## Sagnac secret sharing over telecom fiber networks

Optics Express, Vol. 17, Issue 2, pp. 1055-1063 (2009)

http://dx.doi.org/10.1364/OE.17.001055

Acrobat PDF (114 KB)

### Abstract

We report the first Sagnac quantum secret sharing (in three-and four-party implementations) over 1550 nm single mode fiber (SMF) networks, using a single qubit protocol with phase encoding. Our secret sharing experiment has been based on a single qubit protocol, which has opened the door to practical secret sharing implementation over fiber telecom channels and in free-space. The previous quantum secret sharing proposals were based on multiparticle entangled states, difficult in the practical implementation and not scalable. Our experimental data in the three-party implementation show stable (in regards to birefringence drift) quantum secret sharing transmissions at the total Sagnac transmission loop distances of 55-75 km with the quantum bit error rates (QBER) of 2.3-2.4% for the mean photon number *μ* = 0.1 and 1.7-2.1% for *μ* = 0.3. In the four-party case we have achieved quantum secret sharing transmissions at the total Sagnac transmission loop distances of 45-55 km with the quantum bit error rates (QBER) of 3.0-3.7% for the mean photon number *μ* = 0.1 and 1.8-3.0% for *μ* = 0.3. The stability of quantum transmission has been achieved thanks to our new concept for compensation of SMF birefringence effects in Sagnac, based on a polarization control system and a polarization insensitive phase modulator. The measurement results have showed feasibility of quantum secret sharing over telecom fiber networks in Sagnac configuration, using standard fiber telecom components.

© 2009 Optical Society of America

## 1. Introduction

2. M. Hillery, V. Buzek, and A. Berthiaume, “Quantum secret sharing,” Phys. Rev. A **59**, 1829–1834 (1999). [CrossRef]

3. R. Cleve, D. Gottesmann, and H.-K. Lo, “How to Share a Quantum Secret,” Phys. Rev. Lett. **83**, 648–651 (1999). [CrossRef]

4. W. Tittel, H. Zbinden, and N. Gisin, “Experimental demonstration of quantum secret sharing,” Phys. Rev. A **63**, 042301–042306 (2001). [CrossRef]

5. Y. A. Chen, A. N. Zhang, Z. Zhao, X. Q. Zhou, C. Y. Lu, C. Z. Peng, T. Yang, and J. W. Pan, “Experimental quantum secret sharing and third-man quantum cryptography,” Phys. Rev. Lett. **95**, 200502.1*–*200502.4 (2005). [CrossRef]

6. S. Gaertner, C. Kurtsiefer, M. Bourennane, and H. Weinfurter, “Experimental Demonstration of four-party quantum secret sharing,” Phys. Rev. Lett. **98**, 020503.1*–*020503.4 (2007). [CrossRef]

7. C. Schmid, P. Trojek, H. Weinfurter, M. Bourennane, M. Zukowski, and C. Kurtsiefer, “Experimental single qubit quantum secret sharing,” Phys. Rev. Lett. **95**, 230505.1*–*230505.4 (2005). [CrossRef]

*R*

_{1},…,

*R*[7

_{N}7. C. Schmid, P. Trojek, H. Weinfurter, M. Bourennane, M. Zukowski, and C. Kurtsiefer, “Experimental single qubit quantum secret sharing,” Phys. Rev. Lett. **95**, 230505.1*–*230505.4 (2005). [CrossRef]

*x*⟩ = (|0⟩ + |1⟩)/ √2 by the party

*R*

_{1}and is sent sequentially, from

*R*

_{1}to

*R*, over the quantum channel, until it is measured by the last party

_{N}*R*. Each party

_{N}*R*(

_{i}*i*= 1, …,

*N*- 1) modulates the photon with a randomly chosen phase

*ϕ*equal to 0,

_{i}*π*/2,

*π*, or 3

*π*/2 through the unitary phase operator

*R*

_{1},

*R*

_{2},…, and

*R*

_{N-1}modulating phase choices {0,

*π*/2,

*π*,3

*π*/2} can be assigned into two bases {0,

*π*} and {

*π*/2,3

*π*/2}. The

*R*party’s phase modulation choice

_{N}*ϕ*are two phases only: 0 (which belongs to the basis {0,

_{N}*π*}) and

*π*/2 (which belongs to the basis {

*π*/2,3

*π*/2}). The probability that

*R*detects the state |±

_{N}*x*⟩ = (|0⟩ ± |1⟩)/√2 is

7. C. Schmid, P. Trojek, H. Weinfurter, M. Bourennane, M. Zukowski, and C. Kurtsiefer, “Experimental single qubit quantum secret sharing,” Phys. Rev. Lett. **95**, 230505.1*–*230505.4 (2005). [CrossRef]

## 2. Experimental setup

### 2.1. System configuration

*PM*); a 50/50 coupler (

_{A}*C*

_{3}) dividing the weak laser pulses into clockwise and counterclockwise parts; two interferometers (

*INT*

_{1}and

*INT*

_{2}); and two single photon detectors (

*SPD*

_{1}and (

*SPD*

_{2}) connected to the

*C*

_{3}coupler’s outputs. The detectors (

*PGA*600 from Princeton Lightwave Inc.) implement InGaAs avalanche photodiodes. They provide quantum efficiency of 20% and 10

^{−5}dark count probability per 1 ns gating pulse.

*INT*

_{2}contains a polarizing beam splitter (

*PBS*

_{2}) and a 50/50 coupler (

*C*

_{2}). The interferometer

*INT*

_{1}has additionally a fiber stretcher (from General Photonics Inc.), controlled by the NI6602, a digital acquisition card (DAQ) from National Instrument, and a delay line, which length is matched to stretcher’s fiber length of 18 m. The interferometers are used for removing the different SMF birefringence effects on the clockwise and counterclockwise pulses by converting their polarization (into the horizontal one) after they have propagated over the Sagnac loop and arrived back to Alice’s station. The conversion is necessary since the birefringent SMF channel differently changes polarization of the clockwise and counterclockwise pulses, which would decrease interference visibility in the coupler

*C*

_{3}. Stretcher’s main function is to minimize the amount of energy losses [9

9. A. Kuzin, H. Cerecedo Nez, and N. Korneev, “Alignment of a birefringent fiber Sagnac interferometer by fiber twist,” Opt. Commun. **160**, 37*–*41 (1999). [CrossRef]

10. B. Ibarra-Escamilla, E. A. Kuzin, O. Pottiez, J. W. Haus, F. Gutierrez-Zainos, R. Grajales-Coutin, and P. Zaca-Moran, “Fiber optical loop mirror with a symmetrical coupler nand a quarter-wave retarder plate in the loop,” Opt. Commun. **242**, 191–197 (2004). [CrossRef]

*C*

_{1}and

*C*

_{2}arms that are not connected into the coupler

*C*

_{3}. This energy loss is monitored by an additional single photon detector ((

*SPD*

_{3}) connected to the coupler

*C*

_{1}. The detector’s output is read, once per second, by the NI6602 DAQ card, programmed in LabView. After the reading process, a simple proportional–integral–derivative (PID) controller in LabView, working in one second long time frames, adjusts stretcher’s length (thus the phase of the signal in stretcher’s arm) in order to minimize the interference losses in the couplers

*C*

_{1}and

*C*

_{2}.

*PBS*

_{1}and

*PBS*

_{2}are aligned to the horizontal axis as well as the interconnecting fiber cords.

*C*

_{3}into clockwise and counterclockwise parts. The pulses are sent by Alice as a high-speed burst by burst-pulsing the laser driver with the aid of a programmable pulse generator (PG9528 from Quantum Composers Inc.). Alice waits with a new burst sending until all the burst pulses have been transmitted over the Sagnac loop. The duty cycle (20% in our setup with 400 active and 1600 inactive pulses) of the burst should be chosen in such a way that only the clockwise pulses are phase modulated in Charlie’s and David’s stations while the counterclockwise ones are modulated in Bob’s and Alice’s station (see Fig. 2 showing, with the arrows, directions of the phase modulation). The duty cycle of 20% gives the system’s effective pulsing rate of 400 kHz.

*PM*and Bob’s

_{A}*PM*have to be kept inactive during the clockwise pulse’s passage through Sagnac loop. First at the output of Charlie’s station the pulses are phase modulated and their energy is set to a single photon level [14

_{B}14. N. Gisin, G. Ribordy, W. Tittel, and H. Zbinden, “Quantum cryptography,” Rev. Mod. Phys. **74**, 145–195 (2002). [CrossRef]

*P*(

*n*> 1) ≃

*μ*/2, where

*μ*is the mean photon number. By adjusting the pulse attenuation it is possible to limit the probability that a non-empty weak pulse contains more than one photon to an arbitrary small number. Assuming the attenuation giving one single photon for ten laser pulses (

*μ*= 0.1) we are getting

*P*(

*n*> 1) ≃

*μ*/2 = 0.05, a low number. It should be pointed out that to the total attenuation of the pulses contribute not only the fiber spools and digital attenuator, but also other setup components such as Alice’s PM, PBS, and circulator as well as the other party stations (Bob’s, Charlie’s, and David’s).

### 2.2. Polarization insensitive phase modulator

*INT*

_{1}and

*INT*

_{2}(see Fig. 2) are generally elliptically polarized. However, their polarization changes along the setup’s transmission path since the SMF is birefringent. It differently changes polarization of the clockwise and counterclockwise pulses so they would arrive back to the coupler

*C*

_{3}, (after their propagation over the Sagnac loop) at different polarization states, which would decrease the interference visibility. In order to avoid it the interferometers

*INT*

_{1}and

*INT*

_{2}are used for the polarization back conversion into the horizontal one, which is necessary since all Alice’s station components, including its phase modulator (

*PM*), are polarization maintaining and aligned horizontally. As mentioned above, the standard telecom phase modulator (

_{A}*PM*) is used at Alice’s station. However, at the party stations there is a need of polarization insensitive phase modulators since the SMF channel’s birefringence would cause significant, slowly varying, transmittance changes of the standard telecom phase modulators (usually based on a

_{A}*LiNbO*

_{3}crystal).

14. N. Gisin, G. Ribordy, W. Tittel, and H. Zbinden, “Quantum cryptography,” Rev. Mod. Phys. **74**, 145–195 (2002). [CrossRef]

*μ*.

*PBS*and

_{A}*PBS*. The design’s working principle is simple: it splits horizontal and vertical polarization components into two separately controlled phase modulators.

_{B}*PBS*. The pulse’s horizontal polarization component will be transmitted into the port T, while the vertical one will be ”reflected” into the port R and rotated 90° to the horizontal polarization. Thus, both horizontally aligned components can be transmitted (and modulated) by the phase modulators

_{A}*PM*

_{1}and

*PM*

_{2}. The outputs of the modulators are connected to the

*PBS*, which recreate the original light pulse polarization. The design is bidirectional, which makes it possible to implement it in our setup. Both phase modulators, with a

_{B}*V*around 3 Volts, are controlled by the same pulse generator (PG9528). The design guarantees a stable, polarization insensitive optical insertion loss of 5.0 dB.

_{π}### 2.3. Transmission and error rates

*Rate*=

_{raw}*qμfη*, where

_{det}η_{link}*q*is a setup dependent coefficient,

*μ*is the mean photon number per pulse,

*f*is the laser pulsing frequency,

*η*is the probability of the photon being detected, and

_{det}*η*is the transfer efficiency of the Sagnac loop. The factor

_{link}*q*= 0.5 in our setup since only in 50% of all the measurement cases the measurement basis are coincidental.

*QBER*=

*QBER*+

_{opt}*QBER*=

_{det}*P*+

_{opt}*P*/

_{noise}*P*=

_{photon}*P*+

_{opt}*P*/

_{noise}*μη*, where

_{det}μ_{link}*p*is the probability of a photon going to the wrong detector, and

_{opt}*p*is the probability of getting a noise-count (mainly dark counts) per gating pulse window [13

_{noise}13. D. Stucki, N. Gisin, O. Guinnard, G. Ribordy, and H. Zibiden, “Quantum key distribution over 67 km with a plug & play system,” New J. Phys. **4**, 41.1–41.8 (2002). [CrossRef]

14. N. Gisin, G. Ribordy, W. Tittel, and H. Zbinden, “Quantum cryptography,” Rev. Mod. Phys. **74**, 145–195 (2002). [CrossRef]

*P*= (1 −

_{opt}*V*)/2, where

*V*is the interference visibility.

## 3. Experiment data

**74**, 145–195 (2002). [CrossRef]

*μ*= 0.1 and

*μ*= 0.3. The laser pulse repetition rate was 2 MHz (the rate has been limited by the single photon detectors’ afterpulsing effect). The laser pulsing duty cycle of 20% gives the system’s effective rate of 400 kHz.

*μ*= 0.1 and

*μ*= 0.3 in the three-party and four-party configurations, respectively. In the three-party implementation we have achieved stable (in regards to birefringence drift) quantum secret sharing transmissions at the total Sagnac transmission loop distances of 55-75 km with the quantum bit error rates (QBER) of 2.3-2.4% for the mean photon number

*μ*= 0.1 and 1.7-2.1% for

*μ*= 0.3. The achieved raw transmission rates were of 1275–1954 Hz for

*μ*= 0.1 and 3684–6488 Hz for

*μ*= 0.3. In the four-party configuration we have achieved the total Sagnac transmission loop distances of 45-55 km with QBER of 3.0-3.7% for

*μ*= 0.1 and 1.8-3.0% for

*μ*= 0.3. The achieved raw transmission rates were of 844–504 Hz for

*μ*= 0.1 and 2794–1537 Hz for

*μ*= 0.3.

## 4. Conclusion

*μ*= 0.1 and 1.7-2.1% for

*μ*= 0.3. The achieved raw transmission rates were of 1275–1954 Hz for

*μ*= 0.1. For

*μ*= 0.3 the rates were of 3684–6488 Hz. In the four-party configuration we have achieved the total Sagnac transmission loop distances of 45-55 km with QBER of 3.0-3.7% for

*μ*= 0.1 and 1.8-3.0% for

*μ*= 0.3. The achieved raw transmission rates were of 844–504 Hz for

*μ*= 0.1 and 2794–1537 Hz for

*μ*= 0.3.

16. H. Takesue, S. W. Nam, Q. Zhang, R. H. Hadfield, T. Honjo, K. Tamaki, and Y. Yamamoto, “Quantum key distribution over a 40-dB channel loss using superconducting single-photon detectors,” Nature Photonics **1**, 343–348 (2007)
[CrossRef]

17. E. Udd, “Sensing and instrumentation applications of the Sagnac fiber optic interferometer,” Proc. SPIE **2341**, 52–59 (1994). [CrossRef]

## Acknowledgment

## References and links

1. | B. Schneier, |

2. | M. Hillery, V. Buzek, and A. Berthiaume, “Quantum secret sharing,” Phys. Rev. A |

3. | R. Cleve, D. Gottesmann, and H.-K. Lo, “How to Share a Quantum Secret,” Phys. Rev. Lett. |

4. | W. Tittel, H. Zbinden, and N. Gisin, “Experimental demonstration of quantum secret sharing,” Phys. Rev. A |

5. | Y. A. Chen, A. N. Zhang, Z. Zhao, X. Q. Zhou, C. Y. Lu, C. Z. Peng, T. Yang, and J. W. Pan, “Experimental quantum secret sharing and third-man quantum cryptography,” Phys. Rev. Lett. |

6. | S. Gaertner, C. Kurtsiefer, M. Bourennane, and H. Weinfurter, “Experimental Demonstration of four-party quantum secret sharing,” Phys. Rev. Lett. |

7. | C. Schmid, P. Trojek, H. Weinfurter, M. Bourennane, M. Zukowski, and C. Kurtsiefer, “Experimental single qubit quantum secret sharing,” Phys. Rev. Lett. |

8. | C. Schmid, P. Trojek, M. Bourennane, C. Kurtsiefer, M. Zukowski, and H. Weinfurter, “Comment on experimental single qubit quantum secret sharing,” Phys. Rev. Lett. |

9. | A. Kuzin, H. Cerecedo Nez, and N. Korneev, “Alignment of a birefringent fiber Sagnac interferometer by fiber twist,” Opt. Commun. |

10. | B. Ibarra-Escamilla, E. A. Kuzin, O. Pottiez, J. W. Haus, F. Gutierrez-Zainos, R. Grajales-Coutin, and P. Zaca-Moran, “Fiber optical loop mirror with a symmetrical coupler nand a quarter-wave retarder plate in the loop,” Opt. Commun. |

11. | D. B. Mortimore, “Fiber loop reflectors,” Opt. Commun. |

12. | C. Tsao, “Optical fibre waveguide analysis” (Oxford Science Publ.1992). |

13. | D. Stucki, N. Gisin, O. Guinnard, G. Ribordy, and H. Zibiden, “Quantum key distribution over 67 km with a plug & play system,” New J. Phys. |

14. | N. Gisin, G. Ribordy, W. Tittel, and H. Zbinden, “Quantum cryptography,” Rev. Mod. Phys. |

15. | G. Ribordy, J. D. Gautier, N. Gisin, O. Guinnard, and H. Zbinden, “Fast and user-friendly quantum key distribution,” J. Mod. Opt. |

16. | H. Takesue, S. W. Nam, Q. Zhang, R. H. Hadfield, T. Honjo, K. Tamaki, and Y. Yamamoto, “Quantum key distribution over a 40-dB channel loss using superconducting single-photon detectors,” Nature Photonics |

17. | E. Udd, “Sensing and instrumentation applications of the Sagnac fiber optic interferometer,” Proc. SPIE |

**OCIS Codes**

(040.5570) Detectors : Quantum detectors

(060.4080) Fiber optics and optical communications : Modulation

(040.1345) Detectors : Avalanche photodiodes (APDs)

(270.5565) Quantum optics : Quantum communications

(270.5568) Quantum optics : Quantum cryptography

(060.3510) Fiber optics and optical communications : Lasers, fiber

**ToC Category:**

Quantum Optics

**History**

Original Manuscript: October 1, 2008

Revised Manuscript: November 21, 2008

Manuscript Accepted: November 28, 2008

Published: January 15, 2009

**Citation**

Jan Bogdanski, Johan Ahrens, and Mohamed Bourennane, "Sagnac secret sharing over telecom fiber networks," Opt. Express **17**, 1055-1063 (2009)

http://www.opticsinfobase.org/oe/abstract.cfm?URI=oe-17-2-1055

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### References

- B. Schneier, Applied Cryptography (John Wiley & Sons, Inc. 1996).
- M. Hillery, V. Buzek, and A. Berthiaume, "Quantum secret sharing," Phys. Rev. A 59, 1829-1834 (1999). [CrossRef]
- R. Cleve, D. Gottesmann, and H.-K. Lo, "How to Share a Quantum Secret," Phys. Rev. Lett. 83, 648-651 (1999). [CrossRef]
- W. Tittel, H. Zbinden, and N. Gisin, "Experimental demonstration of quantum secret sharing," Phys. Rev. A 63, 042301-042306 (2001). [CrossRef]
- Y. A. Chen, A. N. Zhang, Z. Zhao, X. Q. Zhou, C. Y. Lu, C. Z. Peng, T. Yang, and J. W. Pan, "Experimental quantum secret sharing and third-man quantum cryptography," Phys. Rev. Lett. 95, 200502.1-200502.4 (2005). [CrossRef]
- S. Gaertner, C. Kurtsiefer, M. Bourennane, and H. Weinfurter, "Experimental demonstration of four-party quantum secret sharing," Phys. Rev. Lett. 98, 020503.1-020503.4 (2007). [CrossRef]
- C. Schmid, P. Trojek, H. Weinfurter, M. Bourennane, M. Zukowski, and C. Kurtsiefer, "Experimental single qubit quantum secret sharing," Phys. Rev. Lett. 95, 230505.1-230505.4 (2005). [CrossRef]
- C. Schmid, P. Trojek, M . Bourennane, C . Kurtsiefer, M . Zukowski, and H . Weinfurter, "Comment on experimental single qubit quantum secret sharing," Phys. Rev. Lett. 98, 028901.1 (2007).
- A. Kuzin, H. Cerecedo Nez, and N. Korneev, "Alignment of a birefringent fiber Sagnac interferometer by fiber twist," Opt. Commun. 160, 37-41 (1999). [CrossRef]
- B. Ibarra-Escamilla, E. A. Kuzin, O. Pottiez, J. W. Haus, F. Gutierrez-Zainos, R. Grajales-Coutin, and P. Zaca-Moran, "Fiber optical loop mirror with a symmetrical coupler nand a quarter-wave retarder plate in the loop," Opt. Commun. 242, 191-197 (2004). [CrossRef]
- D. B. Mortimore, "Fiber loop reflectors," Opt. Commun. 6, 1217-1224 (1988).
- C. Tsao, Optical fibre waveguide analysis, (Oxford Science Publ. 1992).
- D. Stucki, N. Gisin, O. Guinnard, G. Ribordy, and H. Zibiden, "Quantum key distribution over 67 km with a plug and play system," New J. Phys. 4,41.1-41.8 (2002). [CrossRef]
- N. Gisin, G. Ribordy, W. Tittel, and H. Zbinden, "Quantum cryptography," Rev. Mod. Phys. 74, 145-195 (2002). [CrossRef]
- G. Ribordy, J. D. Gautier, N. Gisin, O. Guinnard, and H. Zbinden, "Fast and user-friendly quantum key distribution," J. Mod. Opt. 47, 517-531 (2000).
- H. Takesue, S. W. Nam, Q. Zhang, R. H. Hadfield, T. Honjo, K. Tamaki, and Y. Yamamoto, "Quantum key distribution over a 40-dB channel loss using superconducting single-photon detectors," Nat. Photonics 1, 343-348 (2007) [CrossRef]
- E. Udd, "Sensing and instrumentation applications of the Sagnac fiber optic interferometer," Proc. SPIE 2341, 52-59 (1994). [CrossRef]

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