## Characterization of two-photon polarization mixed states generated from entangled-classical hybrid photon source |

Optics Express, Vol. 19, Issue 15, pp. 14249-14259 (2011)

http://dx.doi.org/10.1364/OE.19.014249

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### Abstract

We experimentally prepare bi-photon mixed states in polarization employing an entangled-classical hybrid photon emitter which can properly model solid-state entangled photon sources with uncorrelated background photons. Polarization-uncorrelated photon pairs in totally mixed (TM) states are embodied with classical thermal radiation, while the polarization-entangled ones in a Bell state are generated by conventional parametric down conversion. The bi-photon states generated from the hybrid photon emitter are characterized in terms of a linear entropy–tangle plane, which reveals the formation of two-qubit Werner states. We also propose a direct way for evaluating the Werner states by means of minimal coincidence counts measurements. This simple method can be widely applicable in examining the bi-photon states from solid-state entangled photon sources, in which the polarization-entangled photon pairs have temporal correlation while the background photons in the TM states do not.

© 2011 OSA

## 1. Introduction

8. H. Kumano, S. Kimura, M. Endo, H. Sasakura, S. Adachi, S. Muto, and I. Suemune, “Deterministic single-photon and polarization-correlated photon pair generations from a single InAlAs quantum dot,” J. Nanoelectron. Optoelectron. **1**, 39–51 (2006). [CrossRef]

18. G. Puentes, A. Aiello, D. Voigt, and J. P. Woerdman, “Entangled mixed-state generation by twin-photon scattering,” Phys. Rev. A **75**, 032319 (2007). [CrossRef]

21. M. Barbieri, F. De Martini, G. Di Nepi, and P. Mataloni, “Generation and characterization of Werner states and maximally entangled mixed states by a universal source of entanglement,” Phys. Rev. Lett. **92**, 177901 (2004). [CrossRef] [PubMed]

22. C. Kurtsiefer, S. Mayer, P. Zarda, and H. Weinfurter, “Stable solid-state source of single photons,” Phys. Rev. Lett. **85**, 290–293 (2000). [CrossRef] [PubMed]

23. P. Michler, A. Imamoğlu, M. D. Mason, P. J. Carson, G. F. Strouse, and S. K. Buratto, “Quantum correlation among photons from a single quantum dot at room temperature,” Nature **406**, 968–970 (2000). [CrossRef] [PubMed]

24. C. Santori, M. Pelton, G. Solomon, Y. Dale, and Y. Yamamoto, “Triggered single photons from a quantum dot,” Phys. Rev. Lett. **86**, 1502–1505 (2001). [CrossRef] [PubMed]

## 2. Experimental

*β*-BaB

_{2}O

_{4}(BBO) crystal, cut for type-II phase matching at

*θ*= 42.3° is used for generating PDC photon pairs with their central wavelength of 802 nm in non-collinear configuration. For degenerated photon-pair emission, the intersection lines of the emission cones form an angle of 6° and the tangents in the crossing points are perpendicular to each other, which is adjusted with an aid of a CCD image sensor (Watec, minimum illumination: 0.00002 lx. F1.4). The down converted photons pass through a half-wave plate (HWP) and additional BBO crystals with a thickness of 1 mm to compensate the transverse and longitudinal walk-off [26

26. P. G. Kwiat, K. Mattle, H. Weinfurter, A. Zeilinger, A. V. Sergienko, and Y. Shih, “New high-intensity source of polarization-entangled photon pairs,” Phys. Rev. Lett. **75**, 4337–4341 (1995). [CrossRef] [PubMed]

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

*σ*∼ 2.4 ns as illustrated in Fig. 2(c), where

*σ*gives a standard deviation of gaussian-distributed histogram. This 4

*σ*time window covers 99.5% of the whole coincidence counts of the PDC photon pairs.

## 3. Evaluation of photon states from constituent emitters

28. R. J. Young, R. M. Stevenson, A. J. Hudson, C. A. Nicoll, D. A. Ritchie, and A. J. Shields, “Bell-inequality violation with a triggered photon-pair source,” Phys. Rev. Lett. **102**, 030406 (2009). [CrossRef] [PubMed]

*T*) [29

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

*) [30*

_{L}30. S. Bose and V. Vedral, “Mixedness and teleportation,” Phys. Rev. A **61**, 040101(R) (2000). [CrossRef]

*HH*〉, |

*HV*〉, |

*VH*〉, |

*VV*〉 as [29

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

30. S. Bose and V. Vedral, “Mixedness and teleportation,” Phys. Rev. A **61**, 040101(R) (2000). [CrossRef]

*ρ*is the measured density matrix,

*λ*(

_{i}*i*=1, 2, 3, 4) is the square root of the eigenvalues in decreasing order of magnitude of the spin-flipped density matrix operator

*R*=

*ρ*(

*σ*⊗

^{y}*σ*)

^{y}*ρ*

^{*}(

*σ*⊗

^{y}*σ*), where

^{y}*σ*is one of the Pauli’s operators, and the asterisk indicates complex conjugation. The tangle is zero for unentangled states and 1 for completely entangled states, while the linear entropy is zero for pure states and 1 for TM states.

^{y}*I*is the identity operator of a single qubit. Therefore, the thermal radiation is shown to be a model photon-pair source in the totally mixed polarization states, which can be an alternative to the so-far reported classical photon-pair sources based on the decohered Bell states [18

18. G. Puentes, A. Aiello, D. Voigt, and J. P. Woerdman, “Entangled mixed-state generation by twin-photon scattering,” Phys. Rev. A **75**, 032319 (2007). [CrossRef]

21. M. Barbieri, F. De Martini, G. Di Nepi, and P. Mataloni, “Generation and characterization of Werner states and maximally entangled mixed states by a universal source of entanglement,” Phys. Rev. Lett. **92**, 177901 (2004). [CrossRef] [PubMed]

## 4. Werner state formation with the entangled-classical hybrid photon source and its temporal correlation

*–*

_{L}*T*plane as shown in Fig. 5, in which the gray area corresponds to unphysical photon-pair states, and the solid curve indicates the Werner state given by Eq. (5). All the measured photon-pair states indicated by the solid circles coincide well with the Werner curve. This reveals that the present hybrid photon emitter works as a photon-pair source in the Werner state. When restricting ourselves to the Werner states by substituting

*ρ*for

_{w}*ρ*, Eqs. (2) and (3) reduce to

*= 1 –*

_{L}*p*

^{2}, respectively [31

31. C. Cinelli, G. Di Nepi, F. De Martini, M. Barbieri, and P. Mataloni, “Parametric source of two-photon states with a tunable degree of entanglement and mixing: experimental preparation of Werner states and maximally entangled mixed states,” Phys. Rev. A **70**, 022321 (2004). [CrossRef]

*p*is the only parameter to specify the Werner state, and

*p*>1/3 (S

*< 8/9) is required for the entangled nonseparable photon pair [21*

_{L}21. M. Barbieri, F. De Martini, G. Di Nepi, and P. Mataloni, “Generation and characterization of Werner states and maximally entangled mixed states by a universal source of entanglement,” Phys. Rev. Lett. **92**, 177901 (2004). [CrossRef] [PubMed]

32. C. H. Bennett, G. Brassard, S. Popescu, B. Schumacher, J. A. Smolin, and W. K. Wootters, “Purification of noisy entanglement and faithful teleportation via noisy channels,” Phys. Rev. Lett. **76**, 722–725 (1996). [CrossRef] [PubMed]

*p*>1/ 2 (S

*< 1/2) for violating the CHSH inequality [33*

_{L}33. J. F. Clauser, M. A. Horne, A. Shimony, and R. A. Holt, “Proposed experiment to test local hidden-variable theories,” Phys. Rev. Lett. **23**, 880–884 (1969). [CrossRef]

*p*<1/ 2, the state is entangled but the CHSH inequality still holds. Based on the above arguments, photon-pair states (i)–(v) are entangled and (i)–(iii) are also violating the CHSH inequality, while the state (vi) is no longer entangled but now separable. Following the above argument, estimation of the singlet weight

*p*is required in order to judge whether the produced Werner state is entangled or not. For this purpose, coincidence counts under at least eight projective measurements including two for normalization are normally required [20

20. M. Barbieri, F. De Martini, G. Di Nepi, P. Mataloni, G. M. D’Ariano, and C. Macchiavello, “Detection of entanglement with polarized photons: experimental realization of an entanglement witness,” Phys. Rev. Lett. **91**, 227901 (2003). [CrossRef] [PubMed]

*p*can be directly obtained from the minimal coincidence counts measurements when the temporal correlation is absent in the bi-photon state

*ρ*. When the detection polarization is set to HV, which gives the highest coincidence count for the incident Bell state |Ψ

_{TM}^{−}〉, the contribution of the state

*ρ*from the PDC source to the coincidence count as a function of singlet weight

_{Bell}*p*is given by

*C*

^{(Bell)}(

*p*) =

*p*〈

*HV*|

*ρ*|

_{Bell}*HV*〉=

*p*/2. On the one hand, the contribution of

*ρ*from the thermal source is expressed as

_{TM}*C*

^{(TM)}(

*p*) =(1 –

*p*)〈

*HV*|

*ρ*|

_{TM}*HV*〉=(1 –

*p*)/4. Therefore, the areal ratio

*C*

^{(Bell)}/

*C*

^{(TM)}for a given time window is expressed as 2

*p*/(1 –

*p*). Then the singlet weight is directly obtained by

*p*from the experimentally obtained coincidence count histogram, it is obvious that clear discriminability between

*C*

^{(Bell)}and

*C*

^{(TM)}associated with each constituent photon sources is a prerequisite. In so-far prepared Werner states [18

18. G. Puentes, A. Aiello, D. Voigt, and J. P. Woerdman, “Entangled mixed-state generation by twin-photon scattering,” Phys. Rev. A **75**, 032319 (2007). [CrossRef]

**92**, 177901 (2004). [CrossRef] [PubMed]

*C*

^{(Bell)}and

*C*

^{(TM)}, as discussed hereafter.

*HH*|

*ρ*|

_{Bell}*HH*〉 = 0 holds, the state

*ρ*has no contribution to the coincidence counts under the HH detection. Thus, the time-independent constant counts (gray area in Fig. 6) originate from the TM state. The contribution of the TM state to the histogram is invariant under detection polarization rotation and independent on the detection angle in another arm. On the other hand, the state

_{Bell}*ρ*under the HV-polarization detection gives coincidence counts localized at around zero time-delay. As shown by the solid line, the overall coincidence counts in the HV detection agree well with the gaussian-shaped coincidence counts from the Bell states superposed on the constant base counts from the TM states, which clearly discriminate the contribution of the constituent sources.

_{Bell}*R*is given by [34

_{Alice}34. B. Lounis, H. A. Bechtela, D. Gerionc, P. Alivisatosc, and W. E. Moernera, “Photon antibunching in single CdSe/ZnS quantum dot fluorescence,” Chem. Phys. Lett. **329**, 399–404 (2000). [CrossRef]

*t*is the time window for integration,

_{win}*T*is the accumulation time, and

_{acc}*J*

^{(Bell)}(

*τ*)(

*J*

^{(TM)}(

*τ*)) is the probability density detecting a photon in Bob’s arm at time

*τ*provided that there was a photon in Alice at time origin for the Bell (TM) state. For the PDC source, due to the simultaneous bi-photon generation, the probability density focuses on rather narrow time region at around

*τ*= 0 within a full time span of 50 ns in the MCA. Therefore,

*J*

^{(Bell)}(

*τ*) can be expressed as

*ηG*(0,

*σ*

^{2}), where

*η*is the system transmission efficiency (including transmission of all optics as well as detection efficiency) and

*G*(0,

*σ*

^{2}) is a normalized Gaussian distribution function centered at

*τ*= 0 with a variance of

*σ*

^{2}. When the

*t*is set so that

_{win}*t*≫

_{win}*σ*, Eq. (7) reduces to

*C*

^{(Bell)}=

*η*

*T*

_{acc}*R*. This explains the linear dependence observed in Fig. 7(a). Here the slope of ∼ 0.01 corresponds to the system transmission

_{Alice}*η*of our setup with

*T*= 1 ns. As for temporal distribution of the coincidence counts, since the

_{acc}*C*

^{(Bell)}does not include

*t*with

_{win}*t*≫

_{win}*σ*, coincidence counts are well localized at around the time origin as experimentally observed in Fig. 6. On the other hand, such temporal correlation is absent for the thermal radiation source. Thus the coincidence counts between photon-pair is regarded as an accidental event in the independent photon detection by Alice and Bob. Thus, through the relation

*J*

^{(TM)}(

*τ*) =

*R*and

_{Bob}*R*≈

_{Alice}*R*, the quadratic relation

_{Bob}^{−9}, which agrees well to the expected value of 4

*σ*∼ 2.4 × 10

^{−9}. With respect to temporal distribution,

*C*

^{(TM)}is now proportional to the

*t*, then the coincidence count density is uniformly distributed over delay time as indicated by the gray area in Fig. 6.

_{win}*C*

^{(cross)}since there is no temporal correlation between these independent photon sources. In the present case, however,

*C*

^{(cross)}/

*C*

^{(Bell)}is estimated to be at most 3.5% for the bi-photon state (vi) in Fig. 5 with the highest intensity of the thermal radiation source. This is below the standard deviation of the amplitude of constant coincidence counts of ∼ 7%, thus no significant difference in the constant coincidence amplitudes between the entangled-classical hybrid photon source and the thermal source alone was discerned under the present experimental conditions. Note that photon-pair states from the thermal radiation source leads to constant coincidence counts, and no effect of photon bunching for chaotic light [35] was detected. This is because the time resolution of our setup (∼6.1 ps) is not enough to detect the bunching structure with a time scale of

*c*is the light velocity,

*λ*is a center wavelength, and

_{c}*δλ*is a bandwidth of the IF filter.

## 5. Determination of the Werner states

*C*

^{(Bell)}and

*C*

^{(TM)}are now independently obtained with the present entangled-classical hybrid photon emitter, we can evaluate the bi-photon Werner states from a single coincidence count histogram in principle. In case of Fig. 6, for example, the singlet weight

*p*obtained from Eq. (6) is 0.32. This is highly close to the 0.34 calculated by the standard approach employing the density matrix built up by the quantum-state tomography for the same S

*assuming the Werner state.*

_{L}*p*values obtained from the Eq. (6) are compared with the ones obtained by the tomographically calculated values in Fig. 8. Uncertainties are also shown as error bars. The S

*values for each datapoints are common with Fig. 5, and the solid curve is a expected singlet weight as a function of the S*

_{L}*for the Werner states. The obtained*

_{L}*p*values from the areal ratio in the coincidence histograms for each points are plotted as circles. Fairly nice agreement of

*p*determined by the two separate measurements is achieved, thus the direct evaluation of the photon-pair states in the Werner state is shown to be possible. The present method is rather instantaneous in the sense that

*p*value can be speculated even in ongoing measurement from the Eq. (6) by glancing at building coincidence histogram and grasping

*C*

^{(Bell)}and

*C*

^{(TM)}. Thus collecting whole data set and subsequent data processing to obtain full knowledge of the biphoton state is not required.

## 6. Conclusion

## Acknowledgments

## References and links

1. | M. A. Nielsen and I. L. Chuang, |

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

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

4. | D. Bouwmeester, J.-W. Pan, K. Mattle, M. Eibl, H. Weinfurter, and A. Zeilinger, “Experimental quantum teleportation,” Nature |

5. | P. W. Shor, “Scheme for reducing decoherence in quantum computer memory,” Phys. Rev. A |

6. | C. H. Bennett, D. P. DiVincenzo, J. A. Smolin, and W. K. Wootters, “Mixed-state entanglement and quantum error correction,” Phys. Rev. A |

7. | P. Michler, |

8. | H. Kumano, S. Kimura, M. Endo, H. Sasakura, S. Adachi, S. Muto, and I. Suemune, “Deterministic single-photon and polarization-correlated photon pair generations from a single InAlAs quantum dot,” J. Nanoelectron. Optoelectron. |

9. | Y. Hayashi, K. Tanaka, T. Akazaki, M. Jo, H. Kumano, and I. Suemune, “Superconductor-based light emitting diode: demonstration of role of cooper pairs in radiative recombination processes,” Appl. Phys. Express |

10. | Y. Asano, I. Suemune, H. Takayanagi, and E. Hanamura, “Luminescence of a Cooper pair,” Phys. Rev. Lett. |

11. | R. M. Stevenson, R. J. Young, P. Atkinson, K. Cooper, D. A. Ritchie, and A. J. Shields, “A semiconductor source of triggered entangled photon pairs,” Nature |

12. | N. Akopian, N. H. Lindner, E. Poem, Y. Berlatzky, J. Avron, D. Gershoni, B. D. Gerardot, and P. M. Petroff, “Entangled photon pairs from semiconductor quantum dots,” Phys. Rev. Lett. |

13. | R. Hafenbrak, S. M. Ulrich, P. Michler, L. Wang, A. Rastelli, and O. G. Schmidt, “Triggered polarization-entangled photon pairs from a single quantum dot up to 30 K,” New J. Phys. |

14. | A. Mohan, M. Felici, P. Gallo, B. Dwir, A. Rudra, J. Faist, and E. Kapon, “Polarization-entangled photons produced with high-symmetry site-controlled quantum dots,” Nat. Photonics |

15. | R. F. Werner, “Quantum states with Einstein-Podolsky-Rosen correlations admitting a hidden-variable model,” Phys. Rev. A |

16. | W. J. Munro, D. F. V. James, A. G. White, and P. G. Kwiat, “Maximizing the entanglement of two mixed qubits,” Phys. Rev. A |

17. | M. Caminati, F. De Martini, R. Perris, F. Sciarrino, and V. Secondi, “Nonseparable Werner states in spontaneous parametric down-conversion,” Phys. Rev. A |

18. | G. Puentes, A. Aiello, D. Voigt, and J. P. Woerdman, “Entangled mixed-state generation by twin-photon scattering,” Phys. Rev. A |

19. | Y.-S. Zhang, Y.-F. Huang, C.-F. Li, and G.-C. Guo, “Experimental preparation of the Werner state via spontaneous parametric down-conversion,” Phys. Rev. A |

20. | M. Barbieri, F. De Martini, G. Di Nepi, P. Mataloni, G. M. D’Ariano, and C. Macchiavello, “Detection of entanglement with polarized photons: experimental realization of an entanglement witness,” Phys. Rev. Lett. |

21. | M. Barbieri, F. De Martini, G. Di Nepi, and P. Mataloni, “Generation and characterization of Werner states and maximally entangled mixed states by a universal source of entanglement,” Phys. Rev. Lett. |

22. | C. Kurtsiefer, S. Mayer, P. Zarda, and H. Weinfurter, “Stable solid-state source of single photons,” Phys. Rev. Lett. |

23. | P. Michler, A. Imamoğlu, M. D. Mason, P. J. Carson, G. F. Strouse, and S. K. Buratto, “Quantum correlation among photons from a single quantum dot at room temperature,” Nature |

24. | C. Santori, M. Pelton, G. Solomon, Y. Dale, and Y. Yamamoto, “Triggered single photons from a quantum dot,” Phys. Rev. Lett. |

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

26. | P. G. Kwiat, K. Mattle, H. Weinfurter, A. Zeilinger, A. V. Sergienko, and Y. Shih, “New high-intensity source of polarization-entangled photon pairs,” Phys. Rev. Lett. |

27. | J. S. Bell, Physics (1965), Vol. |

28. | R. J. Young, R. M. Stevenson, A. J. Hudson, C. A. Nicoll, D. A. Ritchie, and A. J. Shields, “Bell-inequality violation with a triggered photon-pair source,” Phys. Rev. Lett. |

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

30. | S. Bose and V. Vedral, “Mixedness and teleportation,” Phys. Rev. A |

31. | C. Cinelli, G. Di Nepi, F. De Martini, M. Barbieri, and P. Mataloni, “Parametric source of two-photon states with a tunable degree of entanglement and mixing: experimental preparation of Werner states and maximally entangled mixed states,” Phys. Rev. A |

32. | C. H. Bennett, G. Brassard, S. Popescu, B. Schumacher, J. A. Smolin, and W. K. Wootters, “Purification of noisy entanglement and faithful teleportation via noisy channels,” Phys. Rev. Lett. |

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

34. | B. Lounis, H. A. Bechtela, D. Gerionc, P. Alivisatosc, and W. E. Moernera, “Photon antibunching in single CdSe/ZnS quantum dot fluorescence,” Chem. Phys. Lett. |

35. | R. Loudon, |

**OCIS Codes**

(230.5590) Optical devices : Quantum-well, -wire and -dot devices

(270.0270) Quantum optics : Quantum optics

(270.5290) Quantum optics : Photon statistics

(270.5585) Quantum optics : Quantum information and processing

**ToC Category:**

Quantum Optics

**History**

Original Manuscript: May 18, 2011

Revised Manuscript: June 9, 2011

Manuscript Accepted: June 22, 2011

Published: July 11, 2011

**Citation**

H. Kumano, K. Matsuda, S. Ekuni, H. Sasakura, and I. Suemune, "Characterization of two-photon polarization mixed states generated from entangled-classical hybrid photon source," Opt. Express **19**, 14249-14259 (2011)

http://www.opticsinfobase.org/oe/abstract.cfm?URI=oe-19-15-14249

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### References

- M. A. Nielsen and I. L. Chuang, Quantum Computation and Qnautum Information (Cambridge University Press, 2000).
- A. K. Ekert, “Quantum cryptography based on Bell’s theorem,” Phys. Rev. Lett. 67, 661–663 (1991). [CrossRef] [PubMed]
- C. H. Bennett, G. Brassard, C. Crépeau, 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]
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- P. W. Shor, “Scheme for reducing decoherence in quantum computer memory,” Phys. Rev. A 52, R2493–R2496 (1995). [CrossRef] [PubMed]
- C. H. Bennett, D. P. DiVincenzo, J. A. Smolin, and W. K. Wootters, “Mixed-state entanglement and quantum error correction,” Phys. Rev. A 54, 3824–3851 (1996). [CrossRef] [PubMed]
- P. Michler, Single Semiconductor Quantum Dots (Springer, 2009). [CrossRef]
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- Y. Hayashi, K. Tanaka, T. Akazaki, M. Jo, H. Kumano, and I. Suemune, “Superconductor-based light emitting diode: demonstration of role of cooper pairs in radiative recombination processes,” Appl. Phys. Express 1, 1–3 (2008). [CrossRef]
- Y. Asano, I. Suemune, H. Takayanagi, and E. Hanamura, “Luminescence of a Cooper pair,” Phys. Rev. Lett. 103, 187001 (2009).
- R. M. Stevenson, R. J. Young, P. Atkinson, K. Cooper, D. A. Ritchie, and A. J. Shields, “A semiconductor source of triggered entangled photon pairs,” Nature 439, 179–182 (2006). [CrossRef] [PubMed]
- N. Akopian, N. H. Lindner, E. Poem, Y. Berlatzky, J. Avron, D. Gershoni, B. D. Gerardot, and P. M. Petroff, “Entangled photon pairs from semiconductor quantum dots,” Phys. Rev. Lett. 96, 130501 (2006). [CrossRef] [PubMed]
- R. Hafenbrak, S. M. Ulrich, P. Michler, L. Wang, A. Rastelli, and O. G. Schmidt, “Triggered polarization-entangled photon pairs from a single quantum dot up to 30 K,” New J. Phys. 9, 315 (2007). [CrossRef]
- A. Mohan, M. Felici, P. Gallo, B. Dwir, A. Rudra, J. Faist, and E. Kapon, “Polarization-entangled photons produced with high-symmetry site-controlled quantum dots,” Nat. Photonics 4, 302–306 (2010). [CrossRef]
- R. F. Werner, “Quantum states with Einstein-Podolsky-Rosen correlations admitting a hidden-variable model,” Phys. Rev. A 40, 4277–4281 (1989). [CrossRef] [PubMed]
- W. J. Munro, D. F. V. James, A. G. White, and P. G. Kwiat, “Maximizing the entanglement of two mixed qubits,” Phys. Rev. A 64, 030302(R) (2001). [CrossRef]
- M. Caminati, F. De Martini, R. Perris, F. Sciarrino, and V. Secondi, “Nonseparable Werner states in spontaneous parametric down-conversion,” Phys. Rev. A 73, 032312 (2006). [CrossRef]
- G. Puentes, A. Aiello, D. Voigt, and J. P. Woerdman, “Entangled mixed-state generation by twin-photon scattering,” Phys. Rev. A 75, 032319 (2007). [CrossRef]
- Y.-S. Zhang, Y.-F. Huang, C.-F. Li, and G.-C. Guo, “Experimental preparation of the Werner state via spontaneous parametric down-conversion,” Phys. Rev. A 66, 062315 (2002). [CrossRef]
- M. Barbieri, F. De Martini, G. Di Nepi, P. Mataloni, G. M. D’Ariano, and C. Macchiavello, “Detection of entanglement with polarized photons: experimental realization of an entanglement witness,” Phys. Rev. Lett. 91, 227901 (2003). [CrossRef] [PubMed]
- M. Barbieri, F. De Martini, G. Di Nepi, and P. Mataloni, “Generation and characterization of Werner states and maximally entangled mixed states by a universal source of entanglement,” Phys. Rev. Lett. 92, 177901 (2004). [CrossRef] [PubMed]
- C. Kurtsiefer, S. Mayer, P. Zarda, and H. Weinfurter, “Stable solid-state source of single photons,” Phys. Rev. Lett. 85, 290–293 (2000). [CrossRef] [PubMed]
- P. Michler, A. Imamoğlu, M. D. Mason, P. J. Carson, G. F. Strouse, and S. K. Buratto, “Quantum correlation among photons from a single quantum dot at room temperature,” Nature 406, 968–970 (2000). [CrossRef] [PubMed]
- C. Santori, M. Pelton, G. Solomon, Y. Dale, and Y. Yamamoto, “Triggered single photons from a quantum dot,” Phys. Rev. Lett. 86, 1502–1505 (2001). [CrossRef] [PubMed]
- D. F. V. James, P. G. Kwiat, W. J. Munro, and A. G. White, “Measurement of qubits,” Phys. Rev. A 64, 052312 (2001). [CrossRef]
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