Experimental investigation of high-dimensional quantum key distribution protocols with twisted photons

Quantum key distribution is on the verge of real world applications, where perfectly secure information can be distributed among multiple parties. Several quantum cryptographic protocols have been theoretically proposed and independently realized in different experimental conditions. Here, we develop an experimental platform based on high-dimensional orbital angular momentum states of single photons that enables implementation of multiple quantum key distribution protocols with a single experimental apparatus. Our versatile approach allows us to experimentally survey different classes of quantum key distribution techniques, such as the 1984 Bennett \& Brassard (BB84), tomographic protocols including the six-state and the Singapore protocol, and to investigate, for the first time, a recently introduced differential phase shift (Chau15) protocol using twisted photons. This enables us to experimentally compare the performance of these techniques and discuss their benefits and deficiencies in terms of noise tolerance in different dimensions.

[1]  Enrico Santamato,et al.  Statistical moments of quantum-walk dynamics reveal topological quantum transitions , 2016, Nature Communications.

[2]  Qinan Wang,et al.  Experimentally feasible quantum-key-distribution scheme using qubit-like qudits and its comparison with existing qubit- and qudit-based protocols , 2017 .

[3]  H. Bechmann-Pasquinucci,et al.  Quantum cryptography , 2001, quant-ph/0101098.

[4]  H. F. Chau.  Quantum key distribution using qudits that each encode one bit of raw key , 2015 .

[5]  Andrew Forbes,et al.  Creation and detection of optical modes with spatial light modulators , 2016 .

[6]  S. Goyal,et al.  Higher-dimensional orbital-angular-momentum-based quantum key distribution with mutually unbiased bases , 2013, 1402.5810.

[7]  R. Boyd,et al.  Experimental Realization of Quantum Tomography of Photonic Qudits via Symmetric Informationally Complete Positive Operator-Valued Measures , 2015 .

[8]  H. Bechmann-Pasquinucci,et al.  Quantum Cryptography using larger alphabets , 1999, quant-ph/9910095.

[9]  Shuang Wang,et al.  Proof-of-principle experimental realization of a qubit-like qudit-based quantum key distribution scheme , 2017, 1707.00387.

[10]  Fabio Sciarrino,et al.  Test of mutually unbiased bases for six-dimensional photonic quantum systems , 2013, Scientific Reports.

[11]  Enrico Santamato,et al.  Detection of Zak phases and topological invariants in a chiral quantum walk of twisted photons , 2016, Nature Communications.

[12]  Yoshihisa Yamamoto,et al.  Practical quantum key distribution protocol without monitoring signal disturbance , 2014, Nature.

[13]  V. D'Ambrosio,et al.  Complete experimental toolbox for alignment-free quantum communication , 2012, Nature Communications.

[14]  Ueli Maurer,et al.  Generalized privacy amplification , 1994, Proceedings of 1994 IEEE International Symposium on Information Theory.

[15]  D. Bruß.  Optimal Eavesdropping in Quantum Cryptography with Six States , 1998, quant-ph/9805019.

[16]  V. Scarani,et al.  Quantum cloning , 2005, quant-ph/0511088.

[17]  Robert Fickler,et al.  High-dimensional quantum cloning and applications to quantum hacking , 2016, Science Advances.

[18]  Stephen Wiesner,et al.  Conjugate coding , 1983, SIGA.

[19]  Robert Fickler,et al.  Twisted photons: new quantum perspectives in high dimensions , 2017, Light: Science & Applications.

[20]  Dagomir Kaszlikowski,et al.  Tomographic quantum cryptography , 2003 .

[21]  Andrew G. White,et al.  Generation of optical phase singularities by computer-generated holograms. , 1992, Optics letters.

[22]  V. Buzek,et al.  Quantum secret sharing , 1998, quant-ph/9806063.

[23]  Leif Katsuo Oxenløwe,et al.  High-dimensional quantum key distribution based on multicore fiber using silicon photonic integrated circuits , 2016, npj Quantum Information.

[24]  A. Forbes,et al.  Characterizing quantum channels with non-separable states of classical light , 2017, Nature Physics.

[25]  D. Gauthier,et al.  High-dimensional quantum cryptography with twisted light , 2014, 1402.7113.

[26]  G. Vallone,et al.  Experimental quantum process tomography of non-trace-preserving maps , 2010, 1008.5334.

[27]  Marco Genovese,et al.  Review on qudits production and their application to Quantum Communication and Studies on Local Realism , 2007, 0711.1288.

[28]  Robert Fickler,et al.  Quantum process tomography of a high-dimensional quantum communication channel , 2018, Quantum.

[29]  Dagomir Kaszlikowski,et al.  Efficient and robust quantum key distribution with minimal state tomography , 2008 .

[30]  G. Vallone,et al.  Heralded single-photon sources for quantum-key-distribution applications , 2015, 1512.01020.

[31]  Hoi-Kwong Lo,et al.  Efficient Quantum Key Distribution Scheme and a Proof of Its Unconditional Security , 2004, Journal of Cryptology.

[32]  Hiroki Takesue,et al.  Differential-phase-shift quantum key distribution , 2009, 2006 Digest of the LEOS Summer Topical Meetings.

[33]  Isaac L. Chuang,et al.  Prescription for experimental determination of the dynamics of a quantum black box , 1997 .

[34]  Robert Fickler,et al.  Finite-key security analysis for multilevel quantum key distribution , 2015, 1512.05447.

[35]  J. H. Müller,et al.  Quantum memories , 2010, 1003.1107.

[36]  Yoshihisa Yamamoto,et al.  Security aspects of quantum key distribution with sub-Poisson light , 2002 .

[37]  Ebrahim Karimi,et al.  Limitations to the determination of a Laguerre–Gauss spectrum via projective, phase-flattening measurement , 2014, 1401.3512.

[38]  A. Vaziri,et al.  Experimental quantum cryptography with qutrits , 2005, quant-ph/0511163.

[39]  Joseph M. Renes,et al.  Symmetric informationally complete quantum measurements , 2003, quant-ph/0310075.

[40]  J. P. Woerdman,et al.  Orbital angular momentum of light and the transformation of Laguerre-Gaussian laser modes. , 1992, Physical review. A, Atomic, molecular, and optical physics.

[41]  A. Zeilinger,et al.  Twisted photon entanglement through turbulent air across Vienna , 2015, Proceedings of the National Academy of Sciences.

[42]  Marco Tomamichel,et al.  Tight finite-key analysis for quantum cryptography , 2011, Nature Communications.

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

[44]  Robert Fickler,et al.  Underwater Quantum Key Distribution in Outdoor Conditions with Twisted Photons , 2018, 1801.10299.

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

[46]  S. Chaturvedi.  Mutually unbiased bases , 2002 .

[47]  Valerio Scarani,et al.  Security proof for quantum key distribution using qudit systems , 2010, 1003.5464.

[48]  Ebrahim Karimi,et al.  Quantum walks and wavepacket dynamics on a lattice with twisted photons , 2014, Science Advances.

[49]  A. Zeilinger,et al.  High-Dimensional Single-Photon Quantum Gates: Concepts and Experiments. , 2017, Physical review letters.

[50]  R. Boyd,et al.  High-dimensional intracity quantum cryptography with structured photons , 2016, 1612.05195.

[51]  A. Vaziri,et al.  Entanglement of the orbital angular momentum states of photons , 2001, Nature.

[52]  Ebrahim Karimi,et al.  Exact solution to simultaneous intensity and phase encryption with a single phase-only hologram. , 2013, Optics letters.

[53]  G. Vallone,et al.  Free-space quantum key distribution by rotation-invariant twisted photons. , 2014, Physical review letters.

[54]  Gilles Brassard,et al.  Quantum Cryptography , 2005, Encyclopedia of Cryptography and Security.

[55]  Robert Fickler,et al.  Quantum cryptography with twisted photons through an outdoor underwater channel. , 2018, Optics express.

[56]  Robert Fickler,et al.  Round-robin differential-phase-shift quantum key distribution with twisted photons , 2018, Physical Review A.

[57]  A. J. Scott,et al.  Symmetric informationally complete positive-operator-valued measures: A new computer study , 2010 .

[58]  Milburn,et al.  Eavesdropping using quantum-nondemolition measurements. , 1993, Physical review. A, Atomic, molecular, and optical physics.

[59]  V. Scarani,et al.  The security of practical quantum key distribution , 2008, 0802.4155.

[60]  Anders Karlsson,et al.  Security of quantum key distribution using d-level systems. , 2001, Physical review letters.