Coherent versus measurement feedback: Linear systems theory for quantum information

Physical Review X

Volumn 4, Issue 4, 2014, Pages

  Yamamoto, Naoki ^a  

^a KEIO UNIVERSITY   (Japan)

Author keywords

Optics; Quantum information; Quantum physics

Indexed keywords

FEEDBACK CONTROL; LINEAR SYSTEMS; OPTICS; QUANTUM ELECTRONICS; QUANTUM OPTICS; QUANTUM THEORY;

CONTROLLABILITY AND OBSERVABILITIES; DECOHERENCE-FREE SUBSYSTEMS; LINEAR QUANTUM SYSTEMS; MEASUREMENT FEEDBACK; QUANTUM INFORMATION; QUANTUM INFORMATION SCIENCE; QUANTUM PHYSICS; STANDARD DEFINITIONS;

OBSERVABILITY;

EID: 84921530582     PISSN: None     EISSN: 21603308     Source Type: Journal    
DOI: 10.1103/PhysRevX.4.041029     Document Type: Article

References (81)

1. H. M. Wiseman and G. J. Milburn, Quantum Measurement and Control (Cambridge University Press, Cambridge, England, 2010).
2. A. Barchielli and M. Gregoratti, Quantum Trajectories and Measurements in Continuous Time: The Diffusive Case, Lecture Notes in Physics Vol. 782 (Springer, Berlin, 2009).
3. L. Bouten, R. van Handel, and M. R. James, A Discrete Invitation to Quantum Filtering and Feedback Control, SIAM Rev. 51, 239 (2009).
4. V. P. Belavkin, Quantum Stochastic Calculus and Quantum Nonlinear Filtering, J. Multivariate Anal. 42, 171 (1992).
5. V. P. Belavkin, Quantum Diffusion, Measurement and Filtering I, Theory Probab. Appl. 38, 573 (1993).
6. L. Bouten, R. van Handel, and M. R. James, An Introduction to Quantum Filtering, SIAM J. Control Optim. 46, 2199 (2007).
7. T. Kailath, Linear Systems (Prentice-Hall, Englewood Cliffs, NJ, 1980).
8. W. M. Wonham, Linear Multivariable Control: A Geometric Approach, 3rd ed. (Springer-Verlag, Berlin, 1985).
9. K. Zhou and J. C. Doyle, Essentials of Robust Control (Prentice-Hall, Englewood Cliffs, NJ, 1997).
10. A. C. Doherty and K. Jacobs, Feedback Control of Quantum Systems Using Continuous State Estimation, Phys. Rev. A 60, 2700 (1999).
11. A. Hopkins, K. Jacobs, S. Habib, and K. Schwab, Feedback Cooling of a Nanomechanical Resonator, Phys. Rev. B 68, 235328 (2003).
12. R. Hamerly and H. Mabuchi, Advantages of Coherent Feedback for Cooling Quantum Oscillators, Phys. Rev. Lett. 109, 173602 (2012).
13. R. Hamerly and H. Mabuchi, Coherent controllers for optical-feedback cooling of quantum oscillators, Phys. Rev. A 87, 013815 (2013).
14. C. Ahn, A. C. Doherty, and A. J. Landahl, Continuous Quantum Error Correction via Quantum Feedback Control, Phys. Rev. A 65, 042301 (2002).
15. H. Mabuchi, Continuous Quantum Error Correction as Classical Hybrid Control, New J. Phys. 11, 105044 (2009).
16. G. Tajimi and N. Yamamoto, Dynamical Gaussian State Transfer with Quantum Error Correcting Architecture, Phys. Rev. A 85, 022303 (2012).
17. C. Sayrin et al., Real-Time Quantum Feedback Prepares and Stabilizes Photon Number States, Nature (London) 477, 73 (2011).
18. R. Vijay, C. Macklin, D. H. Slichter, S. J. Weber, K.W. Murch, R. Naik, A. N. Korotkov, and I. Siddiqi, Stabilizing Rabi Oscillations in a Superconducting Qubit Using Quantum Feedback, Nature (London) 490, 77 (2012).
19. S. Shankar, M. Hatridge, Z. Leghtas, K. M. Sliwa, A. Narla, U. Vool, S. M. Girvin, L. Frunzio, M. Mirrahimi, and M. H. Devoret, Autonomously Stabilized Entanglement between Two Superconducting Quantum Bits, Nature (London) 504, 419 (2013).
20. R. Inoue, S.-I.-R. Tanaka, R. Namiki, T. Sagawa, and Y. Takahashi, Unconditional Quantum-Noise Suppression via Measurement-Based Quantum Feedback, Phys. Rev. Lett. 110, 163602 (2013).
21. H. M. Wiseman and G. J. Milburn, All-Optical versus Electro-optical Quantum-Limited Feedback, Phys. Rev. A 49, 4110 (1994).
22. M. R. James, H. I. Nurdin, and I. R. Petersen, H8 Control of Linear Quantum Stochastic Systems, IEEE Trans. Autom. Control 53, 1787 (2008).
23. J. E. Gough and M. R. James, The Series Product and Its Application to Quantum Feedforward and Feedback Networks, IEEE Trans. Autom. Control 54, 2530 (2009).
24. H. I. Nurdin, M. R. James, and A. C. Doherty, Network Synthesis of Linear Dynamical Quantum Stochastic Systems, SIAM J. Control Optim. 48, 2686 (2009).
25. J. E. Gough, M. R. James, and H. I. Nurdin, Squeezing Components in Linear Quantum Feedback Networks, Phys. Rev. A 81, 023804 (2010).
26. M. Yanagisawa and H. Kimura, Transfer Function Approach to Quantum Control-;Part I: Dynamics of Quantum Feedback Systems, IEEE Trans. Autom. Control 48, 2107 (2003).
27. J. E. Gough and S. Wildfeuer, Enhancement of Field Squeezing Using Coherent Feedback, Phys. Rev. A 80, 042107 (2009).
28. J. Kerckhoff, H. I. Nurdin, D. S. Pavlichin, and H. Mabuchi, Designing Quantum Memories with Embedded Control: Photonic Circuits for Autonomous Quantum Error Correction, Phys. Rev. Lett. 105, 040502 (2010).
29. H. Mabuchi, Coherent-Feedback Control Strategy to Suppress Spontaneous Switching in Ultra-low Power Optical Bistability, Appl. Phys. Lett. 98, 193109 (2011).
30. H. Mabuchi, Coherent-Feedback Quantum Control with a Dynamic Compensator, Phys. Rev. A 78, 032323 (2008).
31. S. Iida, M. Yukawa, H. Yonezawa, N. Yamamoto, and A. Furusawa, Experimental Demonstration of Coherent Feedback Control on Optical Field Squeezing, IEEE Trans. Autom. Control 57, 2045 (2012).
32. O. Crisafulli, N. Tezak, D. B. S. Soh, M. A. Armen, and H. Mabuchi, Squeezed Light in an Optical Parametric Oscillator Network with Coherent Feedback Quantum Control, Opt. Express 21, 18371 (2013).
33. J. Kerckhoff, R.W. Andrews, H. S. Ku, W. F. Kindel, K. Cicak, R.W. Simmonds, and K.W. Lehnert, Tunable Coupling to a Mechanical Oscillator Circuit Using a Coherent Feedback Network, Phys. Rev. X 3, 021013 (2013).
34. H. I. Nurdin, M. R. James, and I. R. Petersen, Coherent Quantum LQG Control, Automatica 45, 1837 (2009).
35. K. Jacobs, X. Wang, and H. M. Wiseman, Coherent Feedback That Beats All Measurement-Based Feedback Protocols, New J. Phys. 16, 073036 (2014).
36. C.W. Gardiner and P. Zoller, Quantum Noise (Springer, Berlin, 2000).
37. D. F. Walls and G. J. Milburn, Quantum Optics, 2nd ed. (Springer, Berlin, 2008).
38. V. B. Braginsky and F. Y. Khalili, Quantum Measurement (Cambridge University Press, Cambridge, England, 1992).
39. C. M. Caves, K. S. Thorne, R.W. P. Drever, V. D. Sandberg, and M. Zimmermann, On the Measurement of a Weak Classical Force Coupled to a Quantum-Mechanical Oscillator. I. Issues of Principle, Rev. Mod. Phys. 52, 341 (1980).
40. V. B. Braginsky, Y. I. Vorontsov, and K. S. Thorne, Quantum Nondemolition Measurements, Science 209, 547 (1980).
41. P. Zanardi and M. Rasetti, Noiseless Quantum Codes, Phys. Rev. Lett. 79, 3306 (1997).
42. D. A. Lidar and K. B. Whaley, in Irreversible Quantum Dynamics, edited by F. Benatti and R. Floreanini, Lecture Notes in Physics Vol. 622 (Springer, Berlin, 2003), p. 83.
43. J. M. Courty, A. Heidmann, and M. Pinard, Back-action Cancellation in Interferometers by Quantum Locking, Europhys. Lett. 63, 226 (2003).
44. J. M. Courty, A. Heidmann, and M. Pinard, Quantum Locking of Mirrors in Interferometers, Phys. Rev. Lett. 90, 083601 (2003).
45. D. Vitali, M. Punturo, S. Mancini, P. Amico, and P. Tombesi, Noise Reduction in Gravitational Wave Interferometers Using Feedback, J. Opt. B 6, S691 (2004).
46. H. M. Wiseman, Using Feedback to Eliminate Back-action in Quantum Measurements, Phys. Rev. A 51, 2459 (1995).
47. F. Ticozzi and L. Viola, Quantum Markovian Subsystems: Invariance, Attractivity and Control, IEEE Trans. Autom. Control 53, 2048 (2008).
48. F. Ticozzi and L. Viola, Analysis and Synthesis of Attractive Quantum Markovian Dynamics, Automatica 45, 2002 (2009).
49. S. G. Schirmer and X. Wang, Stabilizing Open Quantum Systems by Markovian Reservoir Engineering, Phys. Rev. A 81, 062306 (2010).
50. H. A. Bachor and T. C. Ralph, A Guide to Experiments in Quantum Optics (Wiley-VCH, Weinheim, 2004).
51. C. K. Law, Interaction between a Moving Mirror and Radiation Pressure: A Hamiltonian Formulation, Phys. Rev. A 51, 2537 (1995).
52. M. Tsang and C. M. Caves, Coherent Quantum-Noise Cancellation for Optomechanical Sensors, Phys. Rev. Lett. 105, 123601 (2010).
53. Y. D. Wang and A. A. Clerk, Using Dark Modes for High- Fidelity Optomechanical Quantum State Transfer, New J. Phys. 14, 105010 (2012).
54. Y. D. Wang and A. A. Clerk, Using Interference for High Fidelity Quantum State Transfer in Optomechanics, Phys. Rev. Lett. 108, 153603 (2012).
55. C. Dong, V. Fiore, M. C. Kuzyk, and H. Wang, Optomechanical Dark Mode, Science 338, 1609 (2012).
56. Y. Chen, Macroscopic Quantum Mechanics: Theory and Experimental Concepts of Optomechanics, J. Phys. B 46, 104001 (2013).
57. H. Miao, Exploring Macroscopic Quantum Mechanics in Optomechanical Devices (Springer, Berlin, 2012).
58. L. M. Duan, J. I. Cirac, and P. Zoller, Three-Dimensional Theory for Interaction between Atomic Ensembles and Free-Space Light, Phys. Rev. A 66, 023818 (2002).
59. D. N. Matsukevich, T. Chaneliere, S. D. Jenkins, S. Y. Lan, T. A. B. Kennedy, and A. Kuzmich, Deterministic Single Photons via Conditional Quantum Evolution, Phys. Rev. Lett. 97, 013601 (2006).
60. A. S. Parkins, E. Solano, and J. I. Cirac, Unconditional Two-Mode Squeezing of Separated Atomic Ensembles, Phys. Rev. Lett. 96, 053602 (2006).
61. A. V. Gorshkov, A. Andre, M. D. Lukin, and A. S. Sorensen, Photon Storage in Λ-Type Optically Dense Atomic Media. I. Cavity Model, Phys. Rev. A 76, 033804 (2007).
62. K. Hammerer, A. S. Sorensen, and E. S. Polzik, Quantum Interface between Light and Atomic Ensembles, Rev. Mod. Phys. 82, 1041 (2010).
63. S. L. Braunstein and P. van Loock, Quantum Information with Continuous Variables, Rev. Mod. Phys. 77, 513 (2005).
64. A. Furusawa and P. van Loock, Quantum Teleportation and Entanglement: A Hybrid Approach to Optical Quantum Information Processing (Wiley-VCH, Berlin, 2011).
65. A. Ferraro, S. Olivares, and M. G. A. Paris, Gaussian States in Continuous Variable Quantum Information, arXiv:quantph/0503237.
66. C. Weedbrook, S. Pirandola, R. Garcia-Patron, N. J. Cerf, T. C. Ralph, J. H. Shapiro, and S. Lloyd, Gaussian Quantum Information, Rev. Mod. Phys. 84, 621 (2012).
67. G. J. Milburn, Coherent Control of Single Photon States, Eur. Phys. J. Spec. Top. 159, 113 (2008).
68. F. Khalili, S. Danilishin, H. Miao, H. Muller-Ebhardt, H. Yang, and Y. Chen, Preparing a Mechanical Oscillator in Non-Gaussian Quantum States, Phys. Rev. Lett. 105, 070403 (2010).
69. N. Yamamoto and M. R. James, Zero-Dynamics Principle for Perfect Quantum Memory in Linear Networks, New J. Phys. 16, 073032 (2014).
70. J. K. Stockton, J.M. Geremia, A. C. Doherty, and H. Mabuchi, Robust Quantum Parameter Estimation: Coherent Magnetometry with Feedback, Phys. Rev. A 69, 032109 (2004).
71. L. Bouten, J. Stockton, G. Sarma, and H. Mabuchi, Scattering of Polarized Laser Light by an Atomic Gas in Free Space: A Quantum Stochastic Differential Equation Approach, Phys. Rev. A 75, 052111 (2007).
72. M. Tsang and C. M. Caves, Evading Quantum Mechanics: Engineering a Classical Subsystem within a Quantum Environment, Phys. Rev. X 2, 031016 (2012).
73. J. S. Prauzner-Bechcicki, Two-Mode Squeezed Vacuum State Coupled to the Common Thermal Reservoir, J. Phys. A 37, L173 (2004).
74. G. Manzano, F. Galve, and R. Zambrini, Avoiding Dissipation in a System of Three Quantum Harmonic Oscillators, Phys. Rev. A 87, 032114 (2013).
75. N. Yamamoto, Decoherence-Free Linear Quantum Subsystems, IEEE Trans. Autom. Control 59, 1845 (2014).
76. M. H. Wimmer, D. Steinmeyer, K. Hammerer, and M. Heurs, Coherent Cancellation of Backaction Noise in Optomechanical Force Measurements, Phys. Rev. A 89, 053836 (2014).
77. H. M. Wiseman and G. J. Milburn, Quantum Theory of Field-Quadrature Measurements, Phys. Rev. A 47, 642 (1993).
78. A. Isidori, Nonlinear Control Systems, 3rd ed. (Springer, Berlin, 1995).
79. H. Nijmeijer and A. van der Schaft, Nonlinear Dynamical Control Systems, 3rd ed. (Springer, Berlin, 1996).
80. G. I. Harris, D. L. McAuslan, T. M. Stace, A. C. Doherty, and W. P. Bowen, Minimum Requirements for Feedback Enhanced Force Sensing, Phys. Rev. Lett. 111, 103603 (2013).
81. H. M. Wiseman, Quantum Theory of Continuous Feedback, Phys. Rev. A 49, 2133 (1994).