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Optics Express

  • Editor: Michael Duncan
  • Vol. 14, Iss. 8 — Apr. 17, 2006
  • pp: 3453–3460
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Long-distance distribution of time-bin entanglement generated in a cooled fiber

Hiroki Takesue  »View Author Affiliations


Optics Express, Vol. 14, Issue 8, pp. 3453-3460 (2006)
http://dx.doi.org/10.1364/OE.14.003453


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Abstract

This paper reports the first demonstration of the generation and distribution of time-bin entangled photon pairs in the 1.5-μm band using spontaneous four-wave mixing in a cooled fiber. Noise photons induced by spontaneous Raman scattering were suppressed by cooling a dispersion shifted fiber with liquid nitrogen, which resulted in a significant improvement in the visibility of two-photon interference. By using this scheme, time-bin entangled qubits were successfully distributed over 60 km of optical fiber with a visibility of 76%, which was obtained without removing accidental coincidences.

© 2006 Optical Society of America

1. Introduction

The entangled states of quantum particles constitute the quintessential feature of quantum mechanics because they highlight its non-locality most vividly [1

1. A. Einstein, B. Podolsky, and N. Rosen, “Can quantum-mechanical description of physical reality be considered complete?,” Phys. Rev. 47, 777–780 (1935). [CrossRef]

]. Moreover, entanglements form the basis of quantum information, and facilitate such applications as quantum key distribution (QKD) [2

2. A. K. Ekert, “Quantum cryptography based on Bell’s theorem,” Phys. Rev. Lett. 67, 661–663 (1991). [CrossRef] [PubMed]

, 3

3. C. H. Bennett, G. Brassard, and N. D. Mermin, “Quantum cryptography without Bell’s theorem,” Phys. Rev. Lett. 68, 557–559 (1992). [CrossRef] [PubMed]

], quantum teleportation [4

4. 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 (1993). [CrossRef] [PubMed]

], and quantum repeaters [5

5. H. J. Briegel, W. Dur, J. I. Cirac, and P. Zoller, “Quantum repeaters: the role of imperfect local operations in quantum communication,” Phys. Rev. Lett. 81, 5932–5935 (1998). [CrossRef]

]. Of the many forms of entanglement, entangled photons are important because they are suitable for distributing quantum information over long distances. Although several good sources are available in the short wavelength band [6

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

, 7

7. P. G. Kwiat, E. Waks, A. G. White, I. Appelbaum, and P. H. Eberhard, “Ultrabright source of polarization-entangled photons,” Phys. Rev. A 60, R773–776 (1999). [CrossRef]

], an entangled photon-pair source in the 1.5-μm band is needed if we are to realize quantum information systems over optical fiber networks. Recently, spontaneous four-wave mixing (SFWM) in a dispersion shifted fiber (DSF) has been drawing attention as a promising method for generating entanglement in the 1.5-μm band [8

8. 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, 053601 (2005). [CrossRef] [PubMed]

, 9

9. H. Takesue and K. Inoue, “Generation of polarization entangled photon pairs and violation of Bell’s inequatilty using spontaneous four-wave mixing in fiber loop,” Phys. Rev. A , 70, 031802(R) (2004). [CrossRef]

, 10

10. H. Takesue and K. Inoue, “Generation of 1.5-μm band time-bin entanglement using spontaneous fiber four-wave mixing and planar lightwave circuit interferometers,” Phys. Rev. A 72, 041804(R) (2005). [CrossRef]

]. Polarization [8

8. 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, 053601 (2005). [CrossRef] [PubMed]

, 9

9. H. Takesue and K. Inoue, “Generation of polarization entangled photon pairs and violation of Bell’s inequatilty using spontaneous four-wave mixing in fiber loop,” Phys. Rev. A , 70, 031802(R) (2004). [CrossRef]

] and time-bin entangled photons [10

10. H. Takesue and K. Inoue, “Generation of 1.5-μm band time-bin entanglement using spontaneous fiber four-wave mixing and planar lightwave circuit interferometers,” Phys. Rev. A 72, 041804(R) (2005). [CrossRef]

] have already been generated and successfully distributed over optical fibers [9

9. H. Takesue and K. Inoue, “Generation of polarization entangled photon pairs and violation of Bell’s inequatilty using spontaneous four-wave mixing in fiber loop,” Phys. Rev. A , 70, 031802(R) (2004). [CrossRef]

, 10

10. H. Takesue and K. Inoue, “Generation of 1.5-μm band time-bin entanglement using spontaneous fiber four-wave mixing and planar lightwave circuit interferometers,” Phys. Rev. A 72, 041804(R) (2005). [CrossRef]

, 11

11. X. Li, P. L. Voss, J. Chen, J. E. Sharping, and P. Kumar, “Storage and long-distance distribution of telecommunications-band polarization entanglement generated in an optical fiber,” Opt. Lett. 30, 1201–1203 (2005). [CrossRef] [PubMed]

]. In addition, quantum correlated photon pairs in the shorter wavelength bands have been generated using SFWM in photonic crystal fiber [12

12. J. G. Rarity, J. Fulconis, J. Duligall, W. J. Wadsworth, and P. St. J. Russell, “Photonic crystal fiber source of correlated photon pairs,” Opt. Express 13, 534–544 (2005). [CrossRef] [PubMed]

, 13

13. J. Fan, A. Migdall, and L. J. Wang, “Efficient generation of correlated photon pairs in a microstructure fiber,” Opt. Lett. 30, 3368–3370 (2005). [CrossRef]

]. The merit of this scheme is the good coupling efficiency it provides between nonlinear medium (i.e. a DSF) and transmission fibers.

To solve this problem, the author and K. Inoue recently demonstrated that noise photons caused by spontaneous Raman scattering were suppressed by cooling a DSF with liquid nitrogen [16

16. H. Takesue and K. Inoue, “1.5-μm band quantum-correlated photon pair generation in dispersion-shifted fiber: suppression of noise photons by cooling fiber,” Opt. Express 13, 7832–7839 (2005). [CrossRef] [PubMed]

]. We observed a significant enhancement of the quantum correlation characteristics in a time-correlation measurement. This report has recently been followed by a study of the generation of polarization entanglement using a cooled fiber [17

17. K. F. Lee, J. Chen, C. Liang, X. Li, P. L. Voss, and P. Kumar, “High-purity telecom-band entangled photon-pairs via four-wave mixing in dispersion-shifted fiber,” postdeadline paper presented at the Frontiers in Optics 2005-the 89th OSA Annual Meeting, Tucson, AZ, October 16-20, 2005;paper PDP-A4.

]. However, it is difficult to distribute polarization qubits over optical fiber because polarization mode dispersion (PMD) induces decoherence.

2. Suppression of spontaneous Raman scattering by cooling fiber

Spontaneous Raman scattering is a process in which a spontaneous photon is generated by a nonlinear interaction between a pump photon and a phonon [20

20. M. G. Raymer and I. A. Walmsley, “The quantum coherence properties of stimulated Raman scattering,” Progress in Optics 28, 181–270 (1990). [CrossRef]

]. The numbers of Stokes, ns, and anti-Stokes photons, nas as a function of temperature T are expressed as [16

16. H. Takesue and K. Inoue, “1.5-μm band quantum-correlated photon pair generation in dispersion-shifted fiber: suppression of noise photons by cooling fiber,” Opt. Express 13, 7832–7839 (2005). [CrossRef] [PubMed]

]

ns(T)=gLeαL1exp(kBT),
(1)
nas(T)=gLeαLexp(kBT)1,
(2)

3. Experiments

Fig. 1. Experimental setup.

Figure 1 shows the experimental setup. A continuous lightwave with a wavelength of 1551.1 nm from an external-cavity diode laser is modulated into double pulses with a LiNbO3 intensity modulator. The pulse width and interval are 100 ps and 1 ns, respectively. The coherence time of the continuous lightwave is ~10 μs. The double pulse is amplified by an erbium-doped fiber amplifier (EDFA), and launched into a 500-m DSF after passing through optical filters to eliminate amplified spontaneous emission noise from the EDFA. The DSF is formed into a loose coil about ~30 cm in diameter without a bobbin to reduce the bending stress, and then placed in a Styrofoam container filled with liquid nitrogen. The zero-dispersion wavelength of the DSF was 1551.1 nm. In the DSF, the double pulses work as a pump and generate time-correlated photon pairs through SFWM. The pump, signal and idler frequencies, fp, fs and fi, respectively, have the following energy conservation relationship: 2fp = fs + fi. As a result, the following time-bin entangled state is obtained at the output of the DSF [18

18. J. Brendel, N. Gisin, W. Tittel, and H. Zbinden, “Pulsed energy-time entangled twin-photon source for quantum communication,” Phys. Rev. Lett. 82, 2594–2597 (1999). [CrossRef]

].

Ψ=12(1s1i+e2s2i)
(3)

Here, ∣kx represents a state in which there is a photon in a time slot k in a mode x, signal (s) or idler (i). ϕ is a relative phase term that is equal to 2ϕp, where ϕp is the phase difference between two pump pulses, and is stably fixed because of the long coherent time of the laser output. The output light from the DSF is input into a fiber Bragg grating (FBG) to suppress pump photons, and launched into an arrayed waveguide grating (AWG) to separate the signal and idler channels. AWG output ports with peak frequencies of +400 and -400 GHz from the pump photon frequency are used for the signal and idler, respectively. The 3-dB bandwidths of the signal and idler channels are both 25 GHz (≃0.2 nm). Then the signal and idler photons are launched into optical bandpass filters to further suppress the pump photons.

The photons output from each bandpass filter are transmitted over a 30-km DSF with a loss of 0.2 dB/km and then input into a 1-bit delayed Mach-Zehnder interferometer fabricated using planar lightwave circuit (PLC) technology [23

23. T. Honjo, K. Inoue, and H. Takahashi, “Differential-phase-shift quantum key distribution experiment with a planar light-wave circuit Mach-Zehnder interferometer,” Opt. Lett. 29, 2797–2799 (2004). [CrossRef] [PubMed]

, 10

10. H. Takesue and K. Inoue, “Generation of 1.5-μm band time-bin entanglement using spontaneous fiber four-wave mixing and planar lightwave circuit interferometers,” Phys. Rev. A 72, 041804(R) (2005). [CrossRef]

]. A state |kx is converted as follows by the interferometer.

kx12(k,axk,bx+eiθxk+1,ax+eiθxk+1,bx)
(4)

Here, a and b denote two output ports of the interferometer. θx is the phase difference between the two paths of the interferometer for channel x, and can be tuned by changing the temperature. As a result, the time-bin entangled state ∣Ψ〉 is converted to

Ψ142{1,as1,ai1,as1,bi
1,bs1,ai+1,bs1,bi
+(e+e)2,as2,ai+(ee)2,as2,bi
+(ee)2,bs2,ai+(e+e)2,bs2,bi
ei(ϕ+θ)3,as3,ai+ei(ϕ+θ)3,as3,bi
+ei(ϕ+θ)3,bs3,ai+ei(ϕ+θ)3,bs3,bi
+},
(5)

where θ = θs + θi and 16 non-coincident terms in the parentheses are not shown because they are not observed in a coincidence measurement. We can observe a two-photon interference fringe by changing θ and measuring the coincidence counts in the second time slot.

Port a of each interferometer is connected to a photon counter based on an InGaAs avalanche photodiode operated in a gated mode with a 4-MHz gate frequency. The electric signals from the photon counter for the signal and the idler are input into a time interval analyzer as a start and stop pulse, respectively. The losses of the signal and idler channels including the excess losses of the interferometers are both approximately 8 dB. The quantum efficiencies and dark count rate per gate are 8% and 4 × 10-5 for the signal, and 7% and 5 × 10-5 for the idler, respectively.

This experiment uses two detectors connected to port a of the interferometers, so only the fifth term in parentheses in Eq. (5) is observed in a two-photon interference measurement. This means that a time-bin entangled photon pair is detected with a probability of 1/8 when a constructive interference occurs (i.e. θ = ϕ). When the average number of correlated photon pairs per pulse is μc (which means that the average number per time-bin qubit is 2μc), the count rate of correlated events in a constructive interference, Rc, is expressed as

Rc=μc4αsαi,
(6)

where αs and αi denote transmittances for the signal and idler channels including the quantum efficiency of the photon counters, respectively. On the other hand, the accidental coincidence rate Racc is given by

Racc=(μsαs2+ds)·(μiαi2+di)μsμi4αsαi,
(7)

where μx and dx denote the average number of photons per pulse and the dark count rate of the detector for channel x with x = s, i, respectively. If the average number of noise photons per pulse for channel x is given by μnx, μx is expressed as

μx=μc+μnx.
(8)

A count rate of Rc + Racc and Racc is observed at the maximum and minimum points of a two-photon interference fringe. Therefore, the visibility V is expressed as

V=RcRc+2Raccμcμc+2μsμn.
(9)
Fig. 2. Two-photon interference fringes when the DSF was (a) at room temperature and (b) in liquid nitrogen.

First, I confirmed the effectiveness of fiber cooling for improving the visibility of two-photon interference without connecting 30-km DSF spools. I changed θi by changing the temperature of the interferometer for the idler, while fixing θs, and recorded the coincidence counts. μs and μi were set at approximately 0.05 and 0.06, respectively, for both the cooled and uncooled experiments [24

24. Exactly speaking, μi was set at the same value in both cases, and μs for the cooled fiber was slightly smaller than that for the uncooled fiber. This is because, according to Eqs. (1) and (2), the difference between Raman gain coefficients for the Stokes and anti-Stokes processes increases slightly as the fiber is cooled.

]. The average count rates of the signal and idler channels, respectively, were approximately 1500 and 1600 Hz throughout measurements. Without cooling the DSF, the visibility of the two-photon interference fringe was 64.7%, which was obtained without removing the accidental coincidences (Fig. 2 (a)). Figure 2 (b) shows the fringe when the DSF was cooled. The level of the minimum points of a fringe corresponds to the number of accidental coincidences, which is proportional to μsμi as shown in Eq. (7). Because μs and μi were set at the same value for both measurements, the minimum points of both fringes were at almost the same level, as seen in Fig. 2. However, the peak level of the fringe increased significantly when the DSF was cooled. This implies that the number of noise photons is suppressed and so the portion of correlated photon pairs is effectively increased by cooling the DSF. As a result, the visibility increased to 80.0% with the accidental coincidences included. The average number of correlated photon pairs per pulse μc can be estimated from the obtained visibilities and Eqs. (6)–(9). As a result, μc was ~0.02 when the DSF was uncooled and ~0.04 when cooled. Thus, it is experimentally confirmed that fiber cooling is effective for improving the visibility of a two-photon interference fringe.

I then inserted a 30-km DSF spool between the bandpass filter and the interferometer in both the signal and idler arms, and undertook a two-photon interference experiment. The total losses of the 30-km DSF spools, including connector and splice losses, were both ~6.5 dB. Therefore, the total loss between the cooled fiber output and the photon counter input was ~14.5 dB for both signal and idler channels. The result is shown in Fig. 3. μs and μi were again set at around 0.05 and 0.06, respectively. Squares show the coincidence rate per start pulse and x symbols show the idler count rate as a function of interferometer temperature. The average count rate for the signal was ~430 Hz. The average coincidence rate at the peak of the fringe was as low as ~0.3 Hz, which resulted in a long measurement time (the measurement shown in Fig. 3 took more than three hours to complete). The visibility of the fringe was 75.8%, which was obtained without removing accidental coincidences. Thus, time-bin entangled photon pairs were successfully distributed over 60 km (30 km × 2) of fiber.

Fig. 3. Two-photon interference fringe and idler count rate after transmission over 60-km fiber. Squares: coincidence rate per start pulse, x symbols: idler count rate.

The visibility of the fringe after removing accidental coincidences was 96.8%. This result is slightly worse than >99% visibility after the elimination of the accidental coincidences reported in [10

10. H. Takesue and K. Inoue, “Generation of 1.5-μm band time-bin entanglement using spontaneous fiber four-wave mixing and planar lightwave circuit interferometers,” Phys. Rev. A 72, 041804(R) (2005). [CrossRef]

]. This slight degradation is probably caused by the larger statistical fluctuation as a result of the smaller coincidence rate.

4. Discussions

This experiment used DSF spools because long standard single-mode fibers (SMF) with 1.3-μm zero dispersion wavelength were not available. According to the following calculation, the photons generated from this source are expected to be transmitted over 60 km of SMF, thanks to the narrow bandwidth of the signal/idler photons. Let us assume that the dispersion in the cooled fiber and the optical filters is negligible and the transmittance spectra of signal and idler channels are both Gaussian. Then, the temporal shapes of the signal and idler photons are approximated as transform-limited Gaussian pulses. The half-width at the 1/e-intensity point T 0 is expressed as √ln2/(πΔf), where Δf is the full width at half maximum of the signal/idler spectrum. After transmission over an optical fiber with length z, the half width at the 1/e-intensity point of the output pulse T 1 is expressed as [22

22. G. P. Agrawal, Nonlinear fiber optics (Academic Press, 1995).

]

T1=T01+(zβ2T02)2,
(10)

where β 2 denotes second derivative of the propagation constant in optical fiber. With z = 30 km, Δf = 25 GHz and β 2 = -20 ps2/km, T 1 is calculated to be ~60 ps, which is small compared with the 1-ns pulse interval. Thus, chromatic dispersion does not seem to result in serious degradation of the visibility even when two 30-km SMF spools are used. Nevertheless, it will be important to demonstrate long-distance distribution over SMF experimentally in the future.

5. Conclusion

I have reported an experimental generation of time-bin entanglement using a cooled fiber. A significant improvement in the visibility was observed by cooling the DSF with liquid nitrogen. As a result, entangled photons were successfully distributed over 60-km (30 km × 2) fibers with a fair visibility of 75.8%. The results show that a 1.5-μm band entanglement source based on a cooled fiber is a promising technology for realizing advanced quantum information systems over optical fiber networks.

Acknowledgments

The author thanks K. Inoue for helpful comments and T. Honjo for help in making the measurement software. This work was supported in part by National Institute of Information and Communications Technology (NICT) of Japan.

References and links

1.

A. Einstein, B. Podolsky, and N. Rosen, “Can quantum-mechanical description of physical reality be considered complete?,” Phys. Rev. 47, 777–780 (1935). [CrossRef]

2.

A. K. Ekert, “Quantum cryptography based on Bell’s theorem,” Phys. Rev. Lett. 67, 661–663 (1991). [CrossRef] [PubMed]

3.

C. H. Bennett, G. Brassard, and N. D. Mermin, “Quantum cryptography without Bell’s theorem,” Phys. Rev. Lett. 68, 557–559 (1992). [CrossRef] [PubMed]

4.

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 (1993). [CrossRef] [PubMed]

5.

H. J. Briegel, W. Dur, J. I. Cirac, and P. Zoller, “Quantum repeaters: the role of imperfect local operations in quantum communication,” Phys. Rev. Lett. 81, 5932–5935 (1998). [CrossRef]

6.

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

7.

P. G. Kwiat, E. Waks, A. G. White, I. Appelbaum, and P. H. Eberhard, “Ultrabright source of polarization-entangled photons,” Phys. Rev. A 60, R773–776 (1999). [CrossRef]

8.

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, 053601 (2005). [CrossRef] [PubMed]

9.

H. Takesue and K. Inoue, “Generation of polarization entangled photon pairs and violation of Bell’s inequatilty using spontaneous four-wave mixing in fiber loop,” Phys. Rev. A , 70, 031802(R) (2004). [CrossRef]

10.

H. Takesue and K. Inoue, “Generation of 1.5-μm band time-bin entanglement using spontaneous fiber four-wave mixing and planar lightwave circuit interferometers,” Phys. Rev. A 72, 041804(R) (2005). [CrossRef]

11.

X. Li, P. L. Voss, J. Chen, J. E. Sharping, and P. Kumar, “Storage and long-distance distribution of telecommunications-band polarization entanglement generated in an optical fiber,” Opt. Lett. 30, 1201–1203 (2005). [CrossRef] [PubMed]

12.

J. G. Rarity, J. Fulconis, J. Duligall, W. J. Wadsworth, and P. St. J. Russell, “Photonic crystal fiber source of correlated photon pairs,” Opt. Express 13, 534–544 (2005). [CrossRef] [PubMed]

13.

J. Fan, A. Migdall, and L. J. Wang, “Efficient generation of correlated photon pairs in a microstructure fiber,” Opt. Lett. 30, 3368–3370 (2005). [CrossRef]

14.

X. Li, J. Chen, P. Voss, J. Sharping, and P. Kumar, “All-fiber photon-pair source for quantum communications: Improved generation of correlated photons,” Opt. Express 12, 3737–3744 (2004). [CrossRef] [PubMed]

15.

K. Inoue and K. Shimizu, “Generation of quantum-correlated photon pairs in optical fiber: influence of spontaneous Raman scattering,” Jpn. J. Appl. Phys. 43, 8048–8052 (2004). [CrossRef]

16.

H. Takesue and K. Inoue, “1.5-μm band quantum-correlated photon pair generation in dispersion-shifted fiber: suppression of noise photons by cooling fiber,” Opt. Express 13, 7832–7839 (2005). [CrossRef] [PubMed]

17.

K. F. Lee, J. Chen, C. Liang, X. Li, P. L. Voss, and P. Kumar, “High-purity telecom-band entangled photon-pairs via four-wave mixing in dispersion-shifted fiber,” postdeadline paper presented at the Frontiers in Optics 2005-the 89th OSA Annual Meeting, Tucson, AZ, October 16-20, 2005;paper PDP-A4.

18.

J. Brendel, N. Gisin, W. Tittel, and H. Zbinden, “Pulsed energy-time entangled twin-photon source for quantum communication,” Phys. Rev. Lett. 82, 2594–2597 (1999). [CrossRef]

19.

I. Marcikic, H. de Reidmatten, W. Tittel, H. Zbinden, M. Legre, and N. Gisin, “Distribution of time-bin entangled qubits over 50 km of optical fiber,” Phys. Rev. Lett. 93, 180502 (2004). [CrossRef] [PubMed]

20.

M. G. Raymer and I. A. Walmsley, “The quantum coherence properties of stimulated Raman scattering,” Progress in Optics 28, 181–270 (1990). [CrossRef]

21.

The unit of ns and nas is determined by that of the pump photon number: for example, if the pump photon number is defined per pulse, ns and nas denote the number of Stokes and anti-Stokes photons per pump pulse.

22.

G. P. Agrawal, Nonlinear fiber optics (Academic Press, 1995).

23.

T. Honjo, K. Inoue, and H. Takahashi, “Differential-phase-shift quantum key distribution experiment with a planar light-wave circuit Mach-Zehnder interferometer,” Opt. Lett. 29, 2797–2799 (2004). [CrossRef] [PubMed]

24.

Exactly speaking, μi was set at the same value in both cases, and μs for the cooled fiber was slightly smaller than that for the uncooled fiber. This is because, according to Eqs. (1) and (2), the difference between Raman gain coefficients for the Stokes and anti-Stokes processes increases slightly as the fiber is cooled.

25.

A. G. White, D. F. V. James, P. H. Eberhard, and P. G. Kwiat, “Nonmaximally entangled states: production, characterization and utilization,” Phys. Rev. Lett. 83, 3103–3107 (1999). [CrossRef]

26.

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

27.

P. G. Kwiat, A. M. Steinberg, and R. Y. Chao, “High-visibility interference in a Bell-inequality experiment for energy and time,” Phys. Rev. A 47, R2472 (1993). [CrossRef]

OCIS Codes
(190.4370) Nonlinear optics : Nonlinear optics, fibers
(270.0270) Quantum optics : Quantum optics

ToC Category:
Nonlinear Optics

History
Original Manuscript: February 10, 2006
Revised Manuscript: April 6, 2006
Manuscript Accepted: April 11, 2006
Published: April 17, 2006

Citation
Hiroki Takesue, "Long-distance distribution of time-bin entanglement generated in a cooled fiber," Opt. Express 14, 3453-3460 (2006)
http://www.opticsinfobase.org/oe/abstract.cfm?URI=oe-14-8-3453


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References

  1. A. Einstein, B. Podolsky, and N. Rosen, "Can quantum-mechanical description of physical reality be considered complete?," Phys. Rev. 47, 777-780 (1935). [CrossRef]
  2. A. K. Ekert, "Quantum cryptography based on Bell’s theorem," Phys. Rev. Lett. 67, 661-663 (1991). [CrossRef] [PubMed]
  3. C. H. Bennett, G. Brassard, and N. D. Mermin, "Quantum cryptography without Bell’s theorem," Phys. Rev. Lett. 68, 557-559 (1992). [CrossRef] [PubMed]
  4. 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 (1993). [CrossRef] [PubMed]
  5. H. J. Briegel, W. Dur, J. I. Cirac, and P. Zoller, "Quantum repeaters: the role of imperfect local operations in quantum communication," Phys. Rev. Lett. 81, 5932-5935 (1998). [CrossRef]
  6. P. G. Kwiat, K. Mattle, H. Weinfurter, and A. Zeilinger, "New high-intensity source of polarization-entangled photon pairs," Phys. Rev. Lett. 75, 4337-4341 (1995). [CrossRef] [PubMed]
  7. P. G. Kwiat, E. Waks, A. G. White, I. Appelbaum, and P. H. Eberhard, "Ultrabright source of polarizationentangled photons," Phys. Rev. A 60, R773-776 (1999). [CrossRef]
  8. 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, 053601 (2005). [CrossRef] [PubMed]
  9. H. Takesue and K. Inoue, "Generation of polarization entangled photon pairs and violation of Bell’s inequality using spontaneous four-wave mixing in fiber loop," Phys. Rev. A, 70, 031802(R) (2004). [CrossRef]
  10. H. Takesue and K. Inoue, "Generation of 1.5- μm band time-bin entanglement using spontaneous fiber four-wave mixing and planar lightwave circuit interferometers," Phys. Rev. A 72, 041804(R) (2005). [CrossRef]
  11. X. Li, P. L. Voss, J. Chen, J. E. Sharping, and P. Kumar, "Storage and long-distance distribution of telecommunications-band polarization entanglement generated in an optical fiber," Opt. Lett. 30, 1201-1203 (2005). [CrossRef] [PubMed]
  12. J. G. Rarity, J. Fulconis, J. Duligall, W. J. Wadsworth and P. St. J. Russell, "Photonic crystal fiber source of correlated photon pairs," Opt. Express 13, 534-544 (2005). [CrossRef] [PubMed]
  13. J. Fan, A. Migdall and L. J. Wang, "Efficient generation of correlated photon pairs in a microstructure fiber," Opt. Lett. 30, 3368-3370 (2005). [CrossRef]
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