on Acoustics, Speech and Signal Processing.

[12]  Shih,et al.  Optical imaging by means of two-photon quantum entanglement. , 1995, Physical review. A, Atomic, molecular, and optical physics.

[13]  G. Buller,et al.  Imaging high-dimensional spatial entanglement with a camera , 2012, Nature Communications.

[14]  O. Katz,et al.  Compressive ghost imaging , 2009, 0905.0321.

[15]  Richard G. Baraniuk,et al.  Kronecker Compressive Sensing , 2012, IEEE Transactions on Image Processing.

[16]  S P Walborn,et al.  Quantum key distribution with higher-order alphabets using spatially encoded qudits. , 2006, Physical review letters.

[17]  Andrea Montanari,et al.  The Noise-Sensitivity Phase Transition in Compressed Sensing , 2010, IEEE Transactions on Information Theory.

[18]  Samuel L. Braunstein,et al.  Dense coding for continuous variables , 1999, quant-ph/9910010.

[19]  M C Teich,et al.  Role of entanglement in two-photon imaging. , 2001, Physical review letters.

[20]  David L Donoho,et al.  Compressed sensing , 2006, IEEE Transactions on Information Theory.

[21]  Rebecca Willett,et al.  Performance bounds on compressed sensing with Poisson noise , 2009, 2009 IEEE International Symposium on Information Theory.

[22]  No Value,et al.  IEEE International Conference on Image Processing , 2003 .

[23]  C. Broadbent,et al.  Witnessing Continuous Variable Entanglement with Discrete Measurements , 2012 .

[24]  Ieee Staff,et al.  2014 IEEE International Symposium on Information Theory (ISIT) , 2014 .

[25]  Sergio Verdú,et al.  Optimal Phase Transitions in Compressed Sensing , 2011, IEEE Transactions on Information Theory.

[26]  R.G. Baraniuk,et al.  Compressive Sensing [Lecture Notes] , 2007, IEEE Signal Processing Magazine.

[27]  S. Walborn,et al.  Entropic entanglement criteria for continuous variables. , 2009, Physical review letters.

[28]  Stephen Becker,et al.  Quantum state tomography via compressed sensing. , 2009, Physical review letters.

[29]  Wenlin Gong,et al.  Correlated imaging in scattering media. , 2011, Optics letters.

[30]  J. Pors.  Entangling light in high dimensions , 2011 .

[31]  Valerie C. Coffey.  Seeing in the Dark: Defense Applications of IR imaging , 2011 .

[32]  Charles R. Johnson,et al.  Topics in Matrix Analysis , 1991 .

[33]  Norbert Goertz,et al.  Proceedings IEEE International Symposium on Information Theory (ISIT) , 2008 .

[34]  N. Bohr.  II - Can Quantum-Mechanical Description of Physical Reality be Considered Complete? , 1935 .

[35]  46th Annual Conference on Information Sciences and Systems, CISS 2012, Princeton, NJ, USA, March 21-23, 2012 , 2012, CISS.

[36]  Mário A. T. Figueiredo,et al.  Gradient Projection for Sparse Reconstruction: Application to Compressed Sensing and Other Inverse Problems , 2007, IEEE Journal of Selected Topics in Signal Processing.

[37]  Galen Reeves,et al.  Compressed sensing phase transitions: Rigorous bounds versus replica predictions , 2012, 2012 46th Annual Conference on Information Sciences and Systems (CISS).

[38]  Emmanuel J. Candès,et al.  Robust uncertainty principles: exact signal reconstruction from highly incomplete frequency information , 2004, IEEE Transactions on Information Theory.

[39]  Yin Zhang,et al.  User’s Guide for TVAL3: TV Minimization by Augmented Lagrangian and Alternating Direction Algorithms , 2010 .

[40]  D. G. Kocher,et al.  Three-Dimensional Imaging Laser Radars with Geiger-Mode Avalanche Photodiode Arrays , 2002 .

[41]  S. Walborn,et al.  Revealing hidden Einstein-Podolsky-Rosen nonlocality. , 2011, Physical review letters.

[42]  P. H. Souto Ribeiro,et al.  Continuous-variable quantum computation with spatial degrees of freedom of photons , 2011, 1106.3049.

[43]  Ting Sun,et al.  Single-pixel imaging via compressive sampling , 2008, IEEE Signal Process. Mag..

[44]  Richard G. Baraniuk,et al.  An Architecture for Compressive Imaging , 2006, 2006 International Conference on Image Processing.

[45]  Surya Ganguli,et al.  Statistical mechanics of compressed sensing. , 2010, Physical review letters.

[46]  John C Howell,et al.  Realization of the Einstein-Podolsky-Rosen paradox using momentum- and position-entangled photons from spontaneous parametric down conversion. , 2004, Physical review letters.

[47]  Albert Wang,et al.  The In-Crowd Algorithm for Fast Basis Pursuit Denoising , 2011, IEEE Transactions on Signal Processing.

[48]  Charles H. Bennett,et al.  Communication via one- and two-particle operators on Einstein-Podolsky-Rosen states. , 1992, Physical review letters.

[49]  John R. Tower,et al.  Geiger-mode avalanche photodiode focal plane arrays for three-dimensional imaging LADAR , 2010, Optical Engineering + Applications.

[50]  John C Howell,et al.  Large-alphabet quantum key distribution using energy-time entangled bipartite States. , 2007, Physical review letters.

[51]  Urbashi Mitra,et al.  2008 IEEE International Conference on Acoustics, Speech, and Signal Processing (ICASSP) , 2008 .

[52]  Zachary T. Harmany,et al.  Sparse poisson intensity reconstruction algorithms , 2009, 2009 IEEE/SP 15th Workshop on Statistical Signal Processing.

[53]  Barnett,et al.  Entropy as a measure of quantum optical correlation. , 1989, Physical review. A, General physics.

[54]  James Schneeloch,et al.  Quantum mutual information capacity for high-dimensional entangled states. , 2011, Physical review letters.

[55]  E. Candès,et al.  Sparsity and incoherence in compressive sampling , 2006, math/0611957.

[56]  Ekert,et al.  Quantum cryptography based on Bell's theorem. , 1991, Physical review letters.

[57]  C. Monken,et al.  Direct measurement of transverse-mode entanglement in two-photon states , 2009 .