Advances in Quantum Dense Coding

Quantum dense coding is one of the most important protocols in quantum communication. It derives from the idea of using quantum resources to boost the communication capacity and now serves as a key primitive across a variety of quantum information protocols. Here, we focus on the basic theoretical ideas behind quantum dense coding, discussing its development history from discrete and continuous variables to quantum networks, then to its variant protocols and applications in quantum secure communication. With this basic background in hand, we then review the main experimental achievements, from photonic qubits and qudits to optical modes, nuclear magnetic resonance, and atomic systems. Besides the state of the art, we finally discuss potential future steps.

[1]  Nathan K Langford,et al.  Generation of hyperentangled photon pairs. , 2005, Physical review letters.

[2]  Igor Devetak.  The private classical capacity and quantum capacity of a quantum channel , 2005, IEEE Transactions on Information Theory.

[3]  Fuguo Deng,et al.  Two-step quantum direct communication protocol using the Einstein-Podolsky-Rosen pair block , 2003, quant-ph/0308173.

[4]  Tohya Hiroshima.  Optimal dense coding with mixed state entanglement , 2001 .

[5]  Jing Zhang,et al.  Quantum teleportation and dense coding by means of bright amplitude-squeezed light and direct measurement of a Bell state , 2000 .

[6]  Seth Lloyd,et al.  Dense coding capacity of a quantum channel , 2019, Physical Review Research.

[7]  Wei Zhang,et al.  Quantum Secure Direct Communication with Quantum Memory. , 2016, Physical review letters.

[8]  V. Vedral,et al.  Entanglement measures and purification procedures , 1997, quant-ph/9707035.

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

[10]  Guang-Can Guo,et al.  Efficient superdense coding in the presence of non-Markovian noise , 2015, 1504.07572.

[11]  M. Nielsen,et al.  Information transmission through a noisy quantum channel , 1997, quant-ph/9702049.

[12]  Fuguo Deng,et al.  Quantum secure direct communication with high-dimension quantum superdense coding , 2005 .

[13]  Yan Feng-Li,et al.  A Scheme for Dense Coding in the Non-Symmetric Quantum Channel , 2004 .

[14]  Changde Xie,et al.  Controlled dense coding for continuous variables using three-particle entangled states , 2002 .

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

[16]  A. Divochiy,et al.  Photon-number-resolving SSPDs with system detection efficiency over 50% at telecom range , 2018 .

[17]  K. Boström,et al.  Deterministic secure direct communication using entanglement. , 2002, Physical review letters.

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

[19]  N. Lutkenhaus,et al.  Bell measurements for teleportation , 1998, quant-ph/9809063.

[20]  G. Long,et al.  Theoretically efficient high-capacity quantum-key-distribution scheme , 2000, quant-ph/0012056.

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

[22]  A. Holevo.  On entanglement-assisted classical capacity , 2001, quant-ph/0106075.

[23]  B. Moor,et al.  Four qubits can be entangled in nine different ways , 2001, quant-ph/0109033.

[24]  Schumacher,et al.  Classical information capacity of a quantum channel. , 1996, Physical review. A, Atomic, molecular, and optical physics.

[25]  S. Lloyd.  Capacity of the noisy quantum channel , 1996, quant-ph/9604015.

[26]  Harald Weinfurter,et al.  Embedded Bell-state analysis , 1998 .

[27]  Roberto Morandotti,et al.  On-chip generation of high-dimensional entangled quantum states and their coherent control , 2017, Nature.

[28]  Kevin Barraclough,et al.  I and i , 2001, BMJ : British Medical Journal.

[29]  P. Hayden,et al.  Generalized remote state preparation: Trading cbits, qubits, and ebits in quantum communication , 2003, quant-ph/0308143.

[30]  R. Werner.  All teleportation and dense coding schemes , 2000, quant-ph/0003070.

[31]  C. Xie,et al.  Quantum dense coding exploiting a bright Einstein-Podolsky-Rosen beam. , 2002, Physical review letters.

[32]  Harald Weinfurter,et al.  Secure Communication with a Publicly Known Key , 2001 .

[33]  Hermann Kampermann,et al.  Optimal superdense coding over memory channels , 2011 .

[34]  G. Long,et al.  General scheme for superdense coding between multiparties , 2001, quant-ph/0110112.

[35]  Otfried Gühne,et al.  Characterizing Genuine Multilevel Entanglement. , 2017, Physical review letters.

[36]  Peter van Loock,et al.  3/4-Efficient Bell measurement with passive linear optics and unentangled ancillae. , 2014, Physical review letters.

[37]  A. Harrow,et al.  Superdense coding of quantum states. , 2003, Physical review letters.

[38]  Christian Kurtsiefer,et al.  Complete deterministic linear optics Bell state analysis. , 2006, Physical review letters.

[39]  A. Furusawa,et al.  Hybrid discrete- and continuous-variable quantum information , 2014, Nature Physics.

[40]  Ashish V. Thapliyal,et al.  Entanglement-Assisted Classical Capacity of Noisy Quantum Channels , 1999, Physical Review Letters.

[41]  M D Barrett,et al.  Quantum dense coding with atomic qubits. , 2004, Physical review letters.

[42]  J. Eisert,et al.  Introduction to the basics of entanglement theory in continuous-variable systems , 2003, quant-ph/0312071.

[43]  Guang-Can Guo,et al.  Nonlocal memory effects in the dynamics of open quantum systems. , 2011, Physical review letters.

[44]  G. Guo,et al.  Controlled dense coding using the Greenberger-Horne-Zeilinger state , 2001 .

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

[46]  Paul G. Kwiat,et al.  Hyperentangled Bell-state analysis , 2007 .

[47]  Antoni Wójcik.  Eavesdropping on the "ping-pong" quantum communication protocol. , 2003, Physical review letters.

[48]  P. Knight,et al.  Multiparticle generalization of entanglement swapping , 1998 .

[49]  Y. Yeo,et al.  Teleportation and dense coding with genuine multipartite entanglement. , 2005, Physical review letters.

[50]  Weinfurter,et al.  Dense coding in experimental quantum communication. , 1996, Physical review letters.

[51]  Yongmei Huang,et al.  Satellite-to-ground quantum key distribution , 2017, Nature.

[52]  A. Winter,et al.  Aspects of Generic Entanglement , 2004, quant-ph/0407049.

[53]  L. Vaidman,et al.  Methods for Reliable Teleportation , 1998, quant-ph/9808040.

[54]  Guang-Can Guo,et al.  Experimental Test of Compatibility-Loophole-Free Contextuality with Spatially Separated Entangled Qutrits. , 2016, Physical review letters.

[55]  L. Mandel,et al.  Quantum effects in one-photon and two-photon interference , 1999 .

[56]  Paul G. Kwiat,et al.  Hyper-entangled states , 1997 .

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

[58]  M. Lewenstein,et al.  Distributed quantum dense coding. , 2004, Physical review letters.

[59]  N. Linke,et al.  High-Fidelity Preparation, Gates, Memory, and Readout of a Trapped-Ion Quantum Bit. , 2014, Physical review letters.

[60]  N. Linke,et al.  High-Fidelity Quantum Logic Gates Using Trapped-Ion Hyperfine Qubits. , 2015, Physical review letters.

[61]  Peter van Loock,et al.  Beating the one-half limit of ancilla-free linear optics Bell measurements. , 2013, Physical review letters.

[62]  Yi-You Nie,et al.  Controlled Dense Coding between Multi-Parties , 2009 .

[63]  Jian-Wei Pan,et al.  12-Photon Entanglement and Scalable Scattershot Boson Sampling with Optimal Entangled-Photon Pairs from Parametric Down-Conversion. , 2018, Physical review letters.

[64]  Ronald J Sadlier,et al.  Superdense Coding over Optical Fiber Links with Complete Bell-State Measurements. , 2016, Physical review letters.

[65]  T. R. Tan,et al.  High-Fidelity Universal Gate Set for ^{9}Be^{+} Ion Qubits. , 2016, Physical review letters.

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

[67]  P. Agrawal,et al.  Probabilistic superdense coding , 2005 .

[68]  Y. Shih,et al.  Quantum teleportation with a complete Bell state measurement , 2000, Physical Review Letters.

[69]  T. Wei,et al.  Beating the channel capacity limit for linear photonic superdense coding , 2008 .

[70]  Jian-Wei Pan,et al.  Experimental realization of entanglement concentration and a quantum repeater. , 2003, Physical review letters.

[71]  Christian Nölleke,et al.  A single-atom quantum memory , 2011, Nature.

[72]  Mang Feng,et al.  Experimental implementation of dense coding using nuclear magnetic resonance , 2000 .

[73]  A. Divochiy,et al.  High-performance superconducting photon-number-resolving detectors with 86% system efficiency at telecom range , 2019, Journal of the Optical Society of America B.

[74]  Debbie W. Leung,et al.  Classical capacity of a noiseless quantum channel assisted by noisy entanglement , 2001, Quantum Inf. Comput..

[75]  Jun Luo,et al.  NMR experimental implementation of three-parties quantum superdense coding , 2004 .

[76]  Jeffrey H. Shapiro,et al.  Defeating Active Eavesdropping with Quantum Illumination , 2009, 0904.2490.

[77]  J. Gordon,et al.  Quantum Effects in Communications Systems , 1962, Proceedings of the IRE.

[78]  Marco Lucamarini,et al.  Secure deterministic communication without entanglement. , 2005, Physical review letters.

[79]  C. Xie,et al.  Experimental demonstration of tripartite entanglement and controlled dense coding for continuous variables. , 2002, Physical review letters.

[80]  C. H. Bennett,et al.  Remote state preparation. , 2000, Physical review letters.

[81]  C. Caves,et al.  Quantum limits on bosonic communication rates , 1994 .

[82]  Yongmin Li,et al.  Efficient quantum memory for light , 2010, Nature.

[83]  N. Lutkenhaus,et al.  Intercept-resend attacks in the Bennett-Brassard 1984 quantum-key-distribution protocol with weak coherent pulses , 2004, quant-ph/0411041.

[84]  Qing-yu Cai,et al.  Improving the capacity of the Boström-Felbinger protocol , 2003, quant-ph/0311168.

[85]  Masashi Ban.  LETTER TO THE EDITOR: Quantum dense coding via a two-mode squeezed-vacuum state , 1999 .

[86]  W. Grice.  Arbitrarily complete Bell-state measurement using only linear optical elements , 2011 .

[87]  Manjin Zhong,et al.  Optically addressable nuclear spins in a solid with a six-hour coherence time , 2015, Nature.

[88]  YANFeng-Li,et al.  A Scheme for Dense Coding in the Non-Symmetric Quantum Channel , 2004 .

[89]  M. Plenio,et al.  Quantifying Entanglement , 1997, quant-ph/9702027.

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

[91]  D. Korystov,et al.  Quantum memory for squeezed light. , 2007, Physical review letters.

[92]  Albert Einstein,et al.  Can Quantum-Mechanical Description of Physical Reality Be Considered Complete? , 1935 .

[93]  Guang-Can Guo,et al.  Beating the channel capacity limit for superdense coding with entangled ququarts , 2018, Science Advances.

[94]  J Eisert,et al.  Assessing non-Markovian quantum dynamics. , 2007, Physical review letters.

[95]  Guang-Can Guo,et al.  Arbitrary two-particle high-dimensional Bell-state measurement by auxiliary entanglement , 2019, Physical Review A.

[96]  H. Haus,et al.  Preparation, measurement and information capacity of optical quantum states , 1986 .

[97]  Adetunmise C. Dada,et al.  Experimental high-dimensional two-photon entanglement and violations of generalized Bell inequalities , 2011, 1104.5087.

[98]  A. Zeilinger,et al.  Significant-Loophole-Free Test of Bell's Theorem with Entangled Photons. , 2015, Physical review letters.

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

[100]  Yu-Bo Sheng,et al.  Fault tolerant quantum key distribution based on quantum dense coding with collective noise , 2009, 0904.0056.

[101]  Paolo Mataloni,et al.  Experimental achievement of the entanglement-assisted capacity for the depolarizing channel , 2012, 1206.6881.

[102]  Hermann Kampermann,et al.  Optimal super dense coding over noisy quantum channels , 2010, 1004.5573.

[103]  P. Panigrahi,et al.  Perfect teleportation, quantum-state sharing, and superdense coding through a genuinely entangled five-qubit state , 2007, 0708.3785.

[104]  Guang-Can Guo,et al.  Probabilistic dense coding and teleportation , 2000 .

[105]  V. Vedral.  The role of relative entropy in quantum information theory , 2001, quant-ph/0102094.