Variational Estimation of Optimal Signal States for Quantum Channels

classical communication; Classical-quantum computing; quantum channels; variational algorithms; Channel's capacity; Classical communication; Classical-quantum; Optimal encoding; Quantum channel; Quantum communication systems; Quantum Computing; Variational algorithms; Software; Computer Science (miscellaneous); Condensed Matter Physics; Engineering (miscellaneous); Mechanical Engineering; Computer Science Applications; Electrical and Electronic Engineering

Abstract :

[en] This article explores the performance of quantum communication systems in the presence of noise and focuses on finding the optimal encoding for maximizing the classical communication rate, approaching the classical capacity in some scenarios. Instead of theoretically bounding the ultimate capacity of the channel, we adopt a signal processing perspective to estimate the achievable performance of a physically available but otherwise unknown quantum channel. By employing a variational algorithm to estimate the trace distance between quantum states, we numerically determine the optimal encoding protocol for the amplitude damping and Pauli channels. Our simulations demonstrate the convergence and accuracy of the method with a few iterations, confirming that optimal conditions for binary quantum communication systems can be variationally determined with minimal computation. Furthermore, since the channel knowledge is not required at the transmitter or at the receiver, these results can be employed in arbitrary quantum communication systems, including satellite-based communication systems, a particularly relevant platform for the quantum Internet.

Disciplines :

Electrical & electronics engineering

Author, co-author :

OLEYNIK, Leonardo ; University of Luxembourg > Interdisciplinary Centre for Security, Reliability and Trust (SNT) > SigCom

Rehman, Junaid Ur ; University of Luxembourg > Interdisciplinary Centre for Security, Reliability and Trust (SNT) > SigCom

AL-HRAISHAWI, Hayder

CHATZINOTAS, Symeon ; University of Luxembourg > Interdisciplinary Centre for Security, Reliability and Trust (SNT) > SigCom

External co-authors :

yes

Language :

English

Title :

Variational Estimation of Optimal Signal States for Quantum Channels

Publication date :

25 April 2025

Journal title :

IEEE Transactions on Quantum Engineering

eISSN :

2689-1808

Publisher :

Institute of Electrical and Electronics Engineers Inc.

Volume :

Pages :

1 - 8

Peer reviewed :

Peer Reviewed verified by ORBi

Additional URL :

http://xplorestaging.ieee.org/ielx7/8924785/10379182/10508490.pdf?arnumber=10508490

Available on ORBilu :

since 03 November 2024

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Bibliography

N. Gisin and R. Thew, "Quantum communication, " Nature Photon., vol. 1, no. 3, pp. 165-171, Mar. 2007, doi: 10.1038/nphoton.2007.22.
H. J. Kimble, "The quantum internet, " Nature, vol. 453, no. 7198, pp. 1023-1030, Jun. 2008, doi: 10.1038/nature07127.
S. Wehner, D. Elkouss, and R. Hanson, "Quantum internet: A vision for the road ahead, " Science, vol. 362, no. 6412, Sep. 2018, Art. no. eaam9288, doi: 10.1126/science.aam9288.
C. Simon, "Towards a global quantum network, " Nature Photon., vol. 11, no. 11, pp. 678-680, Nov. 2017, doi: 10.1038/s41566-017-0032-0.
N. Cerf, G. Leuchs, and E. Polzik, Quantum InformationWith Continuous Variables of Atoms and Light. London, U.K.: Imperial College Press, Feb. 2007, doi: 10.1142/p489.
M. S.Winnel, J. J. Guanzon, N. Hosseinidehaj, and T. C. Ralph, "Achieving the ultimate end-to-end rates of lossy quantum communication networks, " npj Quantum Inf., vol. 8, no. 1, Nov. 2022, Art. no. 129, doi: 10.1038/s41534-022-00641-0.
H. Al-Hraishawi, J. U. Rehman, M. Razavi, and S. Chatzinotas, "Characterizing and utilizing the interplay between quantum technologies and non-terrestrial networks, " IEEE Open J. Commun. Soc., vol. 5, pp. 1937-1957, 2024, doi: 10.1109/OJCOMS.2024.3380508.
D. F. Walls, "Squeezed states of light, " Nature, vol. 306, no. 5939, pp. 141-146, Nov. 1983, doi: 10.1038/306141a0.
G. Cariolaro andG. Pierobon, "Performance of quantum data transmission systems in the presence of thermal noise, " IEEE Trans. Commun., vol. 58, no. 2, pp. 623-630, Feb. 2010, doi: 10.1109/TCOMM.2010.02.080013.
G. Cariolaro and G. Pierobon, "Theory of quantum pulse position modulation and related numerical problems, " IEEE Trans. Commun., vol. 58, no. 4, pp. 1213-1222, Apr. 2010, doi: 10.1109/TCOMM.2010.04.090103.
R. L. Cook, P. J. Martin, and J. M. Geremia, "Optical coherent state discrimination using a closed-loop quantum measurement, " Nature, vol. 446, no. 7137, pp. 774-777, Apr. 2007, doi: 10.1038/nature05655.
V. Giovannetti, S. Lloyd, and L. Maccone, "Quantum metrology, " Phys. Rev. Lett., vol. 96, no. 1, Jan. 2006, Art. no. 010401, doi: 10.1103/Phys-RevLett.96.010401.
F. Benatti and D. Braun, "Sub-shot-noise sensitivities without entanglement, " Phys. Rev. A, vol. 87, no. 1, Jan. 2013, Art. no. 012340, doi: 10.1103/PhysRevA.87.012340.
M. L. Shcherbatenko, M. S. Elezov, G. N. Goltsman, and D.V. Sych, "Subshot-noise-limited fiber-optic quantum receiver, " Phys. Rev. A, vol. 101, no. 3, Mar. 2020, Art. no. 032306, doi: 10.1103/PhysRevA.101.032306.
A. Vázquez-Castro and B. Samandarov, "Quantum advantage of binary discrete modulations for space channels, " IEEE Wireless Commun. Lett., vol. 12, no. 5, pp. 903-906, May 2023, doi: 10.1109/LWC.2023.3249282.
M. Mohseni, A. T. Rezakhani, and D. A. Lidar, "Quantum-process tomography: Resource analysis of different strategies, " Phys. Rev. A, vol. 77, no. 3, Mar. 2008, Art. no. 032322, doi: 10.1103/PhysRevA.77.032322.
P. Horodecki and A. Ekert, "Method for direct detection of quantum entanglement, " Phys. Rev. Lett., vol. 89, no. 12, Aug. 2002, Art. no. 127902, doi: 10.1103/PhysRevLett.89.127902.
A. K. Ekert, C. M. Alves, D. K. L. Oi, M. Horodecki, P. Horodecki, and L. C. Kwek, "Direct estimations of linear and nonlinear functionals of a quantum state, " Phys. Rev. Lett., vol. 88, no. 21, May 2002, Art. no. 217901, doi: 10.1103/PhysRevLett.88.217901.
C. Macchiavello and M. F. Sacchi, "Detecting lower bounds to quantum channel capacities, " Phys. Rev. Lett., vol. 116, no. 14, Apr. 2016, Art. no. 140501, doi: 10.1103/PhysRevLett.116.140501.
J. U. Rehman, Y. Jeong, and H. Shin, "Directly estimating the Holevo capacity of discreteWeyl channels, "Phys. Rev. A, vol. 99, no. 4, Apr. 2019, Art. no. 042312, doi: 10.1103/PhysRevA.99.042312.
J. Bae and L.-C. Kwek, "Quantum state discrimination and its applications, " J. Phys. A: Math. Theor., vol. 48, no. 8, Jan. 2015, Art. no. 083001, doi: 10.1088/1751-8113/48/8/083001.
M. M.Wilde, Quantum Information Theory. Cambridge, U.K.: Cambridge Univ. Press, 2013, doi: 10.1017/CBO9781139525343.
R. Chen, Z. Song, X. Zhao, and X.Wang, "Variational quantum algorithms for trace distance and fidelity estimation, " Quantum Sci. Technol., vol. 7, no. 1, Dec. 2022, Art. no. 015019, doi: 10.1088/2058-9565/ac38ba.
R. LaRose, A. Tikku, É O'Neel-Judy, L. Cincio, and P. J. Coles, "Variational quantum state diagonalization, " npj Quantum Inf., vol. 5, no. 1, Jun. 2019, Art. no. 57, doi: 10.1038/s41534-019-0167-6.
M. Cerezo et al., "Variational quantum algorithms, " Nature Rev. Phys., vol. 3, no. 9, pp. 625-644, Sep. 2021, doi: 10.1038/s42254-021-00348-9.
H. Shin and M. Z. Win, "MIMO diversity in the presence of double scattering, " IEEE Trans. Inf. Theory, vol. 54, no. 7, pp. 2976-2996, Jul. 2008, doi: 10.1109/TIT.2008.924672.
J. U. Rehman and H. Shin, "Simultaneous communication and parameter estimation of Pauli channels, " in Proc. IEEE/CVF Int. Conf. Comput. Vis., 2022, pp. 648-653, doi: 10.1109/ICC45855.2022.9838702.
M. A. Nielsen and I. L. Chuang, Quantum Computation and Quantum Information: 10th Anniversary Edition. Cambridge, U.K.: Cambridge Univ. Press, 2010, doi: 10.1017/CBO9780511976667.
C. W. Helstrom, "Quantum detection and estimation theory, " J. Statist. Phys., vol. 1, no. 2, pp. 231-252, Jun. 1969, doi: 10.1007/BF01007479.
H. Yuen, R. Kennedy, and M. Lax, "Optimum testing of multiple hypotheses in quantum detection theory, " IEEE Trans. Inf. Theory, vol. IT-21, no. 2, pp. 125-134, Mar. 1975, doi: 10.1109/TIT.1975.1055351.
D.W. Berry, "Qubit channels that achieve capacity with two states, " Phys. Rev. A, vol. 71, no. 3, Mar. 2005, Art. no. 032334, doi: 10.1103/Phys-RevA.71.032334.
A. Kandala et al., "Hardware-efficient variational quantum eigensolver for small molecules and quantum magnets, " Nature, vol. 549, no. 7671, pp. 242-246, Sep. 2017, doi: 10.1038/nature23879.
B. Commeau, M. Cerezo, Z. Holmes, L. Cincio, P. Coles, and A. Sornborger, "Variational Hamiltonian diagonalization for dynamical quantum simulation, " 2020, arXiv:2009.02559, doi: 10.48550/arXiv.2009.02559.
K. Siudzińska, "Classical capacity of generalized Pauli channels, " J. Phys. A: Math. Theor., vol. 53, no. 44, Oct. 2020, Art. no. 445301, doi: 10.1088/1751-8121/abb276.