Experimental quantum fingerprinting with weak coherent pulses

Quantum communication holds the promise of creating disruptive technologies that will play an essential role in future communication networks. For example, the study of quantum communication complexity has shown that quantum communication allows exponential reductions in the information that must be transmitted to solve distributed computational tasks. Recently, protocols that realize this advantage using optical implementations have been proposed. Here we report a proof-of-concept experimental demonstration of a quantum fingerprinting system that is capable of transmitting less information than the best-known classical protocol. Our implementation is based on a modified version of a commercial quantum key distribution system using off-the-shelf optical components over telecom wavelengths, and is practical for messages as large as 100 Mbits, even in the presence of experimental imperfections. Our results provide a first step in the development of experimental quantum communication complexity.

[1]  Mikhail J. Atallah,et al.  Algorithms and Theory of Computation Handbook , 2009, Chapman & Hall/CRC Applied Algorithms and Data Structures series.

[2]  N. Gisin,et al.  Quantum key distribution over 67 km with a plug , 2002 .

[3]  Juan Miguel Arrazola,et al.  Quantum Communication Complexity with Coherent States and Linear Optics , 2014, TQC.

[4]  Steven G. Johnson,et al.  The Design and Implementation of FFTW3 , 2005, Proceedings of the IEEE.

[5]  G. Brassard,et al.  Quantum Communication Complexity , 2003 .

[6]  Julius Goldhar,et al.  Experimental demonstration of a receiver beating the standard quantum limit for multiple nonorthogonal state discrimination , 2013, Nature Photonics.

[7]  Artur Ekert,et al.  Experimental quantum multimeter and one-qubit fingerprinting , 2006 .

[8]  F. Marsili,et al.  Detecting single infrared photons with 93% system efficiency , 2012, 1209.5774.

[9]  Barry C Sanders,et al.  Single-qubit optical quantum fingerprinting. , 2005, Physical review letters.

[10]  S. Wehner,et al.  Experimental implementation of bit commitment in the noisy-storage model , 2012, Nature Communications.

[11]  László Babai,et al.  Randomized simultaneous messages: solution of a problem of Yao in communication complexity , 1997, Proceedings of Computational Complexity. Twelfth Annual IEEE Conference.

[12]  P. J. Clarke,et al.  Realization of quantum digital signatures without the requirement of quantum memory. , 2013, Physical review letters.

[13]  Bo'az Klartag,et al.  Quantum one-way communication can be exponentially stronger than classical communication , 2011, STOC '11.

[14]  Li Qian,et al.  Experimental demonstration of polarization encoding measurement-device-independent quantum key distribution. , 2013, Physical review letters.

[15]  Gilles Brassard,et al.  Quantum cryptography: Public key distribution and coin tossing , 2014, Theor. Comput. Sci..

[16]  S. Lloyd,et al.  Advances in quantum metrology , 2011, 1102.2318.

[17]  D. E. Daykin Distribution of Bordered Persymmetric Matrices in a Finite Field. , 1960 .

[18]  Alexander Barg,et al.  Random codes: Minimum distances and error exponents , 2002, IEEE Trans. Inf. Theory.

[19]  Ziv Bar-Yossef,et al.  Exponential separation of quantum and classical one-way communication complexity , 2004, STOC '04.

[20]  Juan Miguel Arrazola,et al.  Quantum fingerprinting with coherent states and a constant mean number of photons , 2013, 1309.5005.

[21]  R. Cleve,et al.  Quantum fingerprinting. , 2001, Physical review letters.

[22]  Uriel Feige,et al.  Proceedings of the thirty-ninth annual ACM symposium on Theory of computing , 2007, STOC 2007.

[23]  Ran Raz,et al.  Exponential separation of quantum and classical communication complexity , 1999, STOC '99.

[24]  Xiongfeng Ma,et al.  Ultrafast quantum random number generation based on quantum phase fluctuations. , 2011, Optics express.

[25]  Ran Raz,et al.  Exponential separations for one-way quantum communication complexity, with applications to cryptography , 2006, STOC '07.

[26]  E. Diamanti,et al.  Experimental plug and play quantum coin flipping , 2013, Nature Communications.

[27]  Andrew Chi-Chih Yao,et al.  Informational complexity and the direct sum problem for simultaneous message complexity , 2001, Proceedings 2001 IEEE International Conference on Cluster Computing.

[28]  Juan Miguel Arrazola,et al.  Quantum communication with coherent states and linear optics , 2014, 1406.7189.

[29]  Gilles Brassard,et al.  Experimental loss-tolerant quantum coin flipping , 2011, Nature communications.

[30]  I Lucio-Martinez,et al.  Real-world two-photon interference and proof-of-principle quantum key distribution immune to detector attacks. , 2013, Physical review letters.

[31]  R. Cleve,et al.  Nonlocality and communication complexity , 2009, 0907.3584.

[32]  I. Chuang,et al.  Quantum Digital Signatures , 2001, quant-ph/0105032.

[33]  S. Wehner,et al.  Experimental bit commitment based on quantum communication and special relativity. , 2013, Physical review letters.

[34]  Victor Y. Pan,et al.  Applications of FFT and structured matrices , 2010 .

[35]  Marek Zukowski,et al.  Experimental quantum communication complexity , 2005, quant-ph/0502066.

[36]  A. Razborov Communication Complexity , 2011 .

[37]  Andrew M. Steane,et al.  Physicists triumph at 'Guess My Number' , 2000 .

[38]  Elham Kashefi,et al.  9th Conference on the Theory of Quantum Computation, Communication and Cryptography (TQC 2014) , 2014 .

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

[40]  Max Crochemore,et al.  Algorithms and Theory of Computation Handbook , 2010 .

[41]  Lance Fortnow,et al.  Proceedings of the forty-third annual ACM symposium on Theory of computing , 2011, STOC 2011.

[42]  László Babai,et al.  Proceedings of the thirty-sixth annual ACM symposium on Theory of computing , 2004, STOC 2004.

[43]  E. Gilbert A comparison of signalling alphabets , 1952 .

[44]  Tsuyoshi Ito,et al.  Quantum fingerprints that keep secrets , 2010, Quantum Inf. Comput..

[45]  I. Ial,et al.  Nature Communications , 2010, Nature Cell Biology.

[46]  Jeffrey Scott Vitter,et al.  Proceedings of the Thirty-First Annual ACM Symposium on Theory of Computing, May 1-4, 1999, Atlanta, Georgia, USA , 1999, STOC.

[47]  M. Fejer,et al.  Experimental measurement-device-independent quantum key distribution. , 2012, Physical review letters.

[48]  Hong,et al.  Measurement of subpicosecond time intervals between two photons by interference. , 1987, Physical review letters.

[49]  Peter Hoyer,et al.  Multiparty quantum communication complexity. , 1997 .

[50]  E. Andersson,et al.  Experimentally realizable quantum comparison of coherent states and its applications , 2006, quant-ph/0601130.

[51]  Serge Massar,et al.  Quantum fingerprinting with a single particle , 2003 .

[52]  Yong Zhao,et al.  Experimental unconditionally secure bit commitment. , 2013, Physical review letters.

[53]  Gary L. Miller,et al.  Proceedings of the twenty-eighth annual ACM symposium on Theory of computing , 1996, STOC 1996.

[54]  Andrew Chi-Chih Yao,et al.  Some complexity questions related to distributive computing(Preliminary Report) , 1979, STOC.

[55]  P. J. Clarke,et al.  Experimental demonstration of quantum digital signatures using phase-encoded coherent states of light , 2012, Nature communications.

[56]  Avi Wigderson,et al.  Quantum vs. classical communication and computation , 1998, STOC '98.