Experimental demonstration of delayed-choice decoherence suppression

Abstract

Wheeler's delayed-choice experiment illustrates vividly that the observer plays a central role in quantum physics by demonstrating that complementarity or wave-particle duality can be enforced even after the photon has already entered the interferometer. The delayed-choice quantum eraser experiment further demonstrates that complementarity can be enforced even after detection of a quantum system, elucidating the foundational nature of complementarity in quantum physics. However, the applicability of the delayed-choice method for practical quantum information protocols continues to be an open question. Here, we introduce and experimentally demonstrate the delayed-choice decoherence suppression protocol, in which the decision to suppress decoherence on an entangled two-qubit state is delayed until after the decoherence and even after the detection of a qubit. Our result suggests a new way to tackle Markovian decoherence in a delayed manner, applicable for practical entanglement distribution over a dissipative channel.

ARTICLE

Received 22 Apr 2014 | Accepted 26 Jun 2014 | Published 29 Jul 2014

Wheelers delayed-choice experiment illustrates vividly that the observer plays a central role in quantum physics by demonstrating that complementarity or waveparticle duality can be enforced even after the photon has already entered the interferometer. The delayed-choice quantum eraser experiment further demonstrates that complementarity can be enforced even after detection of a quantum system, elucidating the foundational nature of complementarity in quantum physics. However, the applicability of the delayed-choice method for practical quantum information protocols continues to be an open question. Here, we introduce and experimentally demonstrate the delayed-choice decoherence suppression protocol, in which the decision to suppress decoherence on an entangled two-qubit state is delayed until after the decoherence and even after the detection of a qubit. Our result suggests a new way to tackle Markovian decoherence in a delayed manner, applicable for practical entanglement distribution over a dissipative channel.

DOI: 10.1038/ncomms5522

Experimental demonstration of delayed-choice decoherence suppression

Jong-Chan Lee1, Hyang-Tag Lim1, Kang-Hee Hong1, Youn-Chang Jeong1, M.S. Kim2,3 & Yoon-Ho Kim1

1 Department of Physics, Pohang University of Science and Technology (POSTECH), Pohang 790-784, Korea. 2 QOLS, Blackett Laboratory, Imperial College London, London SW7 2AZ, UK. 3 School of Computational Sciences, Korea Institute for Advanced Study, Seoul 130-722, Korea. Correspondence and requests for materials should be addressed to Y.-H.K. (email: mailto:[email protected]

Web End [email protected] ).

NATURE COMMUNICATIONS | 5:4522 | DOI: 10.1038/ncomms5522 | http://www.nature.com/naturecommunications

Web End =www.nature.com/naturecommunications 1

& 2014 Macmillan Publishers Limited. All rights reserved.

ARTICLE NATURE COMMUNICATIONS | DOI: 10.1038/ncomms5522

t 0 and sent to Alice and Bob with temporal delays tA and tB,

respectively. At time tD, Bobs qubit suffers from Markovian amplitude damping decoherence15, which is described by a quantum map: 0

j iS 0

j iE! 0

j iS 0

j iE; 1

j iS 0

j iE!

D

p 1

j iS 0

j iE

Complementarity normally refers to the waveparticle dual nature in quantum physics. In the delayed-choice experiment proposed by Wheeler, the choice to observe the wave

or particle nature is delayed until after the quantum system has already entered the interferometer1,2. It is even possible to delay the choice after detection of the quantum system by using an ancilla entangled with the quantum system36. For example, a delayed-choice quantum eraser is proposed and demonstrated, where the decision of whether to read out or erase the which-path information can be delayed till after the registration of the quanta3,4. Recently, experiments to investigate the intermediate behaviour between wave and particle nature have been proposed and demonstrated57. It is also recently shown that entanglement swapping, quantum walk and uncertainty principle can be demonstrated using delayed-choice method812. Although the fundamental aspects of delayed-choice experiments have been well studied, practicality of the delayed-choice method was rather obscure.

An intriguing question may arise as to whether the concept of delayed-choice can be adopted for quantum information protocols such as suppressing decoherence, which is a central problem in emerging quantum technology1315. This is a particularly interesting question for Markovian decoherence. Markovian decoherence is considered to be difcult to tackle once the decoherence takes place, since a posteriori methods such as rephasing16,17 or dynamical decoupling18,19 cannot be used.

In this Article, we propose and experimentally demonstrate a delayed-choice decoherence suppression scheme by using photonic polarization qubits. In contrast to the normal decoherence suppression scheme2023, in which the choice whether or not to suppress decoherence is naturally made before the decoherence by the initial weak measurement (WM), our decoherence suppression scheme delays the choice after the decoherence itself. We demonstrate that although the choice to suppress decoherence is made by delayed WM after the decoherence and even after detection of the quantum system, our scheme can suppress decoherence successfully.

ResultsSchematic and theory. The delayed-choice decoherence suppression scenario is schematically shown in Fig. 1a. A two-qubit entangled state, F

j ia 00

j iAB b 11

j iAB, is prepared at the time

n

D

p 0

j iS 1

j iEg, where D is the magnitude of amplitude damping,

D 1 D and subscript S (E) refers to system (environment). As

a result, the two-qubit state becomes mixed, causing reduced entanglement quantied by concurrence, Cd

Cd2 a

j j

1 D

1 a

q :Bobs reversing measurement (RM), applied immediately after the

decoherence, is represented as RMpr

1 0 0 1

j j2

, where pr1 pr and pr is strength of the RM. Alices decision at

time tW whether to suppress the decoherence, by applying the WM on her qubit, may be made after the decoherence (tW4tD)

or even after the detection of Bobs qubit (tW4tB). Alices WM is

represented as WMp

1 0 0

pr p

0 0 1

1 0 0 1

, where p1 p and p is WM strength. The reversing measurement strength is chosen to be pr p D(1 p) (refs 20,21,23). After Alices WM

and Bobs RM, entanglement in the two-qubit is quantied by concurrence Cr (H.-T.L., J.-C.L., K.-H.H. and Y.-H.K., manuscript in preparation),

Cr

2 a

p p

j j

q

1 a

j j2

1 D 1 p

1 a

j j2

:

Note that Cr4Cd that indicates that the delayed-choice decoherence suppression scheme can successfully circumvent Markovian amplitude damping decoherence. It is worth pointing out that, since the WM and RM are both non-unitary, the success probability of our scheme is less than unity. The success probability of the delayed-choice decoherence suppression scheme is PS p

D 1 b

j j2 pD

(refs 21,23).

Experimental implementation. The experimental schematic of delayed-choice decoherence suppression is shown in Fig. 1b. The qubit is encoded in a polarization state of a single-photon: |0S |HS, |1S |VS, where |HS is horizontal polarization and

Time

a b

[afii9848]A

WM

Alice

Bob

tA tW tB

tR

tD

WM

D

RM

[afii9848]A

RM

[afii9848]B

D

[afii9848]B

Alice

Bob

Space

HWP QWP Pol. Fibre Free space

PBS BS BP

Figure 1 | Scheme for delayed-choice decoherence suppression. (a) A two-qubit entangled state is prepared and sent to Alice and Bob. In Bobs quantum channel, amplitude damping decoherence of strength D is present at time tD, causing reduction of entanglement between the two qubits.

Bob performs the RM on his qubit after the decoherence. Alices decision whether to suppress the decoherence, by applying the WM on her qubit, may be made after the decoherence or even after the detection of Bobs qubit. (b) Experimental schematic of delayed-choice decoherence suppression. BP, Brewsters angle glass plate; BS, non-polarizing beam splitter; HWP, half-wave plate; PBS, polarizing beam splitter; Pol, polarizer; QWP, quarter-wave plate.

2 NATURE COMMUNICATIONS | 5:4522 | DOI: 10.1038/ncomms5522 | http://www.nature.com/naturecommunications

Web End =www.nature.com/naturecommunications

& 2014 Macmillan Publishers Limited. All rights reserved.

NATURE COMMUNICATIONS | DOI: 10.1038/ncomms5522 ARTICLE

a

Space-like separation

a

Time

Time

Concurrence

1.0

Space-like separation

Time-like separation

WM by Alice

12.2 ns

Decoherence

on Bob

Decoherence only

Weak measurement strength (p)

6.9 ns

12.2 ns

0.50.0 0.2 0.4 0.6 0.8 1.0

1.00.80.60.40.20.00.0 0.2 0.4 0.6 0.8 1.0

Space

1.8 m

(0,0)

1.0 m

b

0.90.80.70.6

b Time-like separation

WM by Alice 2.1 s

0.4 km

Fibre spool

Time

Time

Concurrence

WM by Alice

Space-like, with WM/RM

Time-like, with WM/RM

Space-like, with D only

Time-like, with D only

0.4 km

Fibre spool

Decoherence (D)

Figure 3 | Experimental concurrence for the space-like and time-like separation experiments. (a) As a function of WM strength for D 0.617.

(b) As a function of decoherence with or without WM/RM (P 0.617). The

results show that our delayed-choice decoherence suppression scheme is able to recover entanglement. Note that both space-like and time-like separation experiments give the same results. The solid lines represent the theoretical curves for Cd and Cr. The error bars represent the statistical error of 1s.d.

Alice

Decoherence

on Bob

6.9 ns

2.1 s

Space

1.8 m

(0,0)

1.0 m

Figure 2 | Spacetime diagrams for space-like and time-like congurations. The two-qubit entangled state generation event is marked as a red star at the origin. The spatial separation between the two events, that is, the decoherence on Bobs qubit and WM on Alices qubit, isL 2.8 m. The shaded regions represent forward light cones of the events.

(a) The two events are space-like separated. The temporal difference between the two events (5.3 ns) is shorter than the time light travels between them (L/c 9.3 ns). The two events are thus not in a causal

relation, that is, no classical communication is possible between the two events. (b) The two events are time-like separated: WM on Alices qubit is in the time-like future of the decoherence event on Bobs qubit.

a

Quantum channel

with decoherence Bob

Memory

Alice Bob

Classical

communication

Alice Bob

RM

WM

N

Memory

|VS is vertical polarization. The initial two-qubit entangled state (|FS with a

j j b

j j) is prepared by using type-I spontaneous

parametric down conversion from a 6-mm thick b-BaB2O4

crystal24. The photons are frequency ltered by a set of interference lters with 5 nm bandwidth. Optical delays tA and tB are implemented with single-mode bres (SMF). Note that wave plates are used to compensate polarization rotation by SMFs at each SMF output. The Markovian amplitude damping decoherence (D) is set up with a displaced Sagnac interferometer21,23. The WM and the RM are implemented with wave plates and Brewsters angle glass plates25. The nal two-qubit state is analysed with wave plates and polarizers via two-qubit quantum state tomography23.

We implement the delayed-choice decoherence suppression scheme in two congurations, space-like separation and time-like separation, by varying the temporal delays tA and tB. The space

time diagrams for the two congurations are shown in Fig. 2. First, in Fig. 2a, we set up the temporal delays such that Alices WM and Bobs decoherence events are in space-like separation. To make sure that the delayed-choice is indeed made after the decoherence itself, we need to consider the timing resolution of the detector (0.35 ns), the coincidence time window for measuring the joint detection events (2.0 ns) and the physical dimensions of the apparatus implementing WM, RM and D. The times for the photon to traverse the apparatus implementing WM, RM and D are 0.10, 0.33 and 1.0 ns, respectively. The overall timing

b

([afii9845]d)N

TrA [[afii9845]d]m

measure D

c

([afii9845]r)(N m) Ps

Figure 4 | Entanglement distribution using delayed-choice decoherence suppression. (a) Alice shares N identical pairs of entangled qubits |FS with

Bob by a quantum channel which has amplitude damping decoherence with unknown D. Alice and Bob store their own qubits in their quantum memories for later use. (b) Bob uses m qubits to measure the magnitude of decoherence D and inform the value of D to Alice via classical communication. (c) Alice and Bob apply delayed-choice decoherence suppression scheme: Alice executes delayed WM to her qubit, while Bob makes RM to his qubit. As a result, Alice and Bob share highly entangled qubits.

NATURE COMMUNICATIONS | 5:4522 | DOI: 10.1038/ncomms5522 | http://www.nature.com/naturecommunications

Web End =www.nature.com/naturecommunications 3

& 2014 Macmillan Publishers Limited. All rights reserved.

ARTICLE NATURE COMMUNICATIONS | DOI: 10.1038/ncomms5522

uncertainty is thus 3.8 ns. Since Alices WM is made 5.3 ns after the decoherence event, it can be guaranteed that no information about Alices choice can be transferred to Bob at the time of decoherence. Furthermore, Alices WM and Bobs decoherence are physically separated by L 2.8 m, so that the time difference

between the two events is shorter than the time at which light travels between them (5.3 nsoL/c 9.3 ns). The two events are,

thus, in space-like separation as neither of the events are within the forward light cones of each other, see Fig. 2a. This ensures that no causal relationship, that is, no classical communication, can be established between the two events in this setting.

Second, we set up the apparatus such that Alices WM is in time-like future of the decoherence event on Bob, see Fig. 2b. Experimentally, we increase tA by inserting a 400-m bre spool on Alices side to achieve tA 2:1 ms. As with the space-like

separation depicted in Fig. 2a, Alices WM is made sufciently after the decoherence itself, hence no information about Alices choice can be sent back to Bobs decoherence event. In the time-like separation, however, it is possible for Bob to send classical information about the decoherence to Alice, possibly affecting Alices WM.

DiscussionThe delayed-choice decoherence suppression is demonstrated in Fig. 3. We rst xed the magnitude of decoherence to be D 0.617 and varied the WM strength p and monitored the

concurrence of the nal two-qubit state, see Fig. 3a. The concurrence increases as the WM strength increases. For both space-like separation shown in Fig. 2a and time-like separation shown in Fig. 2b, the decoherence is successfully circumvented by using our delayed-choice decoherence suppression scheme. Then we set the WM strength at P 0.617 and observe the concurrence

as D increases, see Fig. 3b. When the two-qubit system is subject to decoherence, entanglement of the system signicantly degrades as D becomes large. However, when the delayed-choice decoherence suppression scheme is applied, more entanglement is shared by Alice and Bob, as evidenced in higher concurrences (Cr4Cd). This again conrms that it is indeed possible to perform delayed-choice decoherence suppression.

Our decoherence suppression scheme can be applicable to practical entanglement distribution scenarios, an example of which is shown in Fig. 4. First, Alice generates N identical pairs of entangled qubits F

j i F

h j

N and shares it with Bob through a

quantum channel that has unknown amplitude damping decoherence in the channel, see Fig. 4a. The decoherence causes the two-qubit state to become a mixed state rd and lowers concurrence. Alice and Bob store the qubits in quantum memories to use it on demand. Alice and Bob do not know the existence of decoherence in advance and the ensemble of quantum states shared by Alice and Bob is rd

N, see Fig. 4b.

Bob then uses a small subset of his qubits TrA rd

m to estimate

the magnitude of decoherence D by monitoring the weight between |0S/0| and |1S/1|. Assuming the initial state |FS with a

j j b

j j, the quantum state of Bobs qubit after decoherence

is TrA rd

12 1 D

0

j i 0

h j 12 1 D

1

j i 1

h j. As Bob makes

m independent measurements, the variance of Bobs estimation of D is Var D

m 1 1 D2

. Bob then uses a classical

communication channel to inform the measured D value to Alice. Now, Alice and Bob share N m identical pairs of partially

entangled qubits rd

N m with known D, see Fig. 4c. The

delayed-choice decoherence suppression scheme can be applied with a reversing measurement strength rr (refs 20,21,23). As a result, the two parties now share highly entangled qubits, rr

N mPS with concurrence Cr, while the nal number of

qubits is decreased to (N m)PS due to Bobs estimation of D and

success probability PS of the scheme. Our delayed-choice decoherence suppression scheme provides a new strategy for entanglement distillation over a decoherence channel.

In summary, we have proposed and experimentally demonstrated the delayed-choice decoherence suppression in which the choice whether to suppress decoherence is made after the decoherence and even after the detection of a qubit. It is interesting to note that our delayed-choice decoherence suppression scheme allows to circumvent Markovian amplitude damping decoherence, even though the decision to suppress the decoherence made after the decoherence itself. While the demonstration in this paper utilized photonic polarization entanglement, the delayed-choice scheme demonstrated in this work can be generalized and applied to other quantum systems. Our result thus provides a new direction in tackling decoherence in a delayed manner and has important implications in practical implementations of various quantum information protocols.

References

1. Wheeler, J. A. & Zurek, W. H. (eds) Quantum Theory and Measurement (Princeton University, 1983).

2. Jacques, V. et al. Experimental realization of Wheelers delayed-choice gedanken experiment. Science 315, 966968 (2007).

3. Kim, Y.-H., Yu, R., Kulik, S. P., Shih, Y. & Scully, M. O. Delayed choice quantum eraser. Phys. Rev. Lett. 84, 15 (2000).

4. Ma, X.-S. et al. Quantum erasure with causally disconnected choice. Proc. Natl Acad. Sci. USA 110, 12211226 (2013).

5. Peruzzo, A., Shadbolt, P., Brunner, N., Popescu, S. & OBrien, J. L. A quantum delayed-choice experiment. Science 338, 634637 (2012).

6. Kaiser, F., Coudreau, T., Milman, P., Ostrowsky, D. B. & Tanzilli, S. Entanglement-enabled delayed-choice experiment. Science 338, 637640 (2012).

7. Ionicioiu, R. & Terno, D. R. Proposal for a quantum delayed-choice experiment. Phys. Rev. Lett. 107, 230406 (2011).

8. Ma, X.-S. et al. Experimental delayed-choice entanglement swapping. Nat. Phys. 8, 479484 (2012).

9. Jeong, Y.-C., Di Franco, C., Lim, H.-T., Kim, M. S. & Kim, Y.-H. Experimental realization of a delayed-choice quantum walk. Nat. Commun. 4, 2471 (2013).

10. Berta, M., Christandl, M., Colbeck, R., Renes, J. M. & Renner, R. The uncertainty principle in the presence of quantum memory. Nat. Phys. 6, 659662 (2010).

11. Li, C.-F., Xu, J.-S., Xu, X.-Y., Li, K. & Guo, G.-C. Experimental investigation of the entanglement-assisted entropic uncertainty principle. Nat. Phys. 7, 752756 (2011).

12. Prevedel, R., Hamel, D. R., Colbeck, R., Fisher, K. & Resch, K. J. Experimental investigation of the uncertainty principle in the presence of quantum memory and its application to witnessing entanglement. Nat. Phys. 7, 757761 (2011).

13. Nielsen, M. & Chuang, I. Quantum Computation and Quantum Information (Cambridge University Press, 2000).

14. Zurek, W. H. Decoherence, einselection, and the quantum origins of the classical. Rev. Mod. Phys. 75, 715775 (2003).

15. Almeida, M. P. et al. Environment-induced sudden death of entanglement. Science 316, 579582 (2007).

16. Xu, J.-S. et al. Measurement-induced quantum coherence recovery. New J. Phys. 11, 043010 (2009).

17. Xu, X.-Y., Xu, J.-S., Li, C.-F. & Guo, G.-C. Measurement-induced quantum entanglement recovery. Phys. Rev. A 82, 022324 (2010).

18. Biercuk, M. J. et al. Optimized dynamical decoupling in a model quantum memory. Nature 458, 9961000 (2009).

19. Du, J. et al. Preserving electron spin coherence in solids by optimal dynamical decoupling. Nature 461, 12651268 (2009).

20. Korotkov, A. N. & Keane, K. Decoherence suppression by quantum measurement reversal. Phys. Rev. A 81, 040103(R) (2010).

21. Lee, J.-C., Jeong, Y.-C., Kim, Y.-S. & Kim, Y.-H. Experimental demonstration of decoherence suppression via quantum measurement reversal. Opt. Express 19, 1630916316 (2011).

22. Sun, Q., Al-Amri, M., Davidovich, L. & Zubairy, M. S. Reversing entanglement change by a weak measurement. Phys. Rev. A 82, 052323 (2010).

23. Kim, Y.-S., Lee, J.-C., Kwon, O. & Kim, Y.-H. Protecting entanglement from decoherence using weak measurement and quantum measurement reversal. Nat. Phys. 8, 117120 (2012).

4 NATURE COMMUNICATIONS | 5:4522 | DOI: 10.1038/ncomms5522 | http://www.nature.com/naturecommunications

Web End =www.nature.com/naturecommunications

& 2014 Macmillan Publishers Limited. All rights reserved.

NATURE COMMUNICATIONS | DOI: 10.1038/ncomms5522 ARTICLE

24. Shih, Y. H. & Alley, C. O. New type of Einstein-Podolsky-Rosen-Bohm experiment using pairs of light quanta produced by optical parametric down conversion. Phys. Rev. Lett. 61, 29212924 (1988).

25. Kim, Y.-S., Cho, Y.-W., Ra, Y.-S. & Kim, Y.-H. Reversing the weak quantum measurement for a photonic qubit. Opt. Express 17, 1197811985 (2009).

Acknowledgements

This work was supported in part by the National Research Foundation of Korea

(Grant No. 2011-0021452 and No. 2013R1A2A1A01006029). J.-C.L. and H.-T.L.

acknowledge support from the National Junior Research Fellowship (Grant No.

2012-000741 and 2012-000642, respectively). Y.-C.J. acknowledges support from

BK21. M.S.K. acknowledges support from UK EPSRC. M.S.K. thanks M. Genoni for

discussions.

Author contributions

M.S.K. and Y.-H.K. conceived the idea; J.-C.L., H.-T.L., and Y.-H.K. further developed

the idea and designed the experiment; J.-C.L., H.-T.L. and K.-H.H. carried out the

experiment with the help of Y.-C.J. under the supervision of Y.-H.K.; J.-C.L., H.-T.L.,

K.-H.H. and Y.-H.K. analysed the data; all authors discussed the results and contributed

to writing the manuscript.

Additional information

Competing nancial interests: The authors declare no competing nancial interests. Reprints and permission information is available online at http://npg.nature.com/reprintsandpermissions/

Web End =http://npg.nature.com/

http://npg.nature.com/reprintsandpermissions/

Web End =reprintsandpermissions/

How to cite this article: Lee, J.-C. et al. Experimental demonstration of

delayed-choice decoherence suppression. Nat. Commun. 5:4522

doi: 10.1038/ncomms5522 (2014).

NATURE COMMUNICATIONS | 5:4522 | DOI: 10.1038/ncomms5522 | http://www.nature.com/naturecommunications

Web End =www.nature.com/naturecommunications 5

& 2014 Macmillan Publishers Limited. All rights reserved.