Current Science

Open Access Open Access  Restricted Access Subscription Access

Arthurs-Kelly Joint Measurements and Applications


Affiliations
1 Homi Bhabha Centre for Science Education, Tata Institute of Fundamental Research, Mumbai 400 088, India
 

Originally devised as an extension of von Neumann measurement Hamiltonian to joint measurement of conjugate variables, the Arthurs-Kelly Hamiltonian has been found to have many other practical applications. I summarize in particular, experimental bounds on von Neumann entropy, noiseless quantum tracking of conjugate observables, remote tomography, entanlement swapping and exact measurement of correlation between conjugate observables.

Keywords

Conjugate Variables, Joint Measurements, Quantum Tracking, Remote Tomography, Teleportation.
User
Notifications
Font Size

  • von Neumann, J., Mathematical Foundations of Quantum Mechanics, Princeton University Press, 1955.

  • Arthurs, E. and Kelly Jr, J. L., On the simultaneous measurement of a pair of conjugate observables. Bell System Tech. J., 1965, 44(4), 725–729; Husimi, K., Some formal properties of the density matrix. Proc. Phys. Math. Soc. Jpn, 1940, 22(4), 264–314; Braunstein, S. L., Caves, C. M. and Milburn, G. J., Interpretation for a positive P representation. Phys. Rev. A, 1991, 43(3), 1153–1159; Busch, P., Heinonen, T. and Lahti, P., Heisenhberg’s uncertainty principle. Phys. Rep., 2007, 452(6), 155–176.

  • Stenholm, S., Simultaneous measurement of conjugate variables. Ann. Phys., 1992, 218(2), 233–254.

  • Arthurs, E. and Goodman, M. S., Quantum correlations: A generalized Heisenberg uncertainty relation. Phys. Rev. Lett., 1988, 60(24), 2447–2449; Stulpe, W., Gudder, S. and Hagler, J., An uncertainty relation for joint position–momentum measurements. Found. Phys. Lett., 1988, 1(3), 287–292.

  • Wehrl, A., General properties of entropy. Rev. Mod. Phys., 1978, 50(2), 221–260.

  • Roy, S. M. and Singh, V., Generalized coherent states and the uncertainty principle. Phys. Rev. D, 1982, 25(12), 3413–3416; Senitzky, I. R., Harmonic oscillator wave functions. Phys. Rev., 1954, 95(5), 1115–1116.

  • Roy, S. M., Deshpande, A. and Sakharwade, N., Remote tomography and entanglement swapping via von Neumann–Arthurs–Kelly interaction. Phys. Rev. A, 2014, 89(5), 052107-1 to 5.

  • Bennett, C. H., Brassard, G., Crépeau, C., Jozsa, R., Peres, A. and Wootters, W. K., Teleporting an unknown quantum state via dual classical and Einstein–Podolsky–Rosen channels. Phys. Rev. Lett., 1993, 70(13), 1895–1899.

  • Vaidman, L., Teleportation of quantum states. Phys. Rev. A, 1994, 49(2), 1473–1476.

  • Bouwmeester, D., Pan, J.-W., Mattle, K., Eibl, M., Weinfurter, H. and Zeilinger, A., Experimental quantum teleportation. Nature, 1997, 390(6660), 575–579; Furusawa, A., Sørensen, J. L., Braunstein, S. L., Fuchs, C. A., Kimble, H. J. and Polzik, E. S., Unconditional quantum teleportation. Science, 1998, 282(5389), 706–709.

  • Braunstein, S. L. and van Loock, P., Quantum information with continuous variables. Rev. Mod. Phys., 2005, 77(2), 513–577; Pirandola, S., Mancini, S., Lloyd, S. and Braunstein, S. L., Continuous-variable quantum cryptography using two-way quantum communication. Nature Phys., 2008, 4(9), 726–730; Brassard, G., Braunstein, S. L. and Cleve, R., Teleportation as a quantum computation. Physica D, 1998, 120(1–2), 43–47.

  • Vogel, K. and Risken, H., Determination of quasiprobability distributions in terms of probability distributions for the rotated quadrature phase. Phys. Rev. A, 1989, 40(5), 2847–2849.

  • Braunstein, S. L., Homodyne statistics. Phys. Rev. A, 1990, 42(1), 474–481; Smithey, D. T., Beck, M., Raymer, M. G. and Faridani, A., Measurement of the Wigner distribution and the density matrix of a light mode using optical homodyne tomography: application to squeezed states and the vacuum. Phys. Rev. Lett., 1993, 70(9), 1244–1247; Leonhardt, U. and Paul, H., Measuring the quantum state of light. Prog. Quant. Electron., 1995, 19(2), 89–130.

  • Yuen, H. P. and Shapiro, J. H., Optical communication with twophoton coherent states – Part I: Quantum-state propagation and quantum-noise reduction. IEEE Trans. Inf. Theory, 1978, 24(6), 657–668; Optical communication with two-photon coherent states – Part II: Photoemissive detection and structured receiver performance. IEEE Trans. Inf. Theory, 1979, 25(2), 179–192; Optical communication with two-photon coherent states – Part III: Quantum measurements realizable with photoemissive detectors. IEEE Trans. Inf. Theory, 1980, 26(1), 78–92.

  • Roy, S. M. and Braunstein, S. L., Exponentially enhanced quantum metrology. Phys. Rev. Lett., 2008, 100(22), 220501-1 to 4; Boixo, S., Flammia, S. T., Caves, C. M. and Geremia, J. M., Generalized limits for single-parameter quantum estimation. Phys. Rev. Lett., 2007, 98(9), 090401-1 to 4; Napolitano, M., Koschorreck M., Dubost, B., Behbood, N., Sewell, R. J. and Mitchell, M. W., Interaction-based quantum metrology showing scaling beyond the Heisenberg limit. Nature, 2011, 471(7339), 486–489.

  • Roy, S. M., Exact quantum correlations of conjugate variables from joint quadrature measurements. Phys. Lett. A, 2013, 377(34– 36), 2011–2015.

  • Di Lorenzo, A., Correlations between detectors allow violation of the Heisenberg noise–disturbance principle for position and momentum measurements. Phys. Rev. Lett., 2013, 110(12), 120403-1 to 5.

  • Bullock, T. J. and Busch, P., Focusing in Arthurs–Kelly-type joint measurements with correlated probes. Phys. Rev. Lett., 2014, 113(12), 120401-1 to 5.


Abstract Views: 448

PDF Views: 113




  • Arthurs-Kelly Joint Measurements and Applications

Abstract Views: 448  |  PDF Views: 113

Authors

S. M. Roy
Homi Bhabha Centre for Science Education, Tata Institute of Fundamental Research, Mumbai 400 088, India

Abstract


Originally devised as an extension of von Neumann measurement Hamiltonian to joint measurement of conjugate variables, the Arthurs-Kelly Hamiltonian has been found to have many other practical applications. I summarize in particular, experimental bounds on von Neumann entropy, noiseless quantum tracking of conjugate observables, remote tomography, entanlement swapping and exact measurement of correlation between conjugate observables.

Keywords


Conjugate Variables, Joint Measurements, Quantum Tracking, Remote Tomography, Teleportation.

References





DOI: https://doi.org/10.18520/cs%2Fv109%2Fi11%2F2029-2038