## Scalable fiber integrated source for higher-dimensional path-entangled photonic quNits |

Optics Express, Vol. 20, Issue 15, pp. 16145-16153 (2012)

http://dx.doi.org/10.1364/OE.20.016145

Acrobat PDF (977 KB)

### Abstract

Integrated photonic circuits offer the possibility for complex quantum optical experiments in higher-dimensional photonic systems. However, the advantages of integration and scalability can only be fully utilized with the availability of a source for higher-dimensional entangled photons. Here, a novel fiber integrated source for path-entangled photons in the telecom band at 1.55µm using only standard fiber technology is presented. Due to the special design the source shows good scalability towards higher-dimensional entangled photonic states (quNits), while path entanglement offers direct compatibility with on-chip path encoding. We present an experimental realization of a path-entangled two-qubit source. A very high quality of entanglement is verified by various measurements, i.a. a tomographic state reconstruction is performed leading to a background corrected fidelity of (99.45±0.06)%. Moreover, we describe an easy method for extending our source to arbitrarily high dimensions.

© 2012 OSA

## 1. Introduction

1. A. Politi, M. J. Cryan, J. G. Rarity, S. Yu, and J. L. O’Brien, “Silica-on-silicon waveguide quantum circuits,” Science **320**(5876), 646–649 (2008). [CrossRef] [PubMed]

2. P. J. Shadbolt, M. R. Verde, A. Peruzzo, A. Politi, A. Laing, M. Lobino, J. C. F. Matthews, M. G. Thompson, and J. L. O’Brien, “Generating, manipulating and measuring entanglement and mixture with a reconfigurable photonic circuit,” Nat. Photonics **6**(1), 45–49 (2011). [CrossRef]

*any*N-dimensional unitary transformation (quNit operation) can be realized by a combination of qubit operations acting on different modes [3,4

4. M. Reck, A. Zeilinger, H. J. Bernstein, and P. Bertani, “Experimental realization of any discrete unitary operator,” Phys. Rev. Lett. **73**(1), 58–61 (1994). [CrossRef] [PubMed]

4. M. Reck, A. Zeilinger, H. J. Bernstein, and P. Bertani, “Experimental realization of any discrete unitary operator,” Phys. Rev. Lett. **73**(1), 58–61 (1994). [CrossRef] [PubMed]

5. G. Weihs, M. Reck, H. Weinfurter, and A. Zeilinger, “Two-photon interference in optical fiber multiports,” Phys. Rev. A **54**(1), 893–897 (1996). [CrossRef] [PubMed]

6. M. Zukowski, A. Zeilinger, and M. A. Horne, “Realizable higher-dimensional two-particle entanglements via multiport beam splitters,” Phys. Rev. A **55**(4), 2564–2579 (1997). [CrossRef]

7. G. J. Pryde and A. G. White, “Creation of maximally entangled photon-number states using optical fiber multiports,” Phys. Rev. A **68**(5), 052315 (2003). [CrossRef]

8. Y. L. Lim and A. Beige, “Multiphoton entanglement through a Bell multiport beam splitter,” Phys. Rev. A **71**(6), 062311 (2005). [CrossRef]

9. M. Mohseni, A. M. Steinberg, and J. A. Bergou, “Optical realization of optimal unambiguous discrimination for pure and mixed quantum states,” Phys. Rev. Lett. **93**(20), 200403 (2004). [CrossRef] [PubMed]

10. N. J. Cerf, M. Bourennane, A. Karlsson, and N. Gisin, “Security of quantum key distribution using *d*-level systems,” Phys. Rev. Lett. **88**(12), 127902 (2002). [CrossRef] [PubMed]

11. K. Mattle, H. Weinfurter, P. G. Kwiat, and A. Zeilinger, “Dense coding in experimental quantum communication,” Phys. Rev. Lett. **76**(25), 4656–4659 (1996). [CrossRef] [PubMed]

12. T. Durt, B.-G. Englert, I. Bengtsson, and K. Życzkowski, “On mutually unbiased bases,” Int. J. Quantum Inf. **8**(04), 535–640 (2010). [CrossRef]

1. A. Politi, M. J. Cryan, J. G. Rarity, S. Yu, and J. L. O’Brien, “Silica-on-silicon waveguide quantum circuits,” Science **320**(5876), 646–649 (2008). [CrossRef] [PubMed]

2. P. J. Shadbolt, M. R. Verde, A. Peruzzo, A. Politi, A. Laing, M. Lobino, J. C. F. Matthews, M. G. Thompson, and J. L. O’Brien, “Generating, manipulating and measuring entanglement and mixture with a reconfigurable photonic circuit,” Nat. Photonics **6**(1), 45–49 (2011). [CrossRef]

13. Y. Bromberg, Y. Lahini, R. Morandotti, and Y. Silberberg, “Quantum and classical correlations in waveguide lattices,” Phys. Rev. Lett. **102**(25), 253904 (2009). [CrossRef] [PubMed]

17. L. Sansoni, F. Sciarrino, G. Vallone, P. Mataloni, A. Crespi, R. Ramponi, and R. Osellame, “Polarization entangled state measurement on a chip,” Phys. Rev. Lett. **105**(20), 200503 (2010). [CrossRef] [PubMed]

## 2. Principle of operation of an entangled quNit source

*NxN*beam splitter. Note that in this scheme the photon pairs are separated by their wavelengths and therefore need to be non-degenerate. However, a degenerate path-entangled source can be obtained by replacing the type-I non-linear medium by a type-II SPDC process allowing separation by polarization.

### 2.1 Measuring path-encoded quNits

4. M. Reck, A. Zeilinger, H. J. Bernstein, and P. Bertani, “Experimental realization of any discrete unitary operator,” Phys. Rev. Lett. **73**(1), 58–61 (1994). [CrossRef] [PubMed]

## 3. Experimental realization of an entangled two qubit source

18. S. Tanzilli, H. De Riedmatten, H. Tittel, P. Zbinden, P. Baldi, M. De Micheli, D. B. Ostrowsky, and N. Gisin, “Highly efficient photon-pair source using periodically poled lithium niobate waveguide,” Electron. Lett. **37**(1), 26–28 (2001). [CrossRef]

19. Q. Zhang, C. Langrock, H. Takesue, X. Xie, M. Fejer, and Y. Yamamoto, “Generation of 10-GHz clock sequential time-bin entanglement,” Opt. Express **16**(5), 3293–3298 (2008). [CrossRef] [PubMed]

20. X. Li, P. L. Voss, J. E. Sharping, and P. Kumar, “Optical-fiber source of polarization-entangled photons in the 1550 nm telecom band,” Phys. Rev. Lett. **94**(5), 053601 (2005). [CrossRef] [PubMed]

22. M. A. Horne, A. Shimony, and A. Zeilinger, “Two-particle interferometry,” Phys. Rev. Lett. **62**(19), 2209–2212 (1989). [CrossRef] [PubMed]

6. M. Zukowski, A. Zeilinger, and M. A. Horne, “Realizable higher-dimensional two-particle entanglements via multiport beam splitters,” Phys. Rev. A **55**(4), 2564–2579 (1997). [CrossRef]

23. J. G. Rarity and P. R. Tapster, “Experimental violation of Bell’s inequality based on phase and momentum,” Phys. Rev. Lett. **64**(21), 2495–2498 (1990). [CrossRef] [PubMed]

24. A. Rossi, G. Vallone, A. Chiuri, F. De Martini, and P. Mataloni, “Multipath entanglement of two photons,” Phys. Rev. Lett. **102**(15), 153902 (2009). [CrossRef] [PubMed]

25. J. H. Shapiro and F. N. Wong, “On-demand single-photon generation using a modular array of parametric downconverters with electro-optic polarization controls,” Opt. Lett. **32**(18), 2698–2700 (2007). [CrossRef] [PubMed]

26. X. Ma, S. Zotter, J. Kofler, T. Jennewein, and A. Zeilinger, “Experimental generation of single photons via active multiplexing,” Phys. Rev. A **83**(4), 043814 (2011). [CrossRef]

### 3.1 Measuring path-encoded qubits

6. M. Zukowski, A. Zeilinger, and M. A. Horne, “Realizable higher-dimensional two-particle entanglements via multiport beam splitters,” Phys. Rev. A **55**(4), 2564–2579 (1997). [CrossRef]

### 3.2 Indistinguishability

### 3.3 Phase control

## 4. Results

### 4.1 Visibility of entanglement

*2*(a)) with the setup for realizing projective measurements (Fig. 2(b)) removed.

### 4.2 CHSH inequality

### 4.3 State tomography

28. D. F. V. James, P. G. Kwiat, W. J. Munro, and A. G. White, “Measurement of qubits,” Phys. Rev. A **64**(5), 052312 (2001). [CrossRef]

28. D. F. V. James, P. G. Kwiat, W. J. Munro, and A. G. White, “Measurement of qubits,” Phys. Rev. A **64**(5), 052312 (2001). [CrossRef]

## 5. Extension to higher dimensions and outlook

7. G. J. Pryde and A. G. White, “Creation of maximally entangled photon-number states using optical fiber multiports,” Phys. Rev. A **68**(5), 052315 (2003). [CrossRef]

8. Y. L. Lim and A. Beige, “Multiphoton entanglement through a Bell multiport beam splitter,” Phys. Rev. A **71**(6), 062311 (2005). [CrossRef]

9. M. Mohseni, A. M. Steinberg, and J. A. Bergou, “Optical realization of optimal unambiguous discrimination for pure and mixed quantum states,” Phys. Rev. Lett. **93**(20), 200403 (2004). [CrossRef] [PubMed]

11. K. Mattle, H. Weinfurter, P. G. Kwiat, and A. Zeilinger, “Dense coding in experimental quantum communication,” Phys. Rev. Lett. **76**(25), 4656–4659 (1996). [CrossRef] [PubMed]

**55**(4), 2564–2579 (1997). [CrossRef]

12. T. Durt, B.-G. Englert, I. Bengtsson, and K. Życzkowski, “On mutually unbiased bases,” Int. J. Quantum Inf. **8**(04), 535–640 (2010). [CrossRef]

29. A. Cabello, “Proposal for revealing quantum nonlocality via local contextuality,” Phys. Rev. Lett. **104**(22), 220401 (2010). [CrossRef] [PubMed]

30. P. Heywood and M. L. G. Redhead, “Nonlocality and the Kochen-Specker paradox,” Found. Phys. **13**(5), 481–499 (1983). [CrossRef]

10. N. J. Cerf, M. Bourennane, A. Karlsson, and N. Gisin, “Security of quantum key distribution using *d*-level systems,” Phys. Rev. Lett. **88**(12), 127902 (2002). [CrossRef] [PubMed]

31. Z. Liu and H. Fan, “Decay of multiqudit entanglement,” Phys. Rev. A **79**(6), 064305 (2009). [CrossRef]

## Acknowledgment

## References and links

1. | A. Politi, M. J. Cryan, J. G. Rarity, S. Yu, and J. L. O’Brien, “Silica-on-silicon waveguide quantum circuits,” Science |

2. | P. J. Shadbolt, M. R. Verde, A. Peruzzo, A. Politi, A. Laing, M. Lobino, J. C. F. Matthews, M. G. Thompson, and J. L. O’Brien, “Generating, manipulating and measuring entanglement and mixture with a reconfigurable photonic circuit,” Nat. Photonics |

3. | M. Reck and A. Zeilinger, “Quantum phase tracing of correlated photons in optical multiports,” in |

4. | M. Reck, A. Zeilinger, H. J. Bernstein, and P. Bertani, “Experimental realization of any discrete unitary operator,” Phys. Rev. Lett. |

5. | G. Weihs, M. Reck, H. Weinfurter, and A. Zeilinger, “Two-photon interference in optical fiber multiports,” Phys. Rev. A |

6. | M. Zukowski, A. Zeilinger, and M. A. Horne, “Realizable higher-dimensional two-particle entanglements via multiport beam splitters,” Phys. Rev. A |

7. | G. J. Pryde and A. G. White, “Creation of maximally entangled photon-number states using optical fiber multiports,” Phys. Rev. A |

8. | Y. L. Lim and A. Beige, “Multiphoton entanglement through a Bell multiport beam splitter,” Phys. Rev. A |

9. | M. Mohseni, A. M. Steinberg, and J. A. Bergou, “Optical realization of optimal unambiguous discrimination for pure and mixed quantum states,” Phys. Rev. Lett. |

10. | N. J. Cerf, M. Bourennane, A. Karlsson, and N. Gisin, “Security of quantum key distribution using |

11. | K. Mattle, H. Weinfurter, P. G. Kwiat, and A. Zeilinger, “Dense coding in experimental quantum communication,” Phys. Rev. Lett. |

12. | T. Durt, B.-G. Englert, I. Bengtsson, and K. Życzkowski, “On mutually unbiased bases,” Int. J. Quantum Inf. |

13. | Y. Bromberg, Y. Lahini, R. Morandotti, and Y. Silberberg, “Quantum and classical correlations in waveguide lattices,” Phys. Rev. Lett. |

14. | B. J. Smith, D. Kundys, N. Thomas-Peter, P. G. R. Smith, and I. A. Walmsley, “Phase-controlled integrated photonic quantum circuits,” Opt. Express |

15. | R. Keil, A. Szameit, F. Dreisow, M. Heinrich, S. Nolte, and A. Tünnermann, “Photon correlations in two-dimensional waveguide arrays and their classical estimate,” Phys. Rev. A |

16. | M. F. Saleh, G. Di Giuseppe, B. E. A. Saleh, and M. C. Teich, “Modal and polarization qubits in Ti:LiNbO3 photonic circuits for a universal quantum logic gate,” Opt. Express |

17. | L. Sansoni, F. Sciarrino, G. Vallone, P. Mataloni, A. Crespi, R. Ramponi, and R. Osellame, “Polarization entangled state measurement on a chip,” Phys. Rev. Lett. |

18. | S. Tanzilli, H. De Riedmatten, H. Tittel, P. Zbinden, P. Baldi, M. De Micheli, D. B. Ostrowsky, and N. Gisin, “Highly efficient photon-pair source using periodically poled lithium niobate waveguide,” Electron. Lett. |

19. | Q. Zhang, C. Langrock, H. Takesue, X. Xie, M. Fejer, and Y. Yamamoto, “Generation of 10-GHz clock sequential time-bin entanglement,” Opt. Express |

20. | X. Li, P. L. Voss, J. E. Sharping, and P. Kumar, “Optical-fiber source of polarization-entangled photons in the 1550 nm telecom band,” Phys. Rev. Lett. |

21. | M. A. Horne and A. Zeilinger, “A Bell-type EPR experiment using linear momenta,” in |

22. | M. A. Horne, A. Shimony, and A. Zeilinger, “Two-particle interferometry,” Phys. Rev. Lett. |

23. | J. G. Rarity and P. R. Tapster, “Experimental violation of Bell’s inequality based on phase and momentum,” Phys. Rev. Lett. |

24. | A. Rossi, G. Vallone, A. Chiuri, F. De Martini, and P. Mataloni, “Multipath entanglement of two photons,” Phys. Rev. Lett. |

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

26. | X. Ma, S. Zotter, J. Kofler, T. Jennewein, and A. Zeilinger, “Experimental generation of single photons via active multiplexing,” Phys. Rev. A |

27. | J. F. Clauser, M. A. Horne, A. Shimony, and R. A. Holt, “Proposed experiment to test local hidden-variable theories,” Phys. Rev. Lett. |

28. | D. F. V. James, P. G. Kwiat, W. J. Munro, and A. G. White, “Measurement of qubits,” Phys. Rev. A |

29. | A. Cabello, “Proposal for revealing quantum nonlocality via local contextuality,” Phys. Rev. Lett. |

30. | P. Heywood and M. L. G. Redhead, “Nonlocality and the Kochen-Specker paradox,” Found. Phys. |

31. | Z. Liu and H. Fan, “Decay of multiqudit entanglement,” Phys. Rev. A |

32. | M. Fiorentino, S. M. Spillane, R. G. Beausoleil, T. D. Roberts, P. Battle, and M. W. Munro, “Spontaneous parametric down-conversion in periodically poled KTP waveguides and bulk crystals,” Opt. Express |

**OCIS Codes**

(060.2310) Fiber optics and optical communications : Fiber optics

(130.0130) Integrated optics : Integrated optics

(270.0270) Quantum optics : Quantum optics

**ToC Category:**

Integrated Optics

**History**

Original Manuscript: March 14, 2012

Revised Manuscript: April 19, 2012

Manuscript Accepted: April 19, 2012

Published: July 2, 2012

**Citation**

Christoph Schaeff, Robert Polster, Radek Lapkiewicz, Robert Fickler, Sven Ramelow, and Anton Zeilinger, "Scalable fiber integrated source for higher-dimensional path-entangled photonic quNits," Opt. Express **20**, 16145-16153 (2012)

http://www.opticsinfobase.org/oe/abstract.cfm?URI=oe-20-15-16145

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### References

- A. Politi, M. J. Cryan, J. G. Rarity, S. Yu, and J. L. O’Brien, “Silica-on-silicon waveguide quantum circuits,” Science320(5876), 646–649 (2008). [CrossRef] [PubMed]
- P. J. Shadbolt, M. R. Verde, A. Peruzzo, A. Politi, A. Laing, M. Lobino, J. C. F. Matthews, M. G. Thompson, and J. L. O’Brien, “Generating, manipulating and measuring entanglement and mixture with a reconfigurable photonic circuit,” Nat. Photonics6(1), 45–49 (2011). [CrossRef]
- M. Reck and A. Zeilinger, “Quantum phase tracing of correlated photons in optical multiports,” in Quantum Interferometry, F. DeMartini, and A. Zeilinger, eds. (World Scientific, 1994), pp. 170–177.
- M. Reck, A. Zeilinger, H. J. Bernstein, and P. Bertani, “Experimental realization of any discrete unitary operator,” Phys. Rev. Lett.73(1), 58–61 (1994). [CrossRef] [PubMed]
- G. Weihs, M. Reck, H. Weinfurter, and A. Zeilinger, “Two-photon interference in optical fiber multiports,” Phys. Rev. A54(1), 893–897 (1996). [CrossRef] [PubMed]
- M. Zukowski, A. Zeilinger, and M. A. Horne, “Realizable higher-dimensional two-particle entanglements via multiport beam splitters,” Phys. Rev. A55(4), 2564–2579 (1997). [CrossRef]
- G. J. Pryde and A. G. White, “Creation of maximally entangled photon-number states using optical fiber multiports,” Phys. Rev. A68(5), 052315 (2003). [CrossRef]
- Y. L. Lim and A. Beige, “Multiphoton entanglement through a Bell multiport beam splitter,” Phys. Rev. A71(6), 062311 (2005). [CrossRef]
- M. Mohseni, A. M. Steinberg, and J. A. Bergou, “Optical realization of optimal unambiguous discrimination for pure and mixed quantum states,” Phys. Rev. Lett.93(20), 200403 (2004). [CrossRef] [PubMed]
- N. J. Cerf, M. Bourennane, A. Karlsson, and N. Gisin, “Security of quantum key distribution using d-level systems,” Phys. Rev. Lett.88(12), 127902 (2002). [CrossRef] [PubMed]
- K. Mattle, H. Weinfurter, P. G. Kwiat, and A. Zeilinger, “Dense coding in experimental quantum communication,” Phys. Rev. Lett.76(25), 4656–4659 (1996). [CrossRef] [PubMed]
- T. Durt, B.-G. Englert, I. Bengtsson, and K. Życzkowski, “On mutually unbiased bases,” Int. J. Quantum Inf.8(04), 535–640 (2010). [CrossRef]
- Y. Bromberg, Y. Lahini, R. Morandotti, and Y. Silberberg, “Quantum and classical correlations in waveguide lattices,” Phys. Rev. Lett.102(25), 253904 (2009). [CrossRef] [PubMed]
- B. J. Smith, D. Kundys, N. Thomas-Peter, P. G. R. Smith, and I. A. Walmsley, “Phase-controlled integrated photonic quantum circuits,” Opt. Express17(16), 13516–13525 (2009). [CrossRef] [PubMed]
- R. Keil, A. Szameit, F. Dreisow, M. Heinrich, S. Nolte, and A. Tünnermann, “Photon correlations in two-dimensional waveguide arrays and their classical estimate,” Phys. Rev. A81(2), 023834 (2010). [CrossRef]
- M. F. Saleh, G. Di Giuseppe, B. E. A. Saleh, and M. C. Teich, “Modal and polarization qubits in Ti:LiNbO3 photonic circuits for a universal quantum logic gate,” Opt. Express18(19), 20475–20490 (2010). [CrossRef] [PubMed]
- L. Sansoni, F. Sciarrino, G. Vallone, P. Mataloni, A. Crespi, R. Ramponi, and R. Osellame, “Polarization entangled state measurement on a chip,” Phys. Rev. Lett.105(20), 200503 (2010). [CrossRef] [PubMed]
- S. Tanzilli, H. De Riedmatten, H. Tittel, P. Zbinden, P. Baldi, M. De Micheli, D. B. Ostrowsky, and N. Gisin, “Highly efficient photon-pair source using periodically poled lithium niobate waveguide,” Electron. Lett.37(1), 26–28 (2001). [CrossRef]
- Q. Zhang, C. Langrock, H. Takesue, X. Xie, M. Fejer, and Y. Yamamoto, “Generation of 10-GHz clock sequential time-bin entanglement,” Opt. Express16(5), 3293–3298 (2008). [CrossRef] [PubMed]
- X. Li, P. L. Voss, J. E. Sharping, and P. Kumar, “Optical-fiber source of polarization-entangled photons in the 1550 nm telecom band,” Phys. Rev. Lett.94(5), 053601 (2005). [CrossRef] [PubMed]
- M. A. Horne and A. Zeilinger, “A Bell-type EPR experiment using linear momenta,” in Symposium on the Foundations of Modern Physics, P. Lahti and P. Mittelstaedt, eds. (World Scientific, 1985), pp. 435–439.
- M. A. Horne, A. Shimony, and A. Zeilinger, “Two-particle interferometry,” Phys. Rev. Lett.62(19), 2209–2212 (1989). [CrossRef] [PubMed]
- J. G. Rarity and P. R. Tapster, “Experimental violation of Bell’s inequality based on phase and momentum,” Phys. Rev. Lett.64(21), 2495–2498 (1990). [CrossRef] [PubMed]
- A. Rossi, G. Vallone, A. Chiuri, F. De Martini, and P. Mataloni, “Multipath entanglement of two photons,” Phys. Rev. Lett.102(15), 153902 (2009). [CrossRef] [PubMed]
- J. H. Shapiro and F. N. Wong, “On-demand single-photon generation using a modular array of parametric downconverters with electro-optic polarization controls,” Opt. Lett.32(18), 2698–2700 (2007). [CrossRef] [PubMed]
- X. Ma, S. Zotter, J. Kofler, T. Jennewein, and A. Zeilinger, “Experimental generation of single photons via active multiplexing,” Phys. Rev. A83(4), 043814 (2011). [CrossRef]
- J. F. Clauser, M. A. Horne, A. Shimony, and R. A. Holt, “Proposed experiment to test local hidden-variable theories,” Phys. Rev. Lett.23(15), 880–884 (1969). [CrossRef]
- D. F. V. James, P. G. Kwiat, W. J. Munro, and A. G. White, “Measurement of qubits,” Phys. Rev. A64(5), 052312 (2001). [CrossRef]
- A. Cabello, “Proposal for revealing quantum nonlocality via local contextuality,” Phys. Rev. Lett.104(22), 220401 (2010). [CrossRef] [PubMed]
- P. Heywood and M. L. G. Redhead, “Nonlocality and the Kochen-Specker paradox,” Found. Phys.13(5), 481–499 (1983). [CrossRef]
- Z. Liu and H. Fan, “Decay of multiqudit entanglement,” Phys. Rev. A79(6), 064305 (2009). [CrossRef]
- M. Fiorentino, S. M. Spillane, R. G. Beausoleil, T. D. Roberts, P. Battle, and M. W. Munro, “Spontaneous parametric down-conversion in periodically poled KTP waveguides and bulk crystals,” Opt. Express15(12), 7479–7488 (2007). [CrossRef] [PubMed]

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