## Bragg reflection waveguide as a source of wavelength-multiplexed polarization-entangled photon pairs |

Optics Express, Vol. 20, Issue 14, pp. 15015-15023 (2012)

http://dx.doi.org/10.1364/OE.20.015015

Acrobat PDF (971 KB)

### Abstract

We put forward a new highly efficient source of paired photons entangled in polarization with an ultra-large bandwidth. The photons are generated by means of a conveniently designed spontaneous parametric down-conversion process in a semiconductor type-II Bragg reflection waveguide. The proposed scheme aims at being a key element of an integrated source of polarization-entangled photon pairs highly suitable for its use in a multi-user quantum-key-distribution system.

© 2012 OSA

## 1. Introduction

8. H. Hubel, M. R. Vanner, T. Lederer, B. Blauensteiner, T. Lorunser, A. Poppe, and A. Zeilinger, “High-fidelity transmission of polarization encoded qubits from an entangled source over 100 km of fiber,” Opt. Express **15**, 7853–7862 (2007). [CrossRef] [PubMed]

9. T. E. Chapuran, P. Toliver, N. A. Peters, J. Jackel, M. S. Goodman, R. J. Runser, S. R. McNown, N. Dallmann, R. J. Hughes, K. P. McCabe, J. E. Nordholt, C. G. Peterson, K. T. Tyagi, L. Mercer, and H. Dardy, “Optical networking for quantum key distribution and quantum communications,” New J. Phys. **11**, 105001 (2009). [CrossRef]

10. A. L. Migdall, D. Branning, and S. Castelletto, “Tailoring single-photon and multiphoton probabilities of a single-photon on-demand source,” Phys. Rev. A **66**, 053805 (2002). [CrossRef]

11. J. H. Shapiro and F. N. Wong, “On-demand single-photon generation using a modular array of parametric down-converters with electro-optic polarization controls,” Opt. Lett. **32**, 2698–2700 (2007). [CrossRef] [PubMed]

*λ*(nm) = 5.52/L(mm), where

*L*is the length of the crystal [12

12. A. Fedrizzi, T. Herbst, A. Poppe, T. Jennewein, and A. Zeilinger, “A wavelength-tunable fiber-coupled source of narrowband entangled photons,” Opt. Express **15**, 15377–15386 (2007). [CrossRef] [PubMed]

*L*= 1 mm, the bandwidth is Δ

*λ*∼ 5.5 nm. On the other hand, in a type-0 PPLN configuration with the same crystal length

*L*= 1 mm, Lim et al. [13

13. H. C. Lim, A. Yoshizawa, H. Tsuchida, and K. Kikuchi, “Wavelength-multiplexed distribution of highly entangled photon-pairs over optical fiber,” Opt. Express **26**, 22099–22104 (2008). [CrossRef]

*λ*∼ 50 nm. Even though one can always reduce the length of the nonlinear crystal in a type-II configuration to achieve an increase of the bandwidth, this results in a reduction of the spectral brightness of the source.

*Ga*

_{x}_{1−x}As) offer the possibility to generate polarization-entangled photons with an ultra-large bandwidth. The most striking feature of the use of BRW as a photon source is the capability of controlling the dispersive properties of all interacting waves in the SPDC process, which in turn allows the tailoring of the bandwidth of the down-converted photons: from narrowband (1 – 2 nm) to ultra-broadband (hundreds of nm) [14–16

16. D. Kang and A. S. Helmy, “Generation of polarization entangled photons using concurrent type-I and type-0 processes in AlGaAs ridge waveguides,” Opt. Lett. **37**, 1481–1483 (2012). [CrossRef] [PubMed]

17. I. Shoji, T. Kondo, A. Kitamoto, M. Shirane, and R. Ito, “Absolute scale of second-order nonlinear-optical coefficients,” J. Opt. Soc. Am. B **14**, 2268–2294 (1997). [CrossRef]

*μ*m) and mature fabrication technologies that can be used for integration of the source of entangled photons with a light source and other optical elements. Additionally, a laser based on BRWs has already been demonstrated [18

18. B. J. Bijlani and A. S. Helmy, “Bragg reflection waveguide diode lasers,” Opt. Lett. **34**, 3734–3736 (2009). [CrossRef] [PubMed]

19. R. Horn, P. Abolghasem, B. J. Bijlani, D. Kang, A. S. Helmy, and G. Weihs, “Monolithic source of photon pairs,” Phys. Rev. Lett. **108**, 153605 (2012). [CrossRef] [PubMed]

*Ga*

_{x}_{1−x}As is an optically isotropic semiconductor, precluding birefringent phase matching. However, the modal phase-matching of the interacting waves (pump, signal and idler) can be achieved by letting each wave propagate in a different type of mode supported by the waveguide. For instance, the phase-matching can be successfully achieved if the pump propagates in the waveguide in a Bragg mode, whereas the signal and idler photons propagate in total-internal-reflection (TIR) modes [20

20. A. S. Helmy, B. Bijlani, and P. Abolghasem, “Phase matching in monolithic Bragg reflection waveguides,” Opt. Lett. **32**, 2399–2401 (2007). [CrossRef] [PubMed]

## 2. Description of the quantum state of the down-converted photons

*ω*illuminates the waveguide and mediates the generation of a pair of photons with mutually orthogonal polarizations (signal: TE polarization; idler: TM polarization). The frequencies of the signal and idler photons are

_{p}*ω*=

_{s}*ω*

_{0}+ Ω and

*ω*=

_{i}*ω*

_{0}− Ω, respectively, where

*ω*

_{0}is the degenerate central angular frequency of both photons, and Ω is the angular frequency deviation from the central frequency. The signal photon (TE) propagates as a TIR mode of the waveguide with spatial shape

*U*(

_{s}*x*,

*y*,

*ω*) and propagation constant

_{s}*β*(

_{s}*ω*). The idler photon (TM), also a TIR mode, has a spatial shape

_{s}*U*(

_{i}*x*,

*y*,

*ω*) and propagation constant

_{i}*β*(

_{i}*ω*). The pump beam is a Bragg mode of the waveguide with spatial shape

_{i}*U*(

_{p}*x*,

*y*,

*ω*) and propagation constant

_{p}*β*(

_{p}*ω*).

_{i}21. J. P. Torres, K. Banaszek, and I. A. Walmsley, “Engineering nonlinear optic sources of photonic entanglement,” Prog. Opt. **56**, 227–331 (2011). [CrossRef]

*σ*is defined

*F*is the flux rate of pump photons,

_{p}*n*are their refractive indices. The joint spectral amplitude Φ(Ω) has the form The ket |TE,

_{p,s,i}*ω*

_{0}+ Ω〉

*(|TM,*

_{s}*ω*

_{0}− Ω〉

*) designates a signal (idler) photon that propagates with polarization TE (TM) in a mode of the waveguide with the spatial shape U*

_{i}*(U*

_{s}*) and frequency*

_{i}*ω*

_{0}+ Ω (

*ω*

_{0}− Ω). The phase-mismatch function reads Δ

*(Ω) =*

_{k}*β*−

_{p}*β*(Ω) −

_{s}*β*(−Ω), and

_{i}*s*(Ω) =

_{k}*β*+

_{p}*β*(Ω) +

_{s}*β*(−Ω). The function |Φ(Ω)|

_{i}^{2}is proportional to the probability of detection of a photon with polarization TE and frequency

*ω*

_{0}+ Ω in coincidence with a photon with TM polarization and frequency

*ω*

_{0}− Ω.

*n*frequency channels into coupled fibers leading to the users of the network. The bandwidth of each channel is Δ

*ω*and their central frequencies are

_{Bn}designates the frequency bandwidth from

*U*

_{0}) of the fiber. The coupling efficiency between the signal and idler modes, and the fundamental mode of the single-mode fiber are given by

*= Γ*

_{s}*≈ 0.88 in the whole bandwidth of interest, showing a minimal frequency dependence. All the modes are normalized so that ∫*

_{i}*dxdy*|

*U*(

_{j}*x*,

*y*,

*ω*)|

^{2}= 1 for

*j*=

*s*,

*i*, 0.

*|TE〉*

_{U}*, |TE〉*

_{L}*|TM〉*

_{U}*, |TM〉*

_{L}*|TE〉*

_{U}*, |TM〉*

_{L}*|TM〉*

_{U}*}: where with Tr[*

_{L}*ρ*

_{n}] =

*α*

_{n}+

*β*

_{n}= 1.

## 3. Numerical results

*n*= 1 corresponds to the wavelength 1549.6 nm in the upper path and to 1550.6 nm in the lower path.

22. S. V. Zhukovsky, L. G. Helt, D. Kang, P. Abolghasem, A. S. Helmy, and J. E. Sipe, “Generation of maximally-polarization-entangled photons on a chip,” Phys. Rev. A **85**, 013838 (2012). [CrossRef]

23. J. P. Torres, M. Hendrych, and A. Valencia, “Angular dispersion: an enabling tool in nonlinear and quantum optics,” Adv. Opt. Photon. **2**, 319–369 (2010). [CrossRef]

25. S. Gehrsitz, F. K. Reinhart, C. Gourgon, N. Herres, A. Vonlanthan, and H. Sigg, “The refractive index of Al(x)Ga(1–x)As below the band gap: accurate determination and empirical modeling,” J. Appl. Phys. **87**, 7825–7837 (2000). [CrossRef]

*C*of the biphoton [27

_{n}27. S. Hill and W. K. Wootters, “Entanglement of a pair of quantum bits,” Phys. Rev. Lett. **78**, 5022–5025 (1997). [CrossRef]

28. K. Wootters, “Entanglement of formation of an arbitrary state of two qubits,” Phys. Rev. Lett. **80**, 2245–2248 (1998). [CrossRef]

29. T. Yu and J. H. Eberly, “Quantum open system theory: bipartite aspects,” Phys. Rev. Lett. **97**, 140403 (2006). [CrossRef] [PubMed]

*α*,

_{n}*β*and

_{n}*C*for the first 200 channels.

_{n}*C*> 0.9 is reached for the first 179 channels. The decrease (increase) of the parameters

_{n}*β*(

_{n}*α*) reflects the fact that for frequency channels with a large detuning from the central frequency, one of the two polarization components of the polarization entangled state, |TE〉

_{n}_{1}|TM〉

_{2}or |TM〉

_{1}|TE〉

_{2}, shows a greater amplitude probability. In this case, one of the two options predominates. Therefore, if the goal is to generate a quantum state of the form

_{1}|TM〉

_{2}+ |TM〉

_{1}|TE〉

_{2}) in a specific frequency channel with

*α*,

_{n}*β*≠ 1/2, one can always modify the diagonal elements of the density matrix with a linear transformation optical system, keeping unaltered the degree of entanglement.

_{n}30. Y Kim and W. P. Grice, “Reliability of the beam-splitterbased Bell-state measurement,” Phys. Rev. A **68**, 062305 (2003). [CrossRef]

31. P. P. Rohde and T. C. Ralph, “Frequency and temporal effects in linear optical quantum computing,” Phys. Rev. A **71**, 032320 (2005). [CrossRef]

7. T. S. Humble and W. P. Grice, “Spectral effects in quantum teleportation,” Phys. Rev. A **75**, 022307 (2007). [CrossRef]

*C*> 0.95, we have at our disposal 162 channels, while for

_{n}*C*> 0.99 this number is reduced to 121 channels.

_{n}*real*fiber-optics network, the number of frequency channels available can be limited by several factors. For instance, it can be limited by the operational bandwidth of the demultiplexer (see Fig. 1). This device should be designed to operate with the same broad spectral range of the photon pairs generated in the BRW waveguide.

32. W. Drexler, “Ultrahigh-resolution optical coherence tomography,” J. Biomed. Opt. **9**, 47–74 (2004). [CrossRef] [PubMed]

## 4. Conclusion

*conventional*sources based on the use of more common nonlinear materials, such as KTP or LiNbO

_{3}, might also generate entangled pairs of photons with a large bandwidth, BRWs based on AlGaAs compounds offer two main advantages: an enhanced capability to tailor the general properties of the downconverted photons, and the possibility of integration of different elements (pump source, nonlinear waveguide and diverse optical elements) in a chip platform based on an already mature technology, which could pave the way for entanglement-based technologies in

*out-of-the-lab scenarios*.

## Acknowledgments

## References and links

1. | A. Serafini, S. Mancini, and S. Bose, “Distributed quantum computation via optical fibers,” Phys. Rev. Lett. |

2. | J. I. Cirac, A. K. Ekert, S. F. Huelga, and C. Macchiavello, “Distributed quantum computation over noisy channels,” Phys. Rev. A |

3. | G. Ribordy, J. Brendel, J. Gautier, N. Gisin, and H. Zbinden, “Long-distance entanglement-based quantum key distribution,” Phys. Rev. A |

4. | A. K. Ekert, “Quantum cryptography based on Bell’s theorem,” Phys. Rev. Lett. |

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

6. | C. H. Bennett, G. Brassard, C. Crepeau, R. Jozsa, A. Peres, and W. K. Wootters, “Teleporting an unknown quantum state via dual classical and Einstein-Podolsky-Rosen channels,” Phys. Rev. Lett. |

7. | T. S. Humble and W. P. Grice, “Spectral effects in quantum teleportation,” Phys. Rev. A |

8. | H. Hubel, M. R. Vanner, T. Lederer, B. Blauensteiner, T. Lorunser, A. Poppe, and A. Zeilinger, “High-fidelity transmission of polarization encoded qubits from an entangled source over 100 km of fiber,” Opt. Express |

9. | T. E. Chapuran, P. Toliver, N. A. Peters, J. Jackel, M. S. Goodman, R. J. Runser, S. R. McNown, N. Dallmann, R. J. Hughes, K. P. McCabe, J. E. Nordholt, C. G. Peterson, K. T. Tyagi, L. Mercer, and H. Dardy, “Optical networking for quantum key distribution and quantum communications,” New J. Phys. |

10. | A. L. Migdall, D. Branning, and S. Castelletto, “Tailoring single-photon and multiphoton probabilities of a single-photon on-demand source,” Phys. Rev. A |

11. | J. H. Shapiro and F. N. Wong, “On-demand single-photon generation using a modular array of parametric down-converters with electro-optic polarization controls,” Opt. Lett. |

12. | A. Fedrizzi, T. Herbst, A. Poppe, T. Jennewein, and A. Zeilinger, “A wavelength-tunable fiber-coupled source of narrowband entangled photons,” Opt. Express |

13. | H. C. Lim, A. Yoshizawa, H. Tsuchida, and K. Kikuchi, “Wavelength-multiplexed distribution of highly entangled photon-pairs over optical fiber,” Opt. Express |

14. | P. Abolghasem, J. Han, B. J. Bijlani, A. Arjmand, and A. S. Helmy, “Continuous-wave second harmonic generation in Bragg reflection waveguides,” Opt. Lett. |

15. | K. Thyagarajan, R. Das, O. Alibart, M. Micheli, D. B. Ostrowsky, and S. Tanzilli, “Increased pump acceptance bandwidth in spontaneous parametric downconversion process using Bragg reflection waveguides,” Opt. Express |

16. | D. Kang and A. S. Helmy, “Generation of polarization entangled photons using concurrent type-I and type-0 processes in AlGaAs ridge waveguides,” Opt. Lett. |

17. | I. Shoji, T. Kondo, A. Kitamoto, M. Shirane, and R. Ito, “Absolute scale of second-order nonlinear-optical coefficients,” J. Opt. Soc. Am. B |

18. | B. J. Bijlani and A. S. Helmy, “Bragg reflection waveguide diode lasers,” Opt. Lett. |

19. | R. Horn, P. Abolghasem, B. J. Bijlani, D. Kang, A. S. Helmy, and G. Weihs, “Monolithic source of photon pairs,” Phys. Rev. Lett. |

20. | A. S. Helmy, B. Bijlani, and P. Abolghasem, “Phase matching in monolithic Bragg reflection waveguides,” Opt. Lett. |

21. | J. P. Torres, K. Banaszek, and I. A. Walmsley, “Engineering nonlinear optic sources of photonic entanglement,” Prog. Opt. |

22. | S. V. Zhukovsky, L. G. Helt, D. Kang, P. Abolghasem, A. S. Helmy, and J. E. Sipe, “Generation of maximally-polarization-entangled photons on a chip,” Phys. Rev. A |

23. | J. P. Torres, M. Hendrych, and A. Valencia, “Angular dispersion: an enabling tool in nonlinear and quantum optics,” Adv. Opt. Photon. |

24. | J. Jin, |

25. | S. Gehrsitz, F. K. Reinhart, C. Gourgon, N. Herres, A. Vonlanthan, and H. Sigg, “The refractive index of Al(x)Ga(1–x)As below the band gap: accurate determination and empirical modeling,” J. Appl. Phys. |

26. | A. Ling, A. Lamas-Linares, and C. Kurtsiefer, “Absolute emission rates of spontaneous parametric down-conversion into single transverse Gaussian modes,” Phys. Rev. A |

27. | S. Hill and W. K. Wootters, “Entanglement of a pair of quantum bits,” Phys. Rev. Lett. |

28. | K. Wootters, “Entanglement of formation of an arbitrary state of two qubits,” Phys. Rev. Lett. |

29. | T. Yu and J. H. Eberly, “Quantum open system theory: bipartite aspects,” Phys. Rev. Lett. |

30. | Y Kim and W. P. Grice, “Reliability of the beam-splitterbased Bell-state measurement,” Phys. Rev. A |

31. | P. P. Rohde and T. C. Ralph, “Frequency and temporal effects in linear optical quantum computing,” Phys. Rev. A |

32. | W. Drexler, “Ultrahigh-resolution optical coherence tomography,” J. Biomed. Opt. |

**OCIS Codes**

(190.4410) Nonlinear optics : Nonlinear optics, parametric processes

(270.0270) Quantum optics : Quantum optics

**ToC Category:**

Quantum Optics

**History**

Original Manuscript: April 12, 2012

Revised Manuscript: June 6, 2012

Manuscript Accepted: June 6, 2012

Published: June 20, 2012

**Citation**

Jiří Svozilík, Martin Hendrych, and Juan P. Torres, "Bragg reflection waveguide as a source of wavelength-multiplexed polarization-entangled photon pairs," Opt. Express **20**, 15015-15023 (2012)

http://www.opticsinfobase.org/oe/abstract.cfm?URI=oe-20-14-15015

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### References

- A. Serafini, S. Mancini, and S. Bose, “Distributed quantum computation via optical fibers,” Phys. Rev. Lett.96, 010503 (2006). [CrossRef] [PubMed]
- J. I. Cirac, A. K. Ekert, S. F. Huelga, and C. Macchiavello, “Distributed quantum computation over noisy channels,” Phys. Rev. A59, 4249–4254 (1999). [CrossRef]
- G. Ribordy, J. Brendel, J. Gautier, N. Gisin, and H. Zbinden, “Long-distance entanglement-based quantum key distribution,” Phys. Rev. A63, 012309 (2000). [CrossRef]
- A. K. Ekert, “Quantum cryptography based on Bell’s theorem,” Phys. Rev. Lett.67, 661–663 (1991). [CrossRef] [PubMed]
- M. Hillery, V. Bužek, and A. Berthiaume, “Quantum secret sharing,” Phys. Rev. A59, 1829–1834 (1999). [CrossRef]
- C. H. Bennett, G. Brassard, C. Crepeau, R. Jozsa, A. Peres, and W. K. Wootters, “Teleporting an unknown quantum state via dual classical and Einstein-Podolsky-Rosen channels,” Phys. Rev. Lett.70, 1895–1899 (1993). [CrossRef] [PubMed]
- T. S. Humble and W. P. Grice, “Spectral effects in quantum teleportation,” Phys. Rev. A75, 022307 (2007). [CrossRef]
- H. Hubel, M. R. Vanner, T. Lederer, B. Blauensteiner, T. Lorunser, A. Poppe, and A. Zeilinger, “High-fidelity transmission of polarization encoded qubits from an entangled source over 100 km of fiber,” Opt. Express15, 7853–7862 (2007). [CrossRef] [PubMed]
- T. E. Chapuran, P. Toliver, N. A. Peters, J. Jackel, M. S. Goodman, R. J. Runser, S. R. McNown, N. Dallmann, R. J. Hughes, K. P. McCabe, J. E. Nordholt, C. G. Peterson, K. T. Tyagi, L. Mercer, and H. Dardy, “Optical networking for quantum key distribution and quantum communications,” New J. Phys.11, 105001 (2009). [CrossRef]
- A. L. Migdall, D. Branning, and S. Castelletto, “Tailoring single-photon and multiphoton probabilities of a single-photon on-demand source,” Phys. Rev. A66, 053805 (2002). [CrossRef]
- J. H. Shapiro and F. N. Wong, “On-demand single-photon generation using a modular array of parametric down-converters with electro-optic polarization controls,” Opt. Lett.32, 2698–2700 (2007). [CrossRef] [PubMed]
- A. Fedrizzi, T. Herbst, A. Poppe, T. Jennewein, and A. Zeilinger, “A wavelength-tunable fiber-coupled source of narrowband entangled photons,” Opt. Express15, 15377–15386 (2007). [CrossRef] [PubMed]
- H. C. Lim, A. Yoshizawa, H. Tsuchida, and K. Kikuchi, “Wavelength-multiplexed distribution of highly entangled photon-pairs over optical fiber,” Opt. Express26, 22099–22104 (2008). [CrossRef]
- P. Abolghasem, J. Han, B. J. Bijlani, A. Arjmand, and A. S. Helmy, “Continuous-wave second harmonic generation in Bragg reflection waveguides,” Opt. Lett.34, 9460–9467 (2009).
- K. Thyagarajan, R. Das, O. Alibart, M. Micheli, D. B. Ostrowsky, and S. Tanzilli, “Increased pump acceptance bandwidth in spontaneous parametric downconversion process using Bragg reflection waveguides,” Opt. Express16, 3577–3582 (2008). [CrossRef] [PubMed]
- D. Kang and A. S. Helmy, “Generation of polarization entangled photons using concurrent type-I and type-0 processes in AlGaAs ridge waveguides,” Opt. Lett.37, 1481–1483 (2012). [CrossRef] [PubMed]
- I. Shoji, T. Kondo, A. Kitamoto, M. Shirane, and R. Ito, “Absolute scale of second-order nonlinear-optical coefficients,” J. Opt. Soc. Am. B14, 2268–2294 (1997). [CrossRef]
- B. J. Bijlani and A. S. Helmy, “Bragg reflection waveguide diode lasers,” Opt. Lett.34, 3734–3736 (2009). [CrossRef] [PubMed]
- R. Horn, P. Abolghasem, B. J. Bijlani, D. Kang, A. S. Helmy, and G. Weihs, “Monolithic source of photon pairs,” Phys. Rev. Lett.108, 153605 (2012). [CrossRef] [PubMed]
- A. S. Helmy, B. Bijlani, and P. Abolghasem, “Phase matching in monolithic Bragg reflection waveguides,” Opt. Lett.32, 2399–2401 (2007). [CrossRef] [PubMed]
- J. P. Torres, K. Banaszek, and I. A. Walmsley, “Engineering nonlinear optic sources of photonic entanglement,” Prog. Opt.56, 227–331 (2011). [CrossRef]
- S. V. Zhukovsky, L. G. Helt, D. Kang, P. Abolghasem, A. S. Helmy, and J. E. Sipe, “Generation of maximally-polarization-entangled photons on a chip,” Phys. Rev. A85, 013838 (2012). [CrossRef]
- J. P. Torres, M. Hendrych, and A. Valencia, “Angular dispersion: an enabling tool in nonlinear and quantum optics,” Adv. Opt. Photon.2, 319–369 (2010). [CrossRef]
- J. Jin, The Finite Element Method in Electromagnetics, 2nd ed. (Wiley-IEEE Press, 2002).
- S. Gehrsitz, F. K. Reinhart, C. Gourgon, N. Herres, A. Vonlanthan, and H. Sigg, “The refractive index of Al(x)Ga(1–x)As below the band gap: accurate determination and empirical modeling,” J. Appl. Phys.87, 7825–7837 (2000). [CrossRef]
- A. Ling, A. Lamas-Linares, and C. Kurtsiefer, “Absolute emission rates of spontaneous parametric down-conversion into single transverse Gaussian modes,” Phys. Rev. A77, 043834 (2008). [CrossRef]
- S. Hill and W. K. Wootters, “Entanglement of a pair of quantum bits,” Phys. Rev. Lett.78, 5022–5025 (1997). [CrossRef]
- K. Wootters, “Entanglement of formation of an arbitrary state of two qubits,” Phys. Rev. Lett.80, 2245–2248 (1998). [CrossRef]
- T. Yu and J. H. Eberly, “Quantum open system theory: bipartite aspects,” Phys. Rev. Lett.97, 140403 (2006). [CrossRef] [PubMed]
- Y Kim and W. P. Grice, “Reliability of the beam-splitterbased Bell-state measurement,” Phys. Rev. A68, 062305 (2003). [CrossRef]
- P. P. Rohde and T. C. Ralph, “Frequency and temporal effects in linear optical quantum computing,” Phys. Rev. A71, 032320 (2005). [CrossRef]
- W. Drexler, “Ultrahigh-resolution optical coherence tomography,” J. Biomed. Opt.9, 47–74 (2004). [CrossRef] [PubMed]

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