Abstract
This paper deals with the modeling of an optimum quantum receiver for pulse amplitude modulator (PAM) communication systems. The information bearing sequence \(\{I_k\}_{k=0}^{N-1}\) is estimated using the maximum likelihood (ML) method. The ML method is based on quantum mechanical measurements of an observable X in the Hilbert space of the quantum system at discrete times, when the Hamiltonian of the system is perturbed by an operator obtained by modulating a potential V with a PAM signal derived from the information bearing sequence \(\{I_k\}_{k=0}^{N-1}\). The measurement process at each time instant causes collapse of the system state to an observable eigenstate. All probabilities of getting different outcomes from an observable are calculated using the perturbed evolution operator combined with the collapse postulate. For given probability densities, calculation of the mean square error evaluates the performance of the receiver. Finally, we present an example involving estimating an information bearing sequence that modulates a quantum electromagnetic field incident on a quantum harmonic oscillator.
![](http://media.springernature.com/m312/springer-static/image/art%3A10.1007%2Fs11128-017-1660-5/MediaObjects/11128_2017_1660_Fig1_HTML.gif)
Similar content being viewed by others
Explore related subjects
Discover the latest articles, news and stories from top researchers in related subjects.References
Shapiro, J.H., Zhang, Z., Wong, F.N.C.: Secure communication via quantum illumination. Quantum Inf. Process. 13(10), 2171–2193 (2014)
Dirac, P.A.M.: The Principles of Quantum Mechanics, 4th edn. Oxford University Press, New York (1958)
Schrödinger, E.: An undulatory theory of the mechanics of atoms and molecules. Phys. Rev. 28, 1049 (1926)
Griffiths, D.J.: Introduction to Quantum Mechanics, 2nd edn. Pearson Hall, Oxford (2005)
Christopher, A.F., Carlton, M.C.: Mathematical techniques for quantum communication theory. Open Syst. Inf. Dyn. 3(3), 345–356 (1995)
Von Neumann, J.: Mathematical Foundations of Quantum Mechanics. Princeton University Press, Princeton (1955)
Helstrom, C.W.: Detection theory and quantum mechanics. Inf. Control 10, 254–291 (1967)
Helstrom, C.W.: Detection theory and quantum mechanics (II). Inf. Control 13, 156–171 (1968)
Yuen, H.P., Kennedy, R.S., Lax, M.: On optimal quantum receivers for digital signal detection. Proc. IEEE. 58(10), 1770–1773 (1970)
Li, K., Zuo, Y., Zhu, B.: Suppressing the errors due to mode mismatch for M-ary PSK quantum receivers using photon-number-resolving detector. IEEE Photon. Technol. Lett. 25(22), 2182–2184 (2013)
Shi, J., Shi, R., Guo, Y., Peng, X., Lee, M.H.: Probabilistic quantum relay communication in the noisy channel with analogous space–time code. Quantum Inf. Process. 12, 1859–1870 (2013)
Kato, K., Hirota, O.: Square-root measurement for quantum symmetric mixed state signals. IEEE Trans. Inf. Theory 49(12), 3312–3317 (2003)
Atmanspacher, H., Kurths, J., Scheingraber, H., Wackerbauer, R., Witt, A.: Complexity and meaning in nonlinear dynamical systems. Open Syst. Inf. Dyn. 1(2), 269–289 (1992)
Holevo, A.S.: Statistical decision theory for quantum systems. J. Multivar. Anal. 3, 337–394 (1973)
Yuen, H.P., Kennedy, R.S., Lax, M.: Optimum testing of multiple hypotheses in quantum detection theory. IEEE Trans. Inf. Theory 21(2), 125–134 (1975)
Helstrom, C.W.: Bayes-cost reduction algorithm in quantum hypothesis testing. IEEE Trans. Inf. Theory 28(2), 359–366 (1982)
Kennedy, R.S.: A near-optimum receiver for the binary coherent state quantum channel. Research Laboratory of Electronics MIT Cambridge Technical Report 108 (1973)
Dolinar, S.J.: An optimum receiver for the binary coherent state quantum channel. Research Laboratory of Electronics MIT Cambridge Technical Report 111 (1973)
Sasaki, M., Hirota, O.: Optimum decision scheme with a unitary control process for binary quantum-state signals. Phys. Rev. A 54, 2728 (1996)
Wang, D., Huang, A.J., Sun, W.Y., Shi, J.D., Ye, L.: Practicle single-photon-assisted remote state preparation with non-maximally entenglement. Quantum Inf. Process. 15, 3367–3381 (2016)
Wang, D., Hu, Y.D., Wang, Z.Q., Ye, L.: Efficient and faithful remote preparation of arbitrary three-and four-particle W-class entangled states. Quantum Inf. Process. 14(6), 2135–2151 (2015)
Lo, H.K.: Classical-communication cost in distributed quantum-information processing: a generalization of quantum-communication complexity. Phys. Rev. A 62, 012313 (2000)
Wang, D., Hoen, R.D., Ye, L., Kais, S.: Generalized remote preparation of arbitrary \(m\)-qubit entagled states via genuine entanglements. Entropy 17, 1755–1774 (2015)
Li, X., Ghose, S.: Optimal joint remote state preparation of equatorial states. Quantum Inf. Process. 14(12), 4585–4592 (2015)
Huelga, S.F., Vaccaro, J.A., Chefles, A., Plenio, M.B.: Quantum remote control: teleportation of unitary operations. Phys. Rev. A 63(4), 042303 (2001)
Bennett, C.H., Brassard, G., Popescu, S., Schumacher, B., Smolin, J.A., Wootters, W.K.: Purification of noisy entanglement and faithful teleportation via noisy channels. Phys. Rev. Lett. 76(5), 722 (1996)
Bennett, C.H., DiVincenzo, D.P., Shor, P.W., Smolin, J.A., Terhal, B.M., Wootters, W.K.: Remote state preparation. Phys. Rev. Lett. 87(7), 077902 (2001)
Feng, G., Xu, G., Long, G.: Experimental realization of nonadiabatic holonomic quantum computation. Phys. Rev. Lett. 110(19), 190501 (2013)
Ren, B.C., Du, F.F., Deng, F.G.: Hyperentanglement concentration for two-photon four-qubit systems with linear optics. Phys. Rev. A 88(1), 012302 (2013)
Li, T., Long, G.L.: Hyperparallel optical quantum computation assisted by atomic ensembles embedded in double-sided optical cavities. Phys. Rev. A 94(2), 022343 (2016)
Liu, X.S., Long, G.L., Tong, D.M., Li, F.: General scheme for superdense coding between multiparties. Phys. Rev. A 65(2), 022304 (2002)
Ekert, A.K.: Quantum cryptography based on Bells theorem. Phys. Rev. Lett. 67(6), 661 (1991)
Long, G.L., Xiao, L.: Parallel quantum computing in a single ensemble quantum computer. Phys. Rev. A 69(5), 052303 (2004)
Bennett, C.H., DiVincenzo, D.P., Smolin, J.A., Wootters, W.K.: Mixed-state entanglement and quantum error correction. Phys. Rev. A 54(5), 3824 (1996)
Wang, C., Deng, F.G., Li, Y.S., Liu, X.S., Long, G.L.: Quantum secure direct communication with high-dimension quantum superdense coding. Phys. Rev. A 71(4), 044305 (2005)
Yu, R.F., Lin, Y.J., Zhou, P.: Joint remote preparation of arbitrary two-and three-photon state with linear-optical elements. Quantum Inf. Process. 15(11), 4785–4803 (2016)
Bennett, C.H., Brassard, G., Mermin, N.D.: Quantum cryptography without Bells theorem. Phys. Rev. Lett. 68(5), 557 (1992)
Wei, H.R., Deng, F.G.: Universal quantum gates for hybrid systems assisted by quantum dots inside double-sided optical microcavities. Phys. Rev. A 87(2), 022305 (2013)
Hayashi, M.: Universal coding for classical-quantum channel. Commun. Math. Phys. 289, 1087–1098 (2009)
Nielsen, M.A., Chuang, I.L.: Quantum Computation and Quantum Information, pp. 171–286. Cambridge University Press, Cambridge (2001)
Parthasarathy, K.R.: Coding Theorems of Classical and Quantum Information Theory. Hindustan Book Agency, Gurugram (2013)
Dowker, F., Tabatabai, Y.G.: Dynamical wavefunction collapse models in quantum measure theory. J. Phys. A Math. Theor. 41(20), 205306 (2008)
Rathee, A., Parthasarathy, H.: Perturbation-based stochastic modeling of nonlinear circuits. Circuits Syst. Signal Process. 32, 123–142 (2013)
Mensky, M., Audretsch, J.: Continuous QND measurements: no quantum noise. J. Appl. Phys. B 64(2), 129–136 (1997)
Srikanth, R.: A computational model for quantum measurement. Quantum Inf. Process. 2(3), 153–199 (2003)
Brickmont, J., Kupiainen, A.: Towards a derivation of Fouriers law for coupled anharmonic oscillators. Commun. Math. Phys. 274, 555–626 (2007)
Gautam, K., Chauhan, G., Rawat, T.K., Parthasarathy, H., Sharma, N.: Realization of quantum gates based on three-dimensional harmonic oscillator in a time-varying electromagnetic field. Quantum Inf. Process. 14(9), 3279–3302 (2015)
Gautam, K., Rawat, T.K., Parthasarathy, H., Sharma, N.: Realization of commonly used quantum gates using perturbed harmonic oscillator. Quantum Inf. Process. 14(9), 3257–3277 (2015)
Gisin, N., Popescu, S., Scarani, V., Wolf, S., Wullschleger, J.: Oblivious transfer and quantum channels as communication resources. Nat. Comput. 12(1), 13–17 (2013)
Karlsson, A., Björk, G.: Quantum correlations in dual quantum measurements. J. Appl. Phys. B 64(2), 235–241 (1997)
Garg, N., Parthasarathy, H., Upadhyay, D.K.: Real-time simulation of H–P noisy Schrödinger equation and Belavkin filter. Quantum Inf. Process. (2017). doi:10.1007/s11128-017-1572-4
Gautam, K., Rawat, T.K., Parthasarathy, H., Sharma, N., Upadhyaya, V.: Realization of the three-qubit quantum controlled gate based on matching Hermitian generators. Quantum Inf. Process. 16(5), 113 (2017)
Acknowledgements
The author is deeply indebted to Professors Harish Parthasarathy and Dr. Tarun Kumar Rawat for offering invaluable comments and suggestions. He is very grateful to Kumar Gautam for stimulating discussions and invaluable suggestions.
Author information
Authors and Affiliations
Corresponding author
Rights and permissions
About this article
Cite this article
Sharma, N., Rawat, T.K., Parthasarathy, H. et al. Optimum quantum receiver for detecting weak signals in PAM communication systems. Quantum Inf Process 16, 208 (2017). https://doi.org/10.1007/s11128-017-1660-5
Received:
Accepted:
Published:
DOI: https://doi.org/10.1007/s11128-017-1660-5