## Quantum channel using photon number correlated twin beams

Optics Express, Vol. 11, Issue 26, pp. 3592-3597 (2003)

http://dx.doi.org/10.1364/OE.11.003592

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### Abstract

We report quantum communications channel using photon number correlated twin beams. The twin beams are generated from a nondegenerate optical parametric oscillator, and the photon number difference is used to encode the signal. The bit error rate of our system will be 0.067 by using the twin beams comparing with 0.217 by using the coherent state as the signal carrier.

© 2003 Optical Society of America

## 1. Introduction

## 2. Quantum communication channel with twin beams

*n*〉=〈

*n*

_{1}-

*n*

_{2}〉, where 〈

*n*

_{1}〉 (〈

*n*

_{2}〉) is the mean number of photons in the first (second) polarization mode making up a basis. Alice encodes a logical key in either V/H basis or “±45 basis. Bob measures the photon number difference either in the V/H or in the ±45 basis. Thus, the photon number difference in the correct bases, which means Alice and Bob use the same basis, is

*n*-

_{V}*n*in V/H basis and

_{H}*n*

_{+45}-

*n*

_{-45}in ±45 basis respectively. Alice encodes a logical “1” (“0”) key bit by setting the mean value of the difference number to be in the correct basis 〈

*n*〉=+

*N*(〈

*n*〉=-

*N*), where N is a positive number. The photon number difference, N, is small (≤1%) compared with 〈

*n*〉 and 〈

_{V}*n*〉, which should contain more than 10

_{H}^{4}photons on average. After all the key bits have been transmitted, Alice and Bob communicate via a public channel and compare the bases they used for each encoding/measurement. Alice and Bob can separate their communications wrong basis and uncorrected basis dependence on they used the same and difference basis.

_{0}(≥0) and constructs his bit sequence by using the following decision:

*n*〉=+

*N*as “1” and 〈

*n*〉=-

*N*as “0”. Due to the tails of the distributions for the two bit values, there is a nonzero probability that a key bit encoded by Alice as a logical 1 (0) would be measured by Bob as a logical 0 (1). Such an error is a bit error (i.e. 1↔0). According to the central limit theorem [14], Bob’s photon number difference measurements follow a Gaussian distribution. The distribution can be written as

*n*〉 and the standard derivation ° of the photon number difference. With this probability, we define the postselection efficiency as the probability that the absolute value of photon number difference |〈

*n*〉| exceeds the threshold N

_{0}in the correct basis. The postselection efficiency is [15

15. R. Namiki and T. Hirano, “security of quantum cryptography using balanced homodyne detection,” Phys. Rev. A. **67** 022308 (2003). [CrossRef]

_{0}, the BER can be written as the probability that Bob’s measurements have an outcome 〈

*n*〉<

*N*

_{0}when Alice has sent the 〈

*n*〉=

*N*divided by

*P*(

*N*

_{0}, 〈

*n*〉,

*δ*)

## 3. Experimental setup and result

10. Y. Zhang, K. Kasai, and M. Watanabe, “Investigation of the photon-number statistics of twin beams by direct detection,” Opt. Lett. **27**,1244–1246 (2002). [CrossRef]

17. M. B. Gray, D. A. Shaddock, C. C. Harb, and H.-A. Bachor, “photodetector designs for low-noise, broadband, and high-power applications,” Rev. Sci. Instrum. **69**, 3755–3762, (1998). [CrossRef]

*n*

_{1}〉=〈

*n*

_{2}〉=(4.0±0.1)×10

^{4}, and the photoelectron difference was fixed at 〈

*n*〉=

*N*=200, which is about 0.5% of the total photon number 〈

*n*

_{1}〉(〈

*n*

_{2}〉). The measured mean and standard deviation are listed in Table I. Theoretical probability distributions from equation with 〈

*n*〉=200 and standard derivation δ

_{twin}=145±10 for twin beams, which corresponds to a 70% reduction in the noise below the SNL, and δ

_{coh}=270±10 for coherent beams are also shown in Fig. 2 (blue and yellow curves). To fit the theoretical prediction, a fixed coefficient was introduced to scale all probabilities of the experiment.

*t*, in which they subdivide their measurements. Using Eq. (5) and the measured experiment data, the BERs of our system are 0.217 and 0.067 for the coherent light and twin beams, respectively, when we selected N

_{k}_{0}=20. In a practice implementation, the improvement of the communication can be optimal by selection of the parameters.

_{0}, the security of the system also depends on parameters 〈n〉 and N

_{0}. In a practice implementation, the parameters should be determined to ensure that the system provides high security.

## 4. Conclusions

## References and links

1. | A. Heidmann, R. J. Horowicz, S. Reynaud, E. Giacobino, C. Fabre, and G. Camy, “Observation of quantum noise reduction on twin laser beams” Phys. Rev. Lett. |

2. | L. A. Wu, H. J. Kimble, J. L. Hall, and H. F. Wu, “Generation of squeezed states by parametric down conversion,” Phys. Rev. Lett. |

3. | Y. Zhang, H. Wang, X.Y. Li, J.T. Jing, C.D. Xie, and K.C. Peng, “Experimental generation of bright two-mode quadrature squeezed light from a narrow-band nondegenerate optical parametric amplifier,” Phys. Rev. A, |

4. | J. R. Gao, F. Y. Cui, C. Y. Xue, C. D. Xie, and K. C. Peng, “Generation and application of twin beams from an optical parametric oscillator including an a-cut KTP crystal,” Opt. Lett. |

5. | H. Wang, Y. Zhang, Q. Pan, H. Su, A. Porzio, C. D. Xie, and K. C. Peng, “Experimental realization of a quantum measurement for intensity difference fluctuation using a beam splitter,” Phys. Rev. Lett. |

6. | H. B. Wang, Z. H. Zhai, S. K. Wang, and J. R. Gao, “Generation of frequency-tunable twin beams and its application in sub-shot noise FM spectroscopy,” Europhys. Lett. |

7. | M. Vasilyev, S. K. Choi, P. Kumar, and G. M. D’Ariano, “Tomographic measurement of joint photon statistics of the twin-beam quantum state,” Phys. Rev. Lett. |

8. | D. T. Smithey, M. Beck, M.G. Raymer, and A. Faridani, “Measurement of the wigner distribution and the density matrix of a light mode using optical homodyne tomography: application to squeezed states and the vacuum,” Phys. Rev. Lett. |

9. | D. T. Smithey, M. Beck, M. Belsley, and M. G. Raymer, “Sub-shot-noise correlation of total photon number using macroscopic twin pulses of light,” Phys. Rev. Lett. |

10. | Y. Zhang, K. Kasai, and M. Watanabe, “Investigation of the photon-number statistics of twin beams by direct detection,” Opt. Lett. |

11. | Y. Zhang, K. Kasai, and M. Watanabe, “Experimental investigation of the intensity fluctuation joint probability and conditional distributions of the twin-beam quantum state,” Opt. Express |

12. | J. Laurat, T. Coudreau, N. Treps, A. Maitre, and C. Fabre, “conditional preparation of a quantum state in the continuous variable regime: generation of a sub-Poissonian state from twin beams,” Phys. Rev. Lett. |

13. | A. C. Funk and M. G. Raymer, “quantum key distribution using nonclassical photon-number correlations in macroscopic light pulses,” Phys. Rev. A |

14. | The basic concepts of noise theory used in this paper can be found, for example, in L. Mandel and E. Wolf, |

15. | R. Namiki and T. Hirano, “security of quantum cryptography using balanced homodyne detection,” Phys. Rev. A. |

16. | K. Kasai and M. Watanabe, “Generation of twin photon beams from a thermally self-locked semimonolithic optical parametric oscillator and its application,” in proceeding of 7th International Conference on Squeezed States and Uncertainty Relations, Boston, U.S.A., June 4–8, 2001. |

17. | M. B. Gray, D. A. Shaddock, C. C. Harb, and H.-A. Bachor, “photodetector designs for low-noise, broadband, and high-power applications,” Rev. Sci. Instrum. |

**OCIS Codes**

(270.2500) Quantum optics : Fluctuations, relaxations, and noise

(270.5290) Quantum optics : Photon statistics

(270.6570) Quantum optics : Squeezed states

**ToC Category:**

Research Papers

**History**

Original Manuscript: October 15, 2003

Revised Manuscript: November 20, 2003

Published: December 29, 2003

**Citation**

Yun Zhang, Katsuyuki Kasai, and Kazuhiro Hayasaka, "Quantum channel using photon number correlated twin beams," Opt. Express **11**, 3592-3597 (2003)

http://www.opticsinfobase.org/oe/abstract.cfm?URI=oe-11-26-3592

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### References

- A. Heidmann, R. J. Horowicz, S. Reynaud, E. Giacobino, C. Fabre, and G. Camy, �??Observation of quantum noise reduction on twin laser beams,�?? Phys. Rev. Lett. 59, 2555-2558 (1987). [CrossRef] [PubMed]
- L. A. Wu, H. J. Kimble, J. L. Hall, and H. F. Wu, �??Generation of squeezed states by parametric down conversion,�?? Phys. Rev. Lett. 57, 2520-2524 (1986). [CrossRef] [PubMed]
- Y. Zhang, H. Wang, X.Y. Li, J.T. Jing, C.D. Xie, and K.C. Peng, �??Experimental generation of bright twomode quadrature squeezed light from a narrow-band nondegenerate optical parametric amplifier,�?? Phys. Rev. A 62, 023813 (2000) [CrossRef]
- J. R. Gao, F. Y. Cui, C. Y. Xue, C. D. Xie, K. C. Peng, �??Generation and application of twin beams from an optical parametric oscillator including an a-cut KTP crystal,�?? Opt. Lett. 23, 870-872 (1998). [CrossRef]
- H. Wang, Y. Zhang, Q. Pan, H. Su, A. Porzio, C. D. Xie, and K. C. Peng, �??Experimental realization of a quantum measurement for intensity difference fluctuation using a beam splitter,�?? Phys. Rev. Lett. 82, 1414-1417 (1999). [CrossRef]
- H. B. Wang, Z. H. Zhai, S. K. Wang, and J. R. Gao, �??Generation of frequency-tunable twin beams and its application in sub-shot noise FM spectroscopy,�?? Europhys. Lett. 64, 15-21 (2003) [CrossRef]
- M. Vasilyev, S. K. Choi, P. Kumar, G. M. D�??Ariano, �??Tomographic measurement of joint photon statistics of the twin-beam quantum state,�?? Phys. Rev. Lett. 84, 2354-2357 (2000). [CrossRef] [PubMed]
- D. T. Smithey, M.Beck, M.G. Raymer, and A. Faridani, �??Measurement of the wigner distribution and the density matrix of a light mode using optical homodyne tomography: application to squeezed states and the vacuum,�?? Phys. Rev. Lett. 70, 1244-1247 (1993). [CrossRef] [PubMed]
- D. T. Smithey, M. Beck, M. Belsley, and M. G. Raymer, �??Sub-shot-noise correlation of total photon number using macroscopic twin pulses of light,�?? Phys. Rev. Lett. 69, 2650-2653 (1992). [CrossRef] [PubMed]
- Y. Zhang, K. Kasai, and M. Watanabe, �??Investigation of the photon-number statistics of twin beams by direct detection,�?? Opt. Lett. 27, 1244-1246 (2002). [CrossRef]
- Y. Zhang, K. Kasai, and M. Watanabe, "Experimental investigation of the intensity fluctuation joint probability and conditional distributions of the twin-beam quantum state," Opt. Express 11, 14-19 (2003), <a href="http://www.opticsexpress.org/abstract.cfm?URI=OPEX-11-1-14">http://www.opticsexpress.org/abstract.cfm?URI=OPEX-11-1-14</a>. [CrossRef] [PubMed]
- J. Laurat, T. Coudreau, N. Treps, A. Maitre, and C. Fabre, �??Conditional preparation of a quantum state in the continuous variable regime: generation of a sub-Poissonian state from twin beams,�?? Phys. Rev. Lett. 91, 213601 (2003). [CrossRef] [PubMed]
- A. C. Funk and M. G. Raymer, �??Quantum key distribution using nonclassical photon-number correlations in macroscopic light pulses,�?? Phys. Rev. A 65, 042307 (2002). [CrossRef]
- The basic concepts of noise theory used in this paper can be found, for example, in L. Mandel and E. Wolf, Optical coherence and Quantum optics (Cambridge University Press, New York, 1995).
- R. Namiki, and T. Hirano, �??Security of quantum cryptography using balanced homodyne detection,�?? Phys. Rev. A 67, 022308 (2003). [CrossRef]
- K. Kasai and M. Watanabe, �??Generation of twin photon beams from a thermally self-locked semimonolithic optical parametric oscillator and its application,�?? in proceeding of 7th International Conference on Squeezed States and Uncertainty Relations, Boston, U.S.A., June 4-8, 2001.
- M. B. Gray, D. A. Shaddock, C. C. Harb, and H.-A. Bachor, �??Photodetector designs for low-noise, broadband, and high-power applications,�?? Rev. Sci. Instrum. 69, 3755-3762, (1998). [CrossRef]

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