Abstract

This tutorial reviews the Holevo capacity limit as a universal tool to analyze the ultimate transmission rates in a variety of optical communication scenarios, ranging from conventional optically amplified fiber links to free-space communication with power-limited optical signals. The canonical additive white Gaussian noise model is used to describe the propagation of the optical signal. The Holevo limit exceeds substantially the standard Shannon limit when the power spectral density of noise acquired in the course of propagation is small compared to the energy of a single photon at the carrier frequency per unit time-bandwidth area. General results are illustrated with a discussion of efficient communication strategies in the photon-starved regime.

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2019 (2)

D. Ding, D. S. Pavlichin, and M. M. Wilde, “Quantum channel capacities per unit cost,” IEEE Trans. Inf. Theory, vol. 65, no. 1, pp. 418–435,  2019.

M. T. DiMario, L. Kunz, K. Banaszek, and F. E. Becerra, “Optimized communication strategies with binary coherent states over phase noise channels,” npj Quantum Inf., vol. 5, no. 1, 2019, Art. no. .

2018 (4)

I. A. Burenkov, O. V. Tikhonova, and S. V. Polyakov, “Quantum receiver for large alphabet communication,” Optica, vol. 5, no. 3, pp. 227–232, 2018.

L. Kunz, M. G. A. Paris, and K. Banaszek, “Noisy propagation of coherent states in a lossy kerr medium,” J. Opt. Soc. America B, vol. 35, no. 2, 2018, Art. no. .

W. Zwoliński, M. Jarzyna, and K. Banaszek, “Range dependence of an optical pulse position modulation link in the presence of background noise,” Opt. Express, vol. 26, no. 20, pp. 25 827–25 838, 2018.

D. V. Reddy and M. G. Raymer, “High-selectivity quantum pulse gating of photonic temporal modes using all-optical Ramsey interferometry,” Optica, vol. 5, no. 4, pp. 423–428, 2018.

2017 (4)

M. Allgaier, “Highly efficient frequency conversion with bandwidth compression of quantum light,” Nature Commun., vol. 8, no. 1, 2017, Art. no. .

A. Shahverdi, Y. M. Sua, L. Tumeh, and Y.-P. Huang, “Quantum parametric mode sorting: Beating the time-frequency filtering,” Sci. Rep., vol. 7, no. 1, 2017, Art. no. .

K. Günthner, “Quantum-limited measurements of optical signals from a geostationary satellite,” Opt., vol. 4, no. 6, pp. 611–616,  2017.

M. Jarzyna, “Classical capacity per unit cost for quantum channels,” Phys. Rev. A, vol. 96, no. 3, 2017, Art. no. .

2016 (5)

P. Bayvel, “Maximizing the optical network capacity,” Philos. Trans. Roy. Soc. A: Math., Phys. Eng. Sci., vol. 374, no. 2062, 2016, Art. no. .

K. Kikuchi, “Fundamentals of coherent optical fiber communications,” J. Lightw. Technol., vol. 34, no. 1, pp. 157–179,  2016.

H. W. Chung, S. Guha, and L. Zheng, “Superadditivity of quantum channel coding rate with finite blocklength joint measurements,” IEEE Trans. Inf. Theor., vol. 62, no. 10, pp. 5938–5959,  2016.

A. Klimek, M. Jachura, W. Wasilewski, and K. Banaszek, “Quantum memory receiver for superadditive communication using binary coherent states,” J. Mod. Opt., vol. 63, no. 20, pp. 2074–2080, 2016.

M. Rosati, A. Mari, and V. Giovannetti, “Multiphase Hadamard receivers for classical communication on lossy bosonic channels,” Phys. Rev. A, vol. 94, no. 6, 2016, Art. no. .

2015 (3)

M. Jarzyna, P. Kuszaj, and K. Banaszek, “Incoherent on-off keying with classical and non-classical light,” Opt. Express, vol. 23, no. 3, pp. 3170–3175, 2015.

B. Brecht, D. V. Reddy, C. Silberhorn, and M. G. Raymer, “Photon temporal modes: A complete framework for quantum information science,” Phys. Rev. X, vol. 5, no. 4, 2015, Art. no. .

J. Trapani, B. Teklu, S. Olivares, and M. G. A. Paris, “Quantum phase communication channels in the presence of static and dynamical phase diffusion,” Phys. Rev. A, vol. 92, no. 1, 2015, Art. no. .

2014 (4)

Y. Kochman, L. Wang, and G. W. Wornell, “Toward photon-efficient key distribution over optical channels,” IEEE Trans. Inf. Theory, vol. 60, no. 8, pp. 4958–4972,  2014.

M. Takeoka and S. Guha, “Capacity of optical communication in loss and noise with general quantum Gaussian receivers,” Phys. Rev. A, vol. 89, 2014, Art. no. .

C. Antonelli, A. Mecozzi, M. Shtaif, and P. J. Winzer, “Quantum limits on the energy consumption of optical transmission systems,” J. Lightw. Technol., vol. 32, no. 10, pp. 1853–1860,  2014.

V. Giovannetti, R. García-Patrón, N. J. Cerf, and A. S. Holevo, “Ultimate classical communication rates of quantum optical channels,” Nature Photon., vol. 8, pp. 796–800, 2014.

2013 (2)

F. E. Becerra, J. Fan, G. Baumgartner, J. Goldhar, J. T. Kosloski, and A. Migdall, “Experimental demonstration of a receiver beating the standard quantum limit for multiple nonorthogonal state discrimination,” Nat. Photon., vol. 7, pp. 147–152, 2013.

M. Cooper, L. J. Wright, C. Söller, and B. J. Smith, “Experimental generation of multi-photon Fock states,” Opt. Express, vol. 21, no. 5, 2013, Art. no. .

2012 (6)

P. Jouguet, S. Kunz-Jacques, E. Diamanti, and A. Leverrier, “Analysis of imperfections in practical continuous-variable quantum key distribution,” Phys. Rev. A, vol. 86, no. 3, 2012, Art. no. .

C. R. Müller, “Quadrature phase shift keying coherent state discrimination via a hybrid receiver,” New J. Phys., vol. 14, no. 8, 2012, Art. no. .

J. Chen, J. L. Habif, Z. Dutton, R. Lazarus, and S. Guha, “Optical codeword demodulation with error rates below the standard quantum limit using a conditional nulling receiver,” Nat. Photon., vol. 6, pp. 374–379, 2012.

P. J. Winzer, “High-spectral-efficiency optical modulation formats,” J. Lightw. Technol., vol. 30, no. 24, pp. 3824–3835,  2012.

R. García-Patrón, C. Navarrete-Benlloch, S. Lloyd, J. H. Shapiro, and N. J. Cerf, “Majorization theory approach to the gaussian channel minimum entropy conjecture,” Phys. Rev. Lett., vol. 108, no. 11, 2012, Art. no. .

A. Mecozzi and R.-J. Essiambre, “Nonlinear Shannon limit in pseudolinear coherent systems,” J. Lightw. Technol., vol. 30, no. 12, pp. 2011–2024,  2012.

2011 (2)

A. Waseda, M. Sasaki, M. Takeoka, M. Fujiwara, M. Toyoshima, and A. Assalini, “Numerical evaluation of PPM for deep-space links,” J. Opt. Commun. Netw., vol. 3, no. 6, pp. 514–521, 2011.

S. Guha, “Structured optical receivers to attain superadditive capacity and the Holevo limit,” Phys. Rev. Lett., vol. 106, no. 24, 2011, Art. no. .

2010 (1)

R.-J. Essiambre, G. Kramer, P. J. Winzer, G. J. Foschini, and B. Goebel, “Capacity limits of optical fiber networks,” J. Lightw. Technol., vol. 28, no. 4, pp. 662–701,  2010.

2009 (1)

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