## Full polarization control for fiber optical quantum communication systems using polarization encoding

Optics Express, Vol. 16, Issue 3, pp. 1867-1873 (2008)

http://dx.doi.org/10.1364/OE.16.001867

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### Abstract

A real-time polarization control system employing two non-orthogonal reference signals multiplexed in either time or wavelength with the data signal is presented. It is shown, theoretically and experimentally, that complete control of multiple polarization states can be attained employing polarization controllers in closed-loop configuration. Experimental results on the wavelength multiplexing setup show that negligible added penalties, corresponding to an average added optical Quantum Bit Error Rate of 0.044%, can be achieved with response times smaller than 10 ms, without significant introduction of noise counts in the quantum channel.

© 2008 Optical Society of America

## 1. Introduction

1. N. Gisin, J. P. von der Weid, and J. P. Pellaux, “Polarization mode dispersion in long and short single mode fibers,” J. Lightwave Tech. **9**, 821–827 (1991). [CrossRef]

2. M. Martinelli, P. Martelli, and S. M. Pietralunga, “Polarization stabilization in optical communication systems,” J. Lightwave Technol. **24**, 4172–4183 (2006). [CrossRef]

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

## 2. Theory

*S*

_{1}and

*S*

_{3}, are sent across the fiber as reference states. One can choose, for instance, without loss of generality, the horizontal and +45° linear polarization states, respectively, which are canonically conjugate non-orthogonal states. At the end of the fiber we place a polarization controller which performs a series of two rotations,

*R*

_{1}and

*R*

_{3}, bringing the output SOP into the desired state. Calling

*T*the Jones matrix representing the transformation over the fiber, our control system requires that the following system of equations holds:

*R*

_{1}and

*R*

_{3}cancel out the effects due to birefringence in the fiber for the input SOPs

*S*

_{1}and

*S*

_{3}, respectively. Note that

*R*

_{3}does not have any effect upon

*S*

_{1}, which means that it is a rotation around the axis, in the Poincaré sphere, defined by

*S*

_{1}and its orthogonal state. The first two lines of Eq. (1) can be rewritten in matrix form as follows:

*ϕ*and

*θ*can take any value between 0 and 2

*π*. Combining this result with the third line of Eq. (1), we get:

*θ*+

*ϕ*=0 mod 2π. This means that

*R*

_{3}

*R*

_{1}

*T*must be equal to the identity, or equivalently,

*R*

_{3}

*R*

_{1}=

*T*

^{-1}, which clearly shows that the effect of the polarization controller is to nullify the polarization rotations generated by

*T*. Any polarization state passing through the fiber and the two rotators

*R*

_{1}and

*R*

_{3}will be preserved. Of course, signal and references have all the same optical frequency and the control system must distinguish between them to perform the correct rotations at each controller. This is easily done either by time multiplexing references and signal or by dithering the signal and references at different frequencies and filtering at the receiver.

5. S. Sauge, M. Swillo, S. Albert-Seifried, G. B. Xavier, J. Waldebäck, M. Tengner, D. Ljunggren, and A. Karlsson, “Narrowband polarization-entangled photon pairs distributed over a WDM link for qubit networks,” Opt. Express , **15**, 6926–6933 (2007). [CrossRef] [PubMed]

*S*

_{2}, and the two reference channels

*S*

_{1}and

*S*

_{3}. However, we will show that if the PMD of the fiber is not too high, good quality control can be achieved.

*S*

_{2}of a signal at wavelength

*ω*

_{0}to be controlled by employing reference signals at

*S*

_{1}and

*S*

_{3}at different wavelengths, given by

*ω*

_{1}=

*ω*

_{0}-Δ

*ω*and

*ω*

_{3}=

*ω*

_{0}+Δ

*ω*. It is also important to stress the dependence of

*T*on the wavelength, thus we write

*T*=

*T*(

*ω*). Hence, we get a new system, similarly to Eq. (1):

*T*(

*ω*

_{3})=

*T*(

*ω*

_{1})+2Δ

*ω*(

*∂T*/

*∂ω*) we get:

*T*

^{-1}and

*∂T*/

*∂ω*are calculated at

*ω*

_{1}. The same solution found for the monochromatic case, i.e.

*θ*+

*ϕ*=0 mod 2π, is still valid if the condition below holds:

*τ*/2 [6

6. B. L. Heffner, “Automated measurement of polarization mode dispersion using Jones Matrix Eigenanalysis”. IEEE Photon. Technol. Lett. **4**, 1066–1069 (1992). [CrossRef]

*τ*Δ

*ω*≪1.

## 3. Experiment

*R*

_{1}and

*R*

_{3}, with axes aligned according to the previous description. Control signals were launched from Bob’ side, counter propagating the quantum channel, thus limiting the interference of the side channels to the Rayleigh scattered light. A second filter was used to further reduce the crosstalk to below the dark count level of the single photon counting module in channel 2. At Alice’s side of the link, after passing through all polarization controllers, the control channels were dropped through port 3 of an optical circulator and separated by a second WDM. Channels 1 and 3 were detected (photodiodes D

_{1}and D

_{3}) after passing through the corresponding linear polarizers (P

_{1}and P

_{3}) with polarization controllers adjusting the axes of

*R*

_{1},

*R*

_{3}with respect to the polarizers P

_{1}and P

_{3}such that once the polarization is adjusted in channel 1 it is invariant to rotations performed by

*R*

_{3}. Efficient control was obtained with received powers as low as -20 dBm in the control channels. At Alice’s side, the quantum channel was launched after a polarization controller and a variable attenuator, so that polarization measurements could be made either with classical light or in single photon regime, by placing a polarimeter at Bob’s end or a polarization controller followed by a linear polarizer and a gated photon counter. The rejection ratio of the polarizers was better than 40 dB. Photon counting measurements were made with 0.2 photons per 2.5 ns gate pulse at 100 kHz rate.

*τ*Δ

*ω*~0.3, a value not so small if compared to the unity. However, the performance of the experiment is striking, which means that Eq. (6) seems too restrictive. In fact, it was deduced considering a worst case scenario, as the solution

*θ*+

*ϕ*=0 (mod 2π) is not necessarily the unique solution for Eq. (5). Hence, it is possible that the control algorithm finds better solutions in the general case, somehow relaxing the condition stated in Eq. (6).

^{2}(5°)~0.8%. Figure 4(b) displays the statistical distribution of the power loss that would be added by the polarization control system due to the mismatch between the controlled and target SOPs during the experiment. Of course, this distribution depends on the temporal evolution of the optical fiber transfer function and can be degraded in case of severe fiber vibrations. Moreover, if the PMD of the fiber is much higher than 0.5 ps the accuracy of the control will decrease, and the SOP of the qubits will swing around its target SOP, thus widening the distribution of deviation angles. However, considering the recovery time of the system, the precision of our polarization control system leaves a margin good enough to override the sensitivity of most quantum communications detection systems and is fully compatible with the maximum accepted optical QBER in quantum communications, which is usually around 1%.

^{-5}per nanosecond. Now the advantage of using the control signals in a counter- instead of co-propagating scheme is clear. This last setup would require the side channels to work below the minimum acceptable power, thus reducing the efficiency of the control system. In Fig. 5 we show the single photon counts at Bob for two fixed polarization states (linear 0° and 45°) at Alice, corresponding to the same bit value in the two non-orthogonal bases of a BB84 protocol for instance. In each case, Bob uses a polarization controller to change the polarizer angle along the equator of the Poincaré sphere. It can be seen that, when Bob’s polarizer is orthogonal to the state sent by Alice, the total noise counts are entirely comprised of the single photon counter module’s dark counts. This means that all other sources of noise are negligibly small, which demonstrates the feasibility of the proposed setup.

## 4. Conclusion

## Acknowledgment

## References and links

1. | N. Gisin, J. P. von der Weid, and J. P. Pellaux, “Polarization mode dispersion in long and short single mode fibers,” J. Lightwave Tech. |

2. | M. Martinelli, P. Martelli, and S. M. Pietralunga, “Polarization stabilization in optical communication systems,” J. Lightwave Technol. |

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

4. | C.-Z. Peng, J. Zhang, D. Yang, W.-B. Gao, H.-X. Ma, H. Yin, H.-P. Zeng, T. Yang X.-B. Wang, and J.-W. Pan, “Experimental Long-distance decoy-state quantum key distribution based on polarization encoding,” Phys. Rev. Lett. |

5. | S. Sauge, M. Swillo, S. Albert-Seifried, G. B. Xavier, J. Waldebäck, M. Tengner, D. Ljunggren, and A. Karlsson, “Narrowband polarization-entangled photon pairs distributed over a WDM link for qubit networks,” Opt. Express , |

6. | B. L. Heffner, “Automated measurement of polarization mode dispersion using Jones Matrix Eigenanalysis”. IEEE Photon. Technol. Lett. |

**OCIS Codes**

(060.2330) Fiber optics and optical communications : Fiber optics communications

(120.5410) Instrumentation, measurement, and metrology : Polarimetry

(060.5565) Fiber optics and optical communications : Quantum communications

**ToC Category:**

Fiber Optics and Optical Communications

**History**

Original Manuscript: October 4, 2007

Revised Manuscript: January 9, 2008

Manuscript Accepted: January 25, 2008

Published: January 28, 2008

**Citation**

G. B. Xavier, G. Vilela de Faria, G. P. Temporão, and J. P. von der Weid, "Full polarization control for fiber optical quantum communication systems using polarization encoding," Opt. Express **16**, 1867-1873 (2008)

http://www.opticsinfobase.org/oe/abstract.cfm?URI=oe-16-3-1867

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### References

- N. Gisin, J. P. von der Weid, and J. P. Pellaux, "Polarization mode dispersion in long and short single mode fibers," J. Lightwave Tech. 9,821-827 (1991). [CrossRef]
- M. Martinelli, P. Martelli and S. M. Pietralunga, "Polarization stabilization in optical communication systems," J. Lightwave Technol. 24, 4172-4183 (2006). [CrossRef]
- N. Gisin, G. Ribordy, W. Tittel, and H. Zbinden, "Quantum Cryptography," Rev. Mod. Phys. 74, 145-195 (2002). [CrossRef]
- C.-Z. Peng, J. Zhang, D. Yang, W.-B. Gao, H.-X. Ma, H. Yin, H.-P. Zeng, T. Yang, X.-B. Wang, and J.-W. Pan, "Experimental Long-distance decoy-state quantum key distribution based on polarization encoding," Phys. Rev. Lett. 98, 010505-1-4 (2007). [CrossRef]
- S. Sauge, M. Swillo, S. Albert-Seifried, G. B. Xavier, J. Waldebäck, M. Tengner, D. Ljunggren, and A. Karlsson, "Narrowband polarization-entangled photon pairs distributed over a WDM link for qubit networks," Opt. Express, 15, 6926-6933 (2007). [CrossRef] [PubMed]
- B. L. Heffner, "Automated measurement of polarization mode dispersion using Jones Matrix Eigenanalysis". IEEE Photon. Technol. Lett. 4, 1066-1069 (1992). [CrossRef]

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