Avoiding entanglement sudden death via measurement feedback control in a quantum network

In this paper, we consider a linear quantum network composed of two distantly separated cavities that are connected via a one-way optical field. When one of the cavities is damped and the other undamped, the overall cavity state obtains a large amount of entanglement in its quadratures. This entanglement, however, immediately decays and vanishes in a finite time. That is, entanglement sudden death occurs. We show that the direct measurement feedback method proposed by Wiseman can avoid this entanglement sudden death, and, further, enhance the entanglement. It is also shown that the entangled state under feedback control is robust against signal loss in a realistic detector, indicating the reliability of the proposed direct feedback method in practical situations.

[1]  J. Cirac,et al.  IDEAL QUANTUM COMMUNICATION OVER NOISY CHANNELS : A QUANTUM OPTICAL IMPLEMENTATION , 1997, quant-ph/9702036.

[2]  Wiseman,et al.  Quantum theory of continuous feedback. , 1994, Physical review. A, Atomic, molecular, and optical physics.

[3]  S. Mancini,et al.  Continuous quantum nondemolition feedback and unconditional atomic spin squeezing , 2002 .

[4]  K. Jacobs,et al.  FEEDBACK CONTROL OF QUANTUM SYSTEMS USING CONTINUOUS STATE ESTIMATION , 1999 .

[5]  B. Muzykantskii,et al.  ON QUANTUM NOISE , 1995 .

[6]  Z. Ficek,et al.  Delayed sudden birth of entanglement , 2008, 0802.4287.

[7]  Simón.  Peres-horodecki separability criterion for continuous variable systems , 1999, Physical review letters.

[8]  H. Mabuchi,et al.  Quantum trajectories for realistic detection , 2002 .

[9]  Cirac,et al.  Inseparability criterion for continuous variable systems , 1999, Physical review letters.

[10]  Stefano Mancini,et al.  Optimal control of entanglement via quantum feedback , 2007 .

[11]  Milburn,et al.  Quantum theory of optical feedback via homodyne detection. , 1993, Physical review letters.

[12]  H. M. Wiseman,et al.  Quantum trajectories for realistic photodetection: II. Application and analysis. , 2003 .

[13]  H. J. Kimble,et al.  Quantum state transfer between motion and light , 1999 .

[14]  Carmichael,et al.  Quantum trajectory theory for cascaded open systems. , 1993, Physical review letters.

[15]  G. J. Milburn,et al.  Quantum error correction for continuously detected errors , 2003 .

[16]  A. C. Doherty,et al.  STATE DETERMINATION IN CONTINUOUS MEASUREMENT , 1999 .

[17]  M. G. A. Paris,et al.  Purity of Gaussian states: Measurement schemes and time evolution in noisy channels , 2003 .

[18]  Charles H. Bennett,et al.  Purification of noisy entanglement and faithful teleportation via noisy channels. , 1995, Physical review letters.

[19]  Milburn,et al.  Quantum theory of field-quadrature measurements. , 1993, Physical review. A, Atomic, molecular, and optical physics.

[20]  Ramon van Handel,et al.  Approximation and limit theorems for quantum stochastic models with unbounded coefficients , 2007, 0712.2276.

[21]  T. Yu,et al.  Finite-time disentanglement via spontaneous emission. , 2004, Physical review letters.

[22]  Gerard J. Milburn,et al.  Classical and quantum conditional statistical dynamics , 1996 .

[23]  Robin L. Hudson,et al.  Quantum Ito's formula and stochastic evolutions , 1984 .

[24]  J. J. Hope,et al.  Stabilizing entanglement by quantum-jump-based feedback , 2007 .

[25]  G. Vidal,et al.  Computable measure of entanglement , 2001, quant-ph/0102117.

[26]  Masahiro Yanagisawa,et al.  Quantum feedback control for deterministic entangled photon generation. , 2006, Physical review letters.

[27]  Thierry Paul,et al.  Quantum computation and quantum information , 2007, Mathematical Structures in Computer Science.

[28]  Ting Yu,et al.  The End of an Entanglement , 2007, Science.

[29]  H. Carmichael.  An open systems approach to quantum optics , 1993 .

[30]  P. Warszawski,et al.  Quantum trajectories for realistic photodetection: I. General formalism , 2002 .

[31]  Charles H. Bennett,et al.  Mixed-state entanglement and quantum error correction. , 1996, Physical review. A, Atomic, molecular, and optical physics.

[32]  J. Doyle,et al.  Robust and optimal control , 1995, Proceedings of 35th IEEE Conference on Decision and Control.

[33]  Naoki Yamamoto,et al.  Feedback control of quantum entanglement in a two-spin system , 2005, Proceedings of the 44th IEEE Conference on Decision and Control.

[34]  H. J. Kimble,et al.  Position-momentum Einstein-Podolsky-Rosen state of distantly separated trapped atoms , 2000 .

[35]  S. Braunstein,et al.  Quantum Information with Continuous Variables , 2004, quant-ph/0410100.

[36]  Ramon van Handel,et al.  Singular Perturbation of Quantum Stochastic Differential Equations with Coupling Through an Oscillator Mode , 2007 .

[37]  Mazyar Mirrahimi,et al.  Stabilizing Feedback Controls for Quantum Systems , 2005, SIAM J. Control. Optim..

[38]  G. J. Milburn,et al.  Dynamical creation of entanglement by homodyne-mediated feedback (9 pages) , 2004, quant-ph/0409154.

[39]  M. James,et al.  Stability, gain, and robustness in quantum feedback networks (13 pages) , 2005, quant-ph/0511140.

[40]  J. Cirac,et al.  Quantum State Transfer and Entanglement Distribution among Distant Nodes in a Quantum Network , 1996, quant-ph/9611017.

[41]  A C Doherty,et al.  Optimal unravellings for feedback control in linear quantum systems. , 2005, Physical review letters.

[42]  Miss A.O. Penney.  (b) , 1974, The New Yale Book of Quotations.