Entanglement purification and faithful qubit transmission

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Entanglement purification and faithful qubit
transmission
Fu-Guo Deng (? ? ?)
Department of Physics, Beijing Normal University,
Beijing 100875
2010. 8. 5, Dalian
2
collaborators

• Yu-Bo Sheng,
• ???
• (Tsinghua Unversity)
• Postdoc.

Hong-Yu Zhou ??? (Beijing Normal Unversity)
Xi-Han Li, ??? (Chongqing Unversity) ????
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Outline

• 1. Motivation

2. Entanglement purification
3. Faithful qubit transmission
4. Summary
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1. Motivation
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R. Ursin et al,Entanglement-based quantum
communication over 144km, University of
Vienna,Nature Physics 3481-484 (2007)
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• Long-distance quantum communication

Quantum repeater
Entanglement a) Generation b) Distribution c)
Purification d) Swapping e) Storage
Briegel et al., Phys. Rev. Lett. 81, 5932 (1998)
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Quantum repeater

• Single-photon quantum repeater

L.M. Duan et al., Nature 414, 413 (2001)
two-photon quantum repeater
B. Zhao et al., Phys. Rev. Lett. 98, 240502
(2007) Z. B. Chen et al., Phys. Rev. A 76, 022329
(2007)
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• ????????????,???????????????????,?????????????
  ???????????????????????????????,????????????

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Entanglement purification
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?????????????
Entanglement concentration
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two-photon entanglement purification and
concentration

1. C. H. Bennett, et al., Phys. Rev. Lett. 76, 722
   (1996).
2. D. Deutsch et al., Phys. Rev. Lett. 77, 2818
   (1996).
3. J. W. Pan et al., Nature (London) 410, 1067
   (2001).
4. C. Simon, J. W. Pan, Phys. Rev. Lett. 89, 257901
   (2002).
5. Y. B. Sheng, F. G. Deng, H. Y. Zhou, Phys. Rev. A
   77, 042308 (2008).
6. Y. B. Sheng, F. G. Deng, Phys. Rev. A 81, 032307
   (2010).

(a) C. H. Bennett, et al., Phys. Rev. A 53,
2046 (1996). (b) T. Yamamoto, et al., Phys.
Rev. A 64, 012304 (2001). (c) Z. Zhao, J. W.
Pan, M. S. Zhan, Phys. Rev. A 64, 014301
(2001). (d) Y. B. Sheng, F. G. Deng, H. Y.
Zhou, Phys. Rev. A 77, 062325 (2008).
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• Single-photon entanglement purification and
  concentration

After entanglement generation
Partial entanglement state
(a) N. Sangouard, C. Simon, T. Coudreau, N.
Gisin, Purification of single-photon
entanglement with linear optics, Phys. Rev.
A 78, 50301(R) (2008).
(b) Y. B. Sheng, F. G. Deng, H. Y. Zhou,
Single-photon entanglement concentration for
long-distance quantum communication,
Quantum information computation 10, 272 (2010).
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(1) EPP based on CNOT gates
2. Entanglement purification protocol (EPP)
Charles H. Bennett. et al., Phys. Rev. Lett.
76, 722 (1996)
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???CNOT?????
D. Deutsch et al., Phys. Rev. Lett. 77, 2818
(1996)
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(2) EPP based on linear optical elements
J. W. Pan et al., Nature 410, 1067 (2001)
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(3) EPP based on spatial entanglement
????
????
C. Simon, Jian-Wei Pan, Phys. Rev. Lett. 89,
257901 (2002)
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????????????????????????,??????????,??????????
???????,??????????,????????????????
??????????,???????,?????????????????,???????????
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(4) EPP based on cross-Kerr nonlinearity

• a. The principle of cross-Kerr nonlinearity

b. The principle of PDC entanglement source
Yu-Bo Sheng, Fu-Guo Deng, Hong-Yu Zhou, Phys.
Rev. A 77,  042308 (2008)
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• QND based cross-Kerr nonlinearity for parity
  check

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bit-flip error

• After parity-check measurement with QND

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• Two photon pairs

No errors
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• A bit-flip error on one of the two pairs

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Bit-flip errors take place on the two photon
pairs
fidelity
p1the probability for one photon pair from
PDC p2two photon pairs F0the fidelity of the
original state transmitted
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Entanglement purification for an ideal source
(PDC??????)
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??PBS??? ?????? ????
????!??PBS?? ???????????
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(5) Deterministic entanglement purification (DEPP)

• Difference between conventional EPPs (CEPP) and
  DEPP

CEPP(???????)
??????????????,???????????????????
DEPP
??????????????,??????????????
Yu-Bo Sheng, Fu-Guo Deng, Phys. Rev. A 81, 032307
(2010)
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Hyperentanglement state

• After transformation in a noisy channel, the
  whole state

• The part of polarization

Mixed state
The part of frequency and spatial, do not
suffer from the noise
Robust
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Four admixtures
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a) bit-flip error purification
No error
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Bit-flip error
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• has the same result with

has the same result with
With different phase shifts and output modes, the
two parties in quantum communication can exactly
correct the bit-flip error.
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b) phase-flip error purification
WDM leads the photon to different spatial mode
according to its frequency

• After first step, the initial state will become

The spatial entanglement has consumed

• The part of polarization

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Finally, the two parties will get a maximally
entangled state

• or

Using quantum frequency upconversion, the two
parties can erase distinguishability for
frequency
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3. Faithful qubit transmission
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????

• ????????????????????
• ??????????? VS ????
• ?????(Quantum Error Correction Code-QECC)
• ????(Entanglement purification)
• ????????(Decoherence Free Subspace-DFS)
• ???????
• ????(collective noise)??
• ?????????,?????????????????????????????????????

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(1) ??????????????
????1. ??????2. ????,1/16?1/8
T. Yamamoto. et al. (Japan),Phys. Rev. Lett.
95, 040503 (2005)
1. ??????????? 2. ???? PRL95 ???? 4 ?,?? 1/2
Xi-Han Li, et al., Opt. Commun. 282, 4025 (2009)
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?????????
T. Yamamoto. et al ,Experimental
ancilla-assisted qubit transmission against
correlated noise using quantum parity
checking, New J. Phys. 9191 (2007)
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(2) ?????????
Xi-Han Li, Fu-Guo Deng, Hong-Yu Zhou,Appl. Phys.
Lett.  91, 144101 (2007)
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Success probability 1/2
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General self-error-rejecting qubit transmission
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PS75
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Fu-Guo Deng, Xi-Han Li, Hong-Yu Zhou,2010
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(3) Faithful entanglement distribution
Initial state
Collective noise channel
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Coupled with coherent states
????????????,????????????,????????????
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Entanglement transformation
Yu-Bo Sheng, Fu-Guo Deng, Phys. Rev. A 81,
042332 (2010)
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Faithful entanglement distribution for quantum
key distribution
Hui-Chong Niu, Fu-Guo Deng, 2010
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Summary

• 1. Entanglement purification based nonlinear
  optics.

2. Deterministic entanglement purification .
3. Self-error-rejecting qubit transmission.
4. Faithful entanglement distribution.
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• ????!