Terahertz Quantum Cryptography

A well-known empirical rule for the demand of wireless communication systems is that of Edholm’s law of bandwidth. It states that the demand for bandwidth in wireless short-range communications doubles every 18 months. With the growing demand for bandwidth and the decreasing cell size of wireless systems, terahertz (THz) communication systems are expected to become increasingly important in modern day applications. With this expectation comes the need for protecting users’ privacy and security in the best way possible. With that in mind, we show that quantum key distribution can operate in the THz regime and we derive the relevant secret key rates against realistic collective attacks. In the extended THz range (from 0.1 to 50 THz), we find that below 1 THz, the main detrimental factor is thermal noise, while at higher frequencies it is atmospheric absorption. Our results show that high-rate THz quantum cryptography is possible over distances varying from a few meters using direct reconciliation, to about 220m via reverse reconciliation. We also give a specific example of the physical hardware and architecture that could be used to realize our THz quantum key distribution scheme.

[1]  Christian Weedbrook,et al.  Quantum cryptography without switching. , 2004, Physical review letters.

[2]  J. Fiurášek Gaussian transformations and distillation of entangled Gaussian states. , 2002, Physical review letters.

[3]  Wanyi Gu,et al.  Improvement of two-way continuous-variable quantum key distribution using optical amplifiers , 2014 .

[4]  Hong Guo,et al.  SECURITY OF A NEW TWO-WAY CONTINUOUS-VARIABLE QUANTUM KEY DISTRIBUTION PROTOCOL , 2011, 1110.1818.

[5]  N. Cerf,et al.  Unconditional optimality of Gaussian attacks against continuous-variable quantum key distribution. , 2006, Physical Review Letters.

[6]  Seth Lloyd,et al.  Advances in photonic quantum sensing , 2018, Nature Photonics.

[7]  A. Holevo Bounds for the quantity of information transmitted by a quantum communication channel , 1973 .

[8]  John L. Reno,et al.  Collective non-perturbative coupling of 2D electrons with high-quality-factor terahertz cavity photons , 2016, Nature Physics.

[9]  Stefano Pirandola,et al.  High-rate measurement-device-independent quantum cryptography , 2013, Nature Photonics.

[10]  Hidehiro Yonezawa,et al.  Experimental demonstration of quantum teleportation of broadband squeezing. , 2007, Physical review letters.

[11]  P. Glenn Gulak,et al.  Quasi-cyclic multi-edge LDPC codes for long-distance quantum cryptography , 2017, npj Quantum Information.

[12]  H. J. Kimble,et al.  The quantum internet , 2008, Nature.

[13]  Peng Huang,et al.  Long-distance continuous-variable quantum key distribution by controlling excess noise , 2016, Scientific Reports.

[14]  Jianjun Ma,et al.  Review of weather impact on outdoor terahertz wireless communication links , 2016, Nano Commun. Networks.

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

[16]  Samuel L. Braunstein,et al.  Theory of channel simulation and bounds for private communication , 2017, Quantum Science and Technology.

[17]  R. Renner,et al.  Information-theoretic security proof for quantum-key-distribution protocols , 2005, quant-ph/0502064.

[18]  J. Eisert,et al.  Advances in quantum teleportation , 2015, Nature Photonics.

[19]  N. Cerf,et al.  Quantum key distribution using gaussian-modulated coherent states , 2003, Nature.

[20]  Vladyslav C. Usenko,et al.  Unidimensional continuous-variable quantum key distribution , 2015, 1504.07093.

[21]  John F. Federici,et al.  Terahertz Attenuation in Snow and Sleet , 2019, Journal of Infrared, Millimeter, and Terahertz Waves.

[22]  Jun Terada,et al.  Terahertz wireless communications based on photonics technologies. , 2013, Optics express.

[23]  Xiangyu Wang,et al.  Computing quopit Clifford circuit amplitudes by the sum-over-paths technique , 2016, Quantum Inf. Comput..

[24]  Alexander Semenovich Holevo,et al.  Quantum Systems, Channels, Information: A Mathematical Introduction , 2019 .

[25]  M. Lewenstein,et al.  Quantum Entanglement , 2020, Quantum Mechanics.

[26]  Zheshen Zhang,et al.  Entanglement's benefit survives an entanglement-breaking channel. , 2013, Physical review letters.

[27]  Eleni Diamanti,et al.  Experimental demonstration of long-distance continuous-variable quantum key distribution , 2012, Nature Photonics.

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

[29]  S. Schmid,et al.  Optical detection of radio waves through a nanomechanical transducer , 2013, Nature.

[30]  Samuel L. Braunstein,et al.  Secret key capacity of the thermal-loss channel: improving the lower bound , 2016, Security + Defence.

[31]  S. Braunstein,et al.  Quantum Information with Continuous Variables , 2004, quant-ph/0410100.

[32]  Miguel Navascués,et al.  Optimality of Gaussian attacks in continuous-variable quantum cryptography. , 2006, Physical review letters.

[33]  Tadao Nagatsuma,et al.  A Review on Terahertz Communications Research , 2011 .

[34]  Shan Ma,et al.  A derivation of moment evolution equations for linear open quantum systems , 2018, 2018 33rd Youth Academic Annual Conference of Chinese Association of Automation (YAC).

[35]  S. Lloyd Enhanced Sensitivity of Photodetection via Quantum Illumination , 2008, Science.

[36]  Masayuki Fujita,et al.  Capture of a terahertz wave in a photonic-crystal slab , 2014, Nature Photonics.

[37]  Nicolas J. Cerf,et al.  Virtual entanglement and reconciliation protocols for quantum cryptography with continuous variables , 2003, Quantum Inf. Comput..

[38]  R. W. Andrews,et al.  Bidirectional and efficient conversion between microwave and optical light , 2013, Nature Physics.

[39]  Shota Yokoyama,et al.  Ultra-large-scale continuous-variable cluster states multiplexed in the time domain , 2013, Nature Photonics.

[40]  S. Lloyd,et al.  Characterization of collective Gaussian attacks and security of coherent-state quantum cryptography. , 2008, Physical review letters.

[41]  N. Cerf,et al.  Gaussian postselection and virtual noiseless amplification in continuous-variable quantum key distribution , 2012 .

[42]  Stefano Pirandola,et al.  Continuous-Variable Quantum Key Distribution using Thermal States , 2011, 1110.4617.

[43]  Christian Weedbrook,et al.  Continuous-variable quantum key distribution with entanglement in the middle , 2012, 1205.1497.

[44]  Bing Qi,et al.  Discrete and continuous variables for measurement-device-independent quantum cryptography , 2015, Nature Photonics.

[45]  Jianjun Ma,et al.  Experimental Comparison of Terahertz and Infrared Signaling in Laboratory-Controlled Rain , 2015 .

[46]  Carlo Sirtori,et al.  Optomechanical terahertz detection with single meta-atom resonator , 2017, Nature Communications.

[47]  P. Cochat,et al.  Et al , 2008, Archives de pediatrie : organe officiel de la Societe francaise de pediatrie.

[48]  G. Vallone,et al.  Advances in Quantum Cryptography , 2019, 1906.01645.

[49]  Lothar Moeller,et al.  Experimental comparison of terahertz and infrared data signal attenuation in dust clouds. , 2012, Journal of the Optical Society of America. A, Optics, image science, and vision.

[50]  Joseph Kerckhoff,et al.  Tunable coupling to a mechanical oscillator circuit using a coherent feedback network , 2012, 1211.1950.

[51]  S. Lloyd,et al.  Reply to 'Discrete and continuous variables for measurement-device-independent quantum cryptography' , 2015 .

[52]  S. Lloyd,et al.  Quantum illumination with Gaussian states. , 2008, Physical review letters.

[53]  J Eisert,et al.  Distilling Gaussian states with Gaussian operations is impossible. , 2002, Physical review letters.

[54]  A. Holevo,et al.  Capacity of quantum Gaussian channels , 1999 .

[55]  Seth Lloyd,et al.  Continuous Variable Quantum Cryptography using Two-Way Quantum Communication , 2006, ArXiv.

[56]  S. McLaughlin,et al.  Quantum key distribution over 25 km with an all-fiber continuous-variable system , 2007, 0706.4255.

[57]  Jianjun Ma,et al.  Experimental Comparison of Terahertz and Infrared Signaling in Controlled Atmospheric Turbulence , 2015 .

[58]  S. Braunstein,et al.  Physics: Unite to build a quantum Internet , 2016, Nature.

[59]  Seth Lloyd,et al.  Quantum cryptography approaching the classical limit. , 2010, Physical review letters.

[60]  J. Federici,et al.  Review of terahertz and subterahertz wireless communications , 2010 .

[61]  Seth Lloyd,et al.  Quantum illumination versus coherent-state target detection , 2009, 0902.0986.

[62]  Stefano Pirandola,et al.  Two-way quantum cryptography at different wavelengths , 2013, 1309.7973.

[63]  Jianjun Ma,et al.  Comparison of Experimental and Theoretical Determined Terahertz Attenuation in Controlled Rain , 2015 .

[64]  John Watrous,et al.  The Theory of Quantum Information , 2018 .

[65]  C. E. SHANNON,et al.  A mathematical theory of communication , 1948, MOCO.

[66]  Stefano Pirandola,et al.  Covariance Matrices under Bell-like Detections , 2012, Open Syst. Inf. Dyn..

[67]  P. Grangier,et al.  Continuous variable quantum cryptography using coherent states. , 2001, Physical review letters.

[68]  Ying-Dan Wang,et al.  Using interference for high fidelity quantum state transfer in optomechanics. , 2011, Physical review letters.

[69]  Seth Lloyd,et al.  Gaussian quantum information , 2011, 1110.3234.

[70]  Claude E. Shannon,et al.  The Mathematical Theory of Communication , 1950 .

[71]  Stefano Pirandola,et al.  Gaussian two-mode attacks in one-way quantum cryptography , 2017 .

[72]  Ian F. Akyildiz,et al.  TeraNets: ultra-broadband communication networks in the terahertz band , 2014, IEEE Wireless Communications.

[73]  Tobias Gehring,et al.  Single-quadrature continuous-variable quantum key distribution , 2015, Quantum Inf. Comput..

[74]  Nathan Walk,et al.  Security of continuous-variable quantum cryptography with Gaussian postselection , 2013 .

[75]  Stefano Pirandola,et al.  Gaussian one-way thermal quantum cryptography with finite-size effects , 2018, Physical Review A.

[76]  Anthony Leverrier,et al.  Security of Continuous-Variable Quantum Key Distribution via a Gaussian de Finetti Reduction. , 2017, Physical review letters.

[77]  Lothar Moeller,et al.  Experimental comparison of performance degradation from terahertz and infrared wireless links in fog. , 2012, Journal of the Optical Society of America. A, Optics, image science, and vision.

[78]  Eleni Diamanti,et al.  Distributing Secret Keys with Quantum Continuous Variables: Principle, Security and Implementations , 2015, Entropy.

[79]  K. Vahala,et al.  Optomechanical crystals , 2009, Nature.

[80]  Fangjing Hu,et al.  Predicting Atmospheric Attenuation Under Pristine Conditions Between 0.1 and 100 THz , 2016, IEEE Access.

[81]  Aashish A. Clerk,et al.  High-fidelity bosonic quantum state transfer using imperfect transducers and interference , 2018, npj Quantum Information.

[82]  L. Banchi,et al.  Fundamental limits of repeaterless quantum communications , 2015, Nature Communications.

[83]  Amit Vainsencher,et al.  Nanomechanical coupling between microwave and optical photons , 2013, Nature Physics.

[84]  Ian F. Akyildiz,et al.  Terahertz band: Next frontier for wireless communications , 2014, Phys. Commun..

[85]  Thomas Schneider,et al.  Link Budget Analysis for Terahertz Fixed Wireless Links , 2012, IEEE Transactions on Terahertz Science and Technology.

[86]  Jeffrey H. Shapiro Defeating passive eavesdropping with quantum illumination , 2009 .

[87]  Jayne Thompson,et al.  How discord underlies the noise resilience of quantum illumination , 2013, 1312.3332.

[88]  J. Cirac,et al.  De Finetti representation theorem for infinite-dimensional quantum systems and applications to quantum cryptography. , 2008, Physical review letters.

[89]  M. Barbieri,et al.  Improving the maximum transmission distance of continuous-variable quantum key distribution using a noiseless amplifier , 2012 .

[90]  Stefano Pirandola,et al.  General immunity and superadditivity of two-way Gaussian quantum cryptography , 2016, Scientific Reports.

[91]  Saikat Guha,et al.  Microwave quantum illumination. , 2015, Physical review letters.

[92]  Stefano Mancini,et al.  Two-way Gaussian quantum cryptography against coherent attacks in direct reconciliation , 2015 .