Abstract

Contrary to the usual assumption of at least partial control of quantum dynamics, a surprising recent result proved that an arbitrary quantum state can be probabilistically reset to a state in the past by having it interact with probing systems in a consistent but uncontrolled way. We present a photonic implementation to achieve this resetting process, experimentally verifying that a state can be probabilistically reset to its past with a fidelity of $0.870 \pm 0.012$. We further demonstrate the preservation of an entangled state, which still violates a Bell inequality, after half of the entangled pair was reset. The ability to reset uncontrolled quantum states has implications in the foundations of quantum physics and applications in areas of quantum technology.

© 2020 Optical Society of America under the terms of the OSA Open Access Publishing Agreement

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References

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  1. H. Rabitz, R. de Vivie-Riedle, M. Motzkus, and K. Kompa, “Whither the future of controlling quantum phenomena?” Science 288, 824–828 (2000).
    [Crossref]
  2. E. L. Hahn, “Spin echoes,” Phys. Rev. 80, 580–594 (1950).
    [Crossref]
  3. R. Freeman, Spin Choreography: Basic Steps in High Resolution NMR (Oxford University, 1998).
  4. L. Viola, E. Knill, and S. Lloyd, “Dynamical decoupling of open quantum systems,” Phys. Rev. Lett. 82, 2417–2421 (1999).
    [Crossref]
  5. P. Zanardi, “Symmetrizing evolutions,” Phys. Lett. A 258, 77–82 (1999).
    [Crossref]
  6. I. S. B. Sardharwalla, T. S. Cubitt, A. W. Harrow, and N. Linden, “Universal refocusing of systematic quantum noise,” Tech. Rep. MIT/CTP-4772 (MIT, 2016).
  7. Y. Aharonov, J. Anandan, S. Popescu, and L. Vaidman, “Superpositions of time evolutions of a quantum system and a quantum time-translation machine,” Phys. Rev. Lett. 64, 2965–2968 (1990).
    [Crossref]
  8. V. Drensky and E. Formanek, “Polynomial identity rings,” in Advanced Courses in Mathematics CRM Barcelona (Birkhäuser, 2004).
  9. M. Navascués, “Resetting uncontrolled quantum systems,” Phys. Rev. X 8, 031008 (2018).
    [Crossref]
  10. M. T. Quintino, Q. Dong, A. Shimbo, A. Soeda, and M. Murao, “Reversing unknown quantum transformations: universal quantum circuit for inverting general unitary operations,” Phys. Rev. Lett. 123, 210502 (2019).
    [Crossref]
  11. J. S. Bell, “On the Einstein-Podolsky-Rosen paradox,” Physics 1,195–200 (1964).
    [Crossref]
  12. J. F. Clauser, M. A. Horne, A. Shimony, and R. A. Holt, “Proposed experiment to test local hidden-variable theories,” Phys. Rev. Lett. 23, 880–884 (1969).
    [Crossref]
  13. J.-W. Pan, Z.-B. Chen, C.-Y. Lu, H. Weinfurter, A. Zeilinger, and M. Z. Żukowski, “Multiphoton entanglement and interferometry,” Rev. Mod. Phys. 84, 777–838 (2012).
    [Crossref]
  14. P. G. Kwiat, K. Mattle, H. Weinfurter, A. Zeilinger, A. V. Sergienko, and Y. Shih, “New high-intensity source of polarization-entangled photon pairs,” Phys. Rev. Lett. 75, 4337–4341 (1995).
    [Crossref]
  15. D. Trillo, B. Dive, and M. Navascués, “Remote time manipulation,” arXiv:1903.10568 (2019).

2019 (1)

M. T. Quintino, Q. Dong, A. Shimbo, A. Soeda, and M. Murao, “Reversing unknown quantum transformations: universal quantum circuit for inverting general unitary operations,” Phys. Rev. Lett. 123, 210502 (2019).
[Crossref]

2018 (1)

M. Navascués, “Resetting uncontrolled quantum systems,” Phys. Rev. X 8, 031008 (2018).
[Crossref]

2012 (1)

J.-W. Pan, Z.-B. Chen, C.-Y. Lu, H. Weinfurter, A. Zeilinger, and M. Z. Żukowski, “Multiphoton entanglement and interferometry,” Rev. Mod. Phys. 84, 777–838 (2012).
[Crossref]

2000 (1)

H. Rabitz, R. de Vivie-Riedle, M. Motzkus, and K. Kompa, “Whither the future of controlling quantum phenomena?” Science 288, 824–828 (2000).
[Crossref]

1999 (2)

L. Viola, E. Knill, and S. Lloyd, “Dynamical decoupling of open quantum systems,” Phys. Rev. Lett. 82, 2417–2421 (1999).
[Crossref]

P. Zanardi, “Symmetrizing evolutions,” Phys. Lett. A 258, 77–82 (1999).
[Crossref]

1995 (1)

P. G. Kwiat, K. Mattle, H. Weinfurter, A. Zeilinger, A. V. Sergienko, and Y. Shih, “New high-intensity source of polarization-entangled photon pairs,” Phys. Rev. Lett. 75, 4337–4341 (1995).
[Crossref]

1990 (1)

Y. Aharonov, J. Anandan, S. Popescu, and L. Vaidman, “Superpositions of time evolutions of a quantum system and a quantum time-translation machine,” Phys. Rev. Lett. 64, 2965–2968 (1990).
[Crossref]

1969 (1)

J. F. Clauser, M. A. Horne, A. Shimony, and R. A. Holt, “Proposed experiment to test local hidden-variable theories,” Phys. Rev. Lett. 23, 880–884 (1969).
[Crossref]

1964 (1)

J. S. Bell, “On the Einstein-Podolsky-Rosen paradox,” Physics 1,195–200 (1964).
[Crossref]

1950 (1)

E. L. Hahn, “Spin echoes,” Phys. Rev. 80, 580–594 (1950).
[Crossref]

Aharonov, Y.

Y. Aharonov, J. Anandan, S. Popescu, and L. Vaidman, “Superpositions of time evolutions of a quantum system and a quantum time-translation machine,” Phys. Rev. Lett. 64, 2965–2968 (1990).
[Crossref]

Anandan, J.

Y. Aharonov, J. Anandan, S. Popescu, and L. Vaidman, “Superpositions of time evolutions of a quantum system and a quantum time-translation machine,” Phys. Rev. Lett. 64, 2965–2968 (1990).
[Crossref]

Bell, J. S.

J. S. Bell, “On the Einstein-Podolsky-Rosen paradox,” Physics 1,195–200 (1964).
[Crossref]

Chen, Z.-B.

J.-W. Pan, Z.-B. Chen, C.-Y. Lu, H. Weinfurter, A. Zeilinger, and M. Z. Żukowski, “Multiphoton entanglement and interferometry,” Rev. Mod. Phys. 84, 777–838 (2012).
[Crossref]

Clauser, J. F.

J. F. Clauser, M. A. Horne, A. Shimony, and R. A. Holt, “Proposed experiment to test local hidden-variable theories,” Phys. Rev. Lett. 23, 880–884 (1969).
[Crossref]

Cubitt, T. S.

I. S. B. Sardharwalla, T. S. Cubitt, A. W. Harrow, and N. Linden, “Universal refocusing of systematic quantum noise,” Tech. Rep. MIT/CTP-4772 (MIT, 2016).

de Vivie-Riedle, R.

H. Rabitz, R. de Vivie-Riedle, M. Motzkus, and K. Kompa, “Whither the future of controlling quantum phenomena?” Science 288, 824–828 (2000).
[Crossref]

Dive, B.

D. Trillo, B. Dive, and M. Navascués, “Remote time manipulation,” arXiv:1903.10568 (2019).

Dong, Q.

M. T. Quintino, Q. Dong, A. Shimbo, A. Soeda, and M. Murao, “Reversing unknown quantum transformations: universal quantum circuit for inverting general unitary operations,” Phys. Rev. Lett. 123, 210502 (2019).
[Crossref]

Drensky, V.

V. Drensky and E. Formanek, “Polynomial identity rings,” in Advanced Courses in Mathematics CRM Barcelona (Birkhäuser, 2004).

Formanek, E.

V. Drensky and E. Formanek, “Polynomial identity rings,” in Advanced Courses in Mathematics CRM Barcelona (Birkhäuser, 2004).

Freeman, R.

R. Freeman, Spin Choreography: Basic Steps in High Resolution NMR (Oxford University, 1998).

Hahn, E. L.

E. L. Hahn, “Spin echoes,” Phys. Rev. 80, 580–594 (1950).
[Crossref]

Harrow, A. W.

I. S. B. Sardharwalla, T. S. Cubitt, A. W. Harrow, and N. Linden, “Universal refocusing of systematic quantum noise,” Tech. Rep. MIT/CTP-4772 (MIT, 2016).

Holt, R. A.

J. F. Clauser, M. A. Horne, A. Shimony, and R. A. Holt, “Proposed experiment to test local hidden-variable theories,” Phys. Rev. Lett. 23, 880–884 (1969).
[Crossref]

Horne, M. A.

J. F. Clauser, M. A. Horne, A. Shimony, and R. A. Holt, “Proposed experiment to test local hidden-variable theories,” Phys. Rev. Lett. 23, 880–884 (1969).
[Crossref]

Knill, E.

L. Viola, E. Knill, and S. Lloyd, “Dynamical decoupling of open quantum systems,” Phys. Rev. Lett. 82, 2417–2421 (1999).
[Crossref]

Kompa, K.

H. Rabitz, R. de Vivie-Riedle, M. Motzkus, and K. Kompa, “Whither the future of controlling quantum phenomena?” Science 288, 824–828 (2000).
[Crossref]

Kwiat, P. G.

P. G. Kwiat, K. Mattle, H. Weinfurter, A. Zeilinger, A. V. Sergienko, and Y. Shih, “New high-intensity source of polarization-entangled photon pairs,” Phys. Rev. Lett. 75, 4337–4341 (1995).
[Crossref]

Linden, N.

I. S. B. Sardharwalla, T. S. Cubitt, A. W. Harrow, and N. Linden, “Universal refocusing of systematic quantum noise,” Tech. Rep. MIT/CTP-4772 (MIT, 2016).

Lloyd, S.

L. Viola, E. Knill, and S. Lloyd, “Dynamical decoupling of open quantum systems,” Phys. Rev. Lett. 82, 2417–2421 (1999).
[Crossref]

Lu, C.-Y.

J.-W. Pan, Z.-B. Chen, C.-Y. Lu, H. Weinfurter, A. Zeilinger, and M. Z. Żukowski, “Multiphoton entanglement and interferometry,” Rev. Mod. Phys. 84, 777–838 (2012).
[Crossref]

Mattle, K.

P. G. Kwiat, K. Mattle, H. Weinfurter, A. Zeilinger, A. V. Sergienko, and Y. Shih, “New high-intensity source of polarization-entangled photon pairs,” Phys. Rev. Lett. 75, 4337–4341 (1995).
[Crossref]

Motzkus, M.

H. Rabitz, R. de Vivie-Riedle, M. Motzkus, and K. Kompa, “Whither the future of controlling quantum phenomena?” Science 288, 824–828 (2000).
[Crossref]

Murao, M.

M. T. Quintino, Q. Dong, A. Shimbo, A. Soeda, and M. Murao, “Reversing unknown quantum transformations: universal quantum circuit for inverting general unitary operations,” Phys. Rev. Lett. 123, 210502 (2019).
[Crossref]

Navascués, M.

M. Navascués, “Resetting uncontrolled quantum systems,” Phys. Rev. X 8, 031008 (2018).
[Crossref]

D. Trillo, B. Dive, and M. Navascués, “Remote time manipulation,” arXiv:1903.10568 (2019).

Pan, J.-W.

J.-W. Pan, Z.-B. Chen, C.-Y. Lu, H. Weinfurter, A. Zeilinger, and M. Z. Żukowski, “Multiphoton entanglement and interferometry,” Rev. Mod. Phys. 84, 777–838 (2012).
[Crossref]

Popescu, S.

Y. Aharonov, J. Anandan, S. Popescu, and L. Vaidman, “Superpositions of time evolutions of a quantum system and a quantum time-translation machine,” Phys. Rev. Lett. 64, 2965–2968 (1990).
[Crossref]

Quintino, M. T.

M. T. Quintino, Q. Dong, A. Shimbo, A. Soeda, and M. Murao, “Reversing unknown quantum transformations: universal quantum circuit for inverting general unitary operations,” Phys. Rev. Lett. 123, 210502 (2019).
[Crossref]

Rabitz, H.

H. Rabitz, R. de Vivie-Riedle, M. Motzkus, and K. Kompa, “Whither the future of controlling quantum phenomena?” Science 288, 824–828 (2000).
[Crossref]

Sardharwalla, I. S. B.

I. S. B. Sardharwalla, T. S. Cubitt, A. W. Harrow, and N. Linden, “Universal refocusing of systematic quantum noise,” Tech. Rep. MIT/CTP-4772 (MIT, 2016).

Sergienko, A. V.

P. G. Kwiat, K. Mattle, H. Weinfurter, A. Zeilinger, A. V. Sergienko, and Y. Shih, “New high-intensity source of polarization-entangled photon pairs,” Phys. Rev. Lett. 75, 4337–4341 (1995).
[Crossref]

Shih, Y.

P. G. Kwiat, K. Mattle, H. Weinfurter, A. Zeilinger, A. V. Sergienko, and Y. Shih, “New high-intensity source of polarization-entangled photon pairs,” Phys. Rev. Lett. 75, 4337–4341 (1995).
[Crossref]

Shimbo, A.

M. T. Quintino, Q. Dong, A. Shimbo, A. Soeda, and M. Murao, “Reversing unknown quantum transformations: universal quantum circuit for inverting general unitary operations,” Phys. Rev. Lett. 123, 210502 (2019).
[Crossref]

Shimony, A.

J. F. Clauser, M. A. Horne, A. Shimony, and R. A. Holt, “Proposed experiment to test local hidden-variable theories,” Phys. Rev. Lett. 23, 880–884 (1969).
[Crossref]

Soeda, A.

M. T. Quintino, Q. Dong, A. Shimbo, A. Soeda, and M. Murao, “Reversing unknown quantum transformations: universal quantum circuit for inverting general unitary operations,” Phys. Rev. Lett. 123, 210502 (2019).
[Crossref]

Trillo, D.

D. Trillo, B. Dive, and M. Navascués, “Remote time manipulation,” arXiv:1903.10568 (2019).

Vaidman, L.

Y. Aharonov, J. Anandan, S. Popescu, and L. Vaidman, “Superpositions of time evolutions of a quantum system and a quantum time-translation machine,” Phys. Rev. Lett. 64, 2965–2968 (1990).
[Crossref]

Viola, L.

L. Viola, E. Knill, and S. Lloyd, “Dynamical decoupling of open quantum systems,” Phys. Rev. Lett. 82, 2417–2421 (1999).
[Crossref]

Weinfurter, H.

J.-W. Pan, Z.-B. Chen, C.-Y. Lu, H. Weinfurter, A. Zeilinger, and M. Z. Żukowski, “Multiphoton entanglement and interferometry,” Rev. Mod. Phys. 84, 777–838 (2012).
[Crossref]

P. G. Kwiat, K. Mattle, H. Weinfurter, A. Zeilinger, A. V. Sergienko, and Y. Shih, “New high-intensity source of polarization-entangled photon pairs,” Phys. Rev. Lett. 75, 4337–4341 (1995).
[Crossref]

Zanardi, P.

P. Zanardi, “Symmetrizing evolutions,” Phys. Lett. A 258, 77–82 (1999).
[Crossref]

Zeilinger, A.

J.-W. Pan, Z.-B. Chen, C.-Y. Lu, H. Weinfurter, A. Zeilinger, and M. Z. Żukowski, “Multiphoton entanglement and interferometry,” Rev. Mod. Phys. 84, 777–838 (2012).
[Crossref]

P. G. Kwiat, K. Mattle, H. Weinfurter, A. Zeilinger, A. V. Sergienko, and Y. Shih, “New high-intensity source of polarization-entangled photon pairs,” Phys. Rev. Lett. 75, 4337–4341 (1995).
[Crossref]

Zukowski, M. Z.

J.-W. Pan, Z.-B. Chen, C.-Y. Lu, H. Weinfurter, A. Zeilinger, and M. Z. Żukowski, “Multiphoton entanglement and interferometry,” Rev. Mod. Phys. 84, 777–838 (2012).
[Crossref]

Phys. Lett. A (1)

P. Zanardi, “Symmetrizing evolutions,” Phys. Lett. A 258, 77–82 (1999).
[Crossref]

Phys. Rev. (1)

E. L. Hahn, “Spin echoes,” Phys. Rev. 80, 580–594 (1950).
[Crossref]

Phys. Rev. Lett. (5)

L. Viola, E. Knill, and S. Lloyd, “Dynamical decoupling of open quantum systems,” Phys. Rev. Lett. 82, 2417–2421 (1999).
[Crossref]

Y. Aharonov, J. Anandan, S. Popescu, and L. Vaidman, “Superpositions of time evolutions of a quantum system and a quantum time-translation machine,” Phys. Rev. Lett. 64, 2965–2968 (1990).
[Crossref]

M. T. Quintino, Q. Dong, A. Shimbo, A. Soeda, and M. Murao, “Reversing unknown quantum transformations: universal quantum circuit for inverting general unitary operations,” Phys. Rev. Lett. 123, 210502 (2019).
[Crossref]

J. F. Clauser, M. A. Horne, A. Shimony, and R. A. Holt, “Proposed experiment to test local hidden-variable theories,” Phys. Rev. Lett. 23, 880–884 (1969).
[Crossref]

P. G. Kwiat, K. Mattle, H. Weinfurter, A. Zeilinger, A. V. Sergienko, and Y. Shih, “New high-intensity source of polarization-entangled photon pairs,” Phys. Rev. Lett. 75, 4337–4341 (1995).
[Crossref]

Phys. Rev. X (1)

M. Navascués, “Resetting uncontrolled quantum systems,” Phys. Rev. X 8, 031008 (2018).
[Crossref]

Physics (1)

J. S. Bell, “On the Einstein-Podolsky-Rosen paradox,” Physics 1,195–200 (1964).
[Crossref]

Rev. Mod. Phys. (1)

J.-W. Pan, Z.-B. Chen, C.-Y. Lu, H. Weinfurter, A. Zeilinger, and M. Z. Żukowski, “Multiphoton entanglement and interferometry,” Rev. Mod. Phys. 84, 777–838 (2012).
[Crossref]

Science (1)

H. Rabitz, R. de Vivie-Riedle, M. Motzkus, and K. Kompa, “Whither the future of controlling quantum phenomena?” Science 288, 824–828 (2000).
[Crossref]

Other (4)

R. Freeman, Spin Choreography: Basic Steps in High Resolution NMR (Oxford University, 1998).

V. Drensky and E. Formanek, “Polynomial identity rings,” in Advanced Courses in Mathematics CRM Barcelona (Birkhäuser, 2004).

I. S. B. Sardharwalla, T. S. Cubitt, A. W. Harrow, and N. Linden, “Universal refocusing of systematic quantum noise,” Tech. Rep. MIT/CTP-4772 (MIT, 2016).

D. Trillo, B. Dive, and M. Navascués, “Remote time manipulation,” arXiv:1903.10568 (2019).

Supplementary Material (1)

NameDescription
» Supplement 1       The details of experimental setup and more experimental results.

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Figures (4)

Fig. 1.
Fig. 1. Illustration of the protocol and corresponding experimental setup. (a) Schematic diagram of the quantum resetting protocol for a single photon. A target photon (qubit) $S$, initialized at an arbitrary state, evolves over four unknown time-independent Hamiltonians ${{\cal H}_0}$ and interacts with four probes. A measurement result in Q heralds the target’s reset to its initial state. (b) Quantum circuit I based on SWAP gates. (c) Quantum circuit II based on Hadamard and nonunitary PBS gates. (d),(e) Photonic implementation for circuit I and circuit II. A pulsed ultraviolet laser successively pumps three sandwich-like combinations of $\beta$-barium borate crystals (C-BBO) to generate three entangled photon pairs. Photon 2, heralded by photon 1, serves as the target system, while photons 3–6 serve as the probes. These photons pass through the free evolutions and the interactions, and finally they are detected by projection measurements. SC-${\text{YVO}_4}$ and TC-${\text{YVO}_4}$ represent spatial compensation (SC) and temporal compensation (TC) yttrium orthovanadate (${\text{YVO}_4}$) crystals. QWP and HWP represent quarter- and half-wave plates, respectively.
Fig. 2.
Fig. 2. Illustration of the quantum resetting process. (a),(b),(c) Visual description of the evolution process before and after the resetting processing for circuit I and circuit II. (b)–(d) The evolution of state fidelity during the resetting process for circuit I with free Hamiltonians ${{\cal H}_0} = {\sigma _z}/2$. (f)–(h) The evolution of state fidelity during the resetting process for circuit II with free Hamiltonians ${{\cal H}_0} = {\sigma _z}/2$. (j)–(l) The evolution of state fidelity during the resetting process for circuit I with free Hamiltonians ${{\cal H}_0} = {\sigma _y}/2$. The dashed curves and the blue asterisks denote, respectively, the ideal and the experimental fidelity with free time-dependent Hamiltonian evolution, without the resetting process. The solid line and the red dots denote the experimental results of quantum resetting.
Fig. 3.
Fig. 3. Fidelity for different types of target states. With resetting, all fidelities are well above the classical limit of 2/3 (indicated by the dashed curve). The average fidelity for circuit I (II) with free Hamiltonian ${{\cal H}_0} = {\sigma _z}/2$ is $F = 0.870 \pm 0.012$ ($F = 0.869 \pm 0.021$), and the average fidelity for circuit I with free Hamiltonians ${{\cal H}_0} = {\sigma _y}/2$ is $F = 0.874 \pm 0.016$. Without resetting, the average fidelity for circuit I (II) with free Hamiltonian ${{\cal H}_0} = {\sigma _z}/2$ is $F = 0.5100 \pm 0.0005$ ($F = 0.5186 \pm 0.0003$), and the average fidelity for circuit I with free Hamiltonians ${{\cal H}_0} = {\sigma _y}/2$ is $F = 0.5121 \pm 0.0003$.
Fig. 4.
Fig. 4. Measured fraction and correlation of reset entanglement. The measurement of entanglement fidelity and the CHSH inequality was conducted for entangled photon pairs, where one party of the pairs goes through the quantum resetting process. (a) The measurement was performed in bases $XX$, $YY$, and $ZZ$ for transmitted (T) and reflected (R) modes of the PBS. The entanglement fidelity for circuit I with free Hamiltonian ${{\cal H}_0} = {\sigma _z}/2$ is $F = 0.805 \pm 0.017$. (b) The entanglement fidelity for circuit II with free Hamiltonian ${{\cal H}_0} = {\sigma _z}/2$ is $F = 0.807 \pm 0.033$. (c) The entanglement fidelity for circuit I with free Hamiltonian ${{\cal H}_0} = {\sigma _y}/2$ is $F = 0.811 \pm 0.024$. (d) The CHSH inequality value for circuit I with free Hamiltonian ${{\cal H}_0} = {\sigma _z}/2$ is $2.13 \pm 0.05$. (e) The CHSH inequality value for circuit II with free Hamiltonian ${{\cal H}_0} = {\sigma _z}/2$ is $2.26 \pm 0.08$. (f) The CHSH inequality value for circuit I with free Hamiltonian ${{\cal H}_0} = {\sigma _y}/2$ is $2.19 \pm 0.05$.

Equations (3)

Equations on this page are rendered with MathJax. Learn more.

| m 1 = | 0000 , | m 2 = ( | 0001 + | 0010 + | 0100 + | 1000 ) / 2 , | m 3 = ( | 0101 + | 0110 + | 1001 + | 1010 ) / 2 , | m 4 = ( | 0011 + | 1100 ) / 2 , | m 5 = ( | 0111 + | 1011 + | 1101 + | 1110 ) / 2 , | m 6 = | 1111 .
V S P I = SWAP = ( 1 0 0 0 0 0 1 0 0 1 0 0 0 0 0 1 ) .
V S P II = ( I H ) G PBS ( X I ) = ( 0 0 1 2 0 0 0 1 2 0 0 1 2 0 0 0 1 2 0 0 ) .

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