Dissipative production of a maximally entangled steady state of two quantum bits


Entangled states are a key resource in fundamental quantum physics, quantum cryptography and quantum computation1. Introduction of controlled unitary processes—quantum gates—to a quantum system has so far been the most widely used method to create entanglement deterministically2. These processes require high-fidelity state preparation and minimization of the decoherence that inevitably arises from coupling between the system and the environment, and imperfect control of the system parameters. Here we combine unitary processes with engineered dissipation to deterministically produce and stabilize an approximate Bell state of two trapped-ion quantum bits (qubits), independent of their initial states. Compared with previous studies that involved dissipative entanglement of atomic ensembles3 or the application of sequences of multiple time-dependent gates to trapped ions4, we implement our combined process using trapped-ion qubits in a continuous time-independent fashion (analogous to optical pumping of atomic states). By continuously driving the system towards the steady state, entanglement is stabilized even in the presence of experimental noise and decoherence. Our demonstration of an entangled steady state of two qubits represents a step towards dissipative state engineering, dissipative quantum computation and dissipative phase transitions5,6,7. Following this approach, engineered coupling to the environment may be applied to a broad range of experimental systems to achieve desired quantum dynamics or steady states. Indeed, concurrently with this work, an entangled steady state of two superconducting qubits was demonstrated using dissipation8.

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Figure 1: Energy levels and entanglement preparation scheme.
Figure 2: Steady-state entanglement.
Figure 3: Entanglement with stepwise scheme.


  1. 1

    Nielsen, M. A. & Chuang, I. L. Quantum Computation and Quantum Information (Cambridge Univ. Press, 2000)

    Google Scholar 

  2. 2

    Ladd, T. D. et al. Quantum computers. Nature 464, 45–53 (2010)

    CAS  Article  ADS  Google Scholar 

  3. 3

    Krauter, H. et al. Entanglement generated by dissipation and steady state entanglement of two macroscopic objects. Phys. Rev. Lett. 107, 080503 (2011)

    Article  ADS  Google Scholar 

  4. 4

    Barreiro, J. T. et al. An open-system quantum simulator with trapped ions. Nature 470, 486–491 (2011)

    CAS  Article  ADS  Google Scholar 

  5. 5

    Kraus, B. et al. Preparation of entangled states by quantum Markov processes. Phys. Rev. A 78, 042307 (2008)

    Article  ADS  Google Scholar 

  6. 6

    Diehl, S. et al. Quantum states and phases in driven open quantum systems with cold atoms. Nature Phys. 4, 878–883 (2008)

    CAS  Article  ADS  Google Scholar 

  7. 7

    Verstraete, F., Wolf, M. M. & Cirac, J. I. Quantum computation and quantum-state engineering driven by dissipation. Nature Phys. 5, 633–636 (2009)

    CAS  Article  ADS  Google Scholar 

  8. 8

    Shankar, S. et al. Autonomously stabilized entanglement between two superconducting quantum bits. Nature http://dx.doi.org/10.1038/nature12802 (this issue)

  9. 9

    Lanyon, B. P. et al. Universal digital quantum simulation with trapped ions. Science 334, 57–61 (2011)

    CAS  Article  ADS  Google Scholar 

  10. 10

    Hanneke, D. et al. Realization of a programmable two-qubit quantum processor. Nature Phys. 6, 13–16 (2010)

    CAS  Article  ADS  Google Scholar 

  11. 11

    Sayrin, C. et al. Real-time quantum feedback prepares and stabilizes photon number states. Nature 477, 73–77 (2011)

    CAS  Article  ADS  Google Scholar 

  12. 12

    Vijay, R. et al. Stabilizing Rabi oscillations in a superconducting qubit using quantum feedback. Nature 490, 77–80 (2012)

    CAS  Article  ADS  Google Scholar 

  13. 13

    Ristè, D., Bultink, C. C., Lehnert, K. W. & DiCarlo, L. Feedback control of a solid-state qubit using high-fidelity projective measurement. Phys. Rev. Lett. 109, 240502 (2012)

    Article  ADS  Google Scholar 

  14. 14

    Brakhane, S. et al. Bayesian feedback control of a two-atom spin-state in an atom-cavity system. Phys. Rev. Lett. 109, 173601 (2012)

    Article  ADS  Google Scholar 

  15. 15

    Schindler, P. et al. Quantum simulation of dynamical maps with trapped ions. Nature Phys. 9, 361–367 (2013)

    CAS  Article  ADS  Google Scholar 

  16. 16

    Campagne-Ibarcq, P. et al. Persistent control of a superconducting qubit by stroboscopic measurement feedback. Phys. Rev. X 3, 021008 (2013)

    Google Scholar 

  17. 17

    Ristè, D. et al. Deterministic entanglement of superconducting qubits by parity measurement and feedback. Nature 502, 350–354 (2013)

    Article  ADS  Google Scholar 

  18. 18

    Poyatos, J. F., Cirac, J. I. & Zoller, P. Quantum reservoir engineering with laser cooled trapped ions. Phys. Rev. Lett. 77, 4728–4731 (1996)

    CAS  Article  ADS  Google Scholar 

  19. 19

    Plenio, M. B., Huelga, S., Beige, A. & Knight, P. L. Cavity-loss-induced generation of entangled atoms. Phys. Rev. A 59, 2468–2475 (1999)

    CAS  Article  ADS  Google Scholar 

  20. 20

    Clark, S., Peng, A., Gu, M. & Parkins, S. Unconditional preparation of entanglement between atoms in cascaded optical cavities. Phys. Rev. Lett. 91, 177901 (2003)

    Article  ADS  Google Scholar 

  21. 21

    Parkins, A. S., Solano, E. & Cirac, J. I. Unconditional two-mode squeezing of separated atomic ensembles. Phys. Rev. Lett. 96, 053602 (2006)

    CAS  Article  ADS  Google Scholar 

  22. 22

    Kastoryano, M. J., Reiter, F. & Sørensen, A. S. Dissipative preparation of entanglement in optical cavities. Phys. Rev. Lett. 106, 090502 (2011)

    CAS  Article  ADS  Google Scholar 

  23. 23

    Cho, J., Bose, S. & Kim, M. S. Optical pumping into many-body entanglement. Phys. Rev. Lett. 106, 020504 (2011)

    Article  ADS  Google Scholar 

  24. 24

    Bermudez, A., Schaetz, T. & Plenio, M. B. Dissipation-assisted quantum information processing with trapped ions. Phys. Rev. Lett. 110, 110502 (2013)

    CAS  Article  ADS  Google Scholar 

  25. 25

    Leghtas, Z. et al. Stabilizing a Bell state of two superconducting qubits by dissipation engineering. Phys. Rev. A 88, 023849 (2013)

    Article  ADS  Google Scholar 

  26. 26

    Reiter, F., Tornberg, L., Johansson, G. & Sørensen, A. S. Steady state entanglement of two superconducting qubits by engineered dissipation. Phys. Rev. A 88, 032317 (2013)

    Article  ADS  Google Scholar 

  27. 27

    Cormick, C., Bermudez, A., Huelga, S. F. & Plenio, M. B. Dissipative ground-state preparation of a spin chain by a structured environment. New J. Phys. 15, 073027 (2013)

    Article  ADS  Google Scholar 

  28. 28

    Ticozzi, F. & Viola, L. Steady-state entanglement by engineered quasi-local Markovian dissipation: Hamiltonian-assisted and conditional stabilization. Quantum Inform. Comput.. (in the press); preprint at http://arXiv.org/abs/1304.4270 (2013)

  29. 29

    Barrett, M. D. et al. Sympathetic cooling of 9Be+ and 24Mg+ for quantum logic. Phys. Rev. A 68, 042302 (2003)

    Article  ADS  Google Scholar 

  30. 30

    Reiter, F. & Sørensen, A. S. Effective operator formalism for open quantum systems. Phys. Rev. A 85, 032111 (2012)

    Article  ADS  Google Scholar 

  31. 31

    Monroe, C. et al. Resolved-sideband Raman cooling of a bound atom to the 3D zero-point energy. Phys. Rev. Lett. 75, 4011–4014 (1995)

    MathSciNet  CAS  Article  ADS  Google Scholar 

  32. 32

    Jost, J. D. et al. Entangled mechanical oscillators. Nature 459, 683–685 (2009)

    CAS  Article  ADS  Google Scholar 

  33. 33

    Ozeri, R. et al. Errors in trapped-ion quantum gates due to spontaneous photon scattering. Phys. Rev. A 75, 042329 (2007)

    Article  ADS  Google Scholar 

  34. 34

    Uys, H. et al. Decoherence due to elastic Rayleigh scattering. Phys. Rev. Lett. 105, 200401 (2010)

    CAS  Article  ADS  Google Scholar 

  35. 35

    Tan, S. M. A computation toolbox for quantum and atomic optics. J. Opt. B 1, 424–432 (1999)

    CAS  Article  ADS  Google Scholar 

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This research was funded in part by the Office of the Director of National Intelligence (ODNI), Intelligence Advanced Research Projects Activity (IARPA). All statements of fact, opinion or conclusions contained herein are those of the authors and should not be construed as representing the official views or policies of IARPA or the ODNI. This work was also supported by ONR, by the NIST Quantum Information Program, and by the European Union’s Seventh Framework Program through SIQS (grant no. 600645) and through the ERC grant QIOS (grant no. 306576). We thank D. Allcock and B. Sawyer for comments on the manuscript and E. Knill for conversations. F.R. acknowledges conversations with B. Lanyon, R. Blatt and J. Home and support from the Studienstiftung des deutschen Volkes. This Letter is a contribution of NIST and is not subject to US copyright.

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Y.L. and J.P.G. performed the experiments, analysed the data and developed the numerical model. F.R. proposed the entanglement scheme and developed the analytic rate model described in Supplementary Information under the guidance of A.S.S. T.R.T. contributed to the numerical model and the experimental apparatus. R.B. contributed to the experimental apparatus. D.L. and D.J.W. directed the experiments. All authors provided important suggestions for the experiments, discussed the results and contributed to the manuscript.

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Correspondence to Y. Lin.

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Lin, Y., Gaebler, J., Reiter, F. et al. Dissipative production of a maximally entangled steady state of two quantum bits. Nature 504, 415–418 (2013). https://doi.org/10.1038/nature12801

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