Multiuser-to-multiuser entanglement distribution based on 1550 nm ...

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May 15, 2015 - Dong-Yang Cao; Bi-Heng LiuEmail author; Zhao Wang; Yun-Feng HuangEmail author; Chuan-Feng LiEmail author; Guang-Can Guo.
Sci. Bull. (2015) 60(12):1128–1132 DOI 10.1007/s11434-015-0801-4

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Article

Physics & Astronomy

Multiuser-to-multiuser entanglement distribution based on 1550 nm polarization-entangled photons Dong-Yang Cao • Bi-Heng Liu • Zhao Wang Yun-Feng Huang • Chuan-Feng Li • Guang-Can Guo



Received: 31 March 2015 / Accepted: 10 April 2015 / Published online: 15 May 2015 Ó Science China Press and Springer-Verlag Berlin Heidelberg 2015

Abstract Telecom-band polarization-entangled photonpair source has been widely used in quantum communication due to its acceptable transmission loss. It is also used in cooperation with wavelength-division multiplexing (WDM) to construct entanglement distributor. However, previous schemes generally are not suitable for multinode scenario. In this paper, we construct a telecom-band polarization-entangled photon-pair source, and it shows ultrahigh fidelity and concurrence which are both greater than 90 % (raw data). Moreover, we set up a four-by-four entanglement distributor based on WDM. We check the 16 Clauser–Horne–Shimony–Holt inequalities, which show nonlocality. Lastly, as an example of practical application of this source, we estimate the quantum bit error rates and quantum secret key rates when it is used in quantum key distribution. Furthermore, the transmission of entanglement in long optical fibers is also demonstrated.

D.-Y. Cao  B.-H. Liu (&)  Z. Wang  Y.-F. Huang (&)  C.-F. Li (&)  G.-C. Guo Key Laboratory of Quantum Information, University of Science and Technology of China, Chinese Academy of Sciences, Hefei 230026, China e-mail: [email protected] Y.-F. Huang e-mail: [email protected] C.-F. Li e-mail: [email protected] D.-Y. Cao  B.-H. Liu  Z. Wang  Y.-F. Huang  C.-F. Li  G.-C. Guo Synergetic Innovation Center of Quantum Information and Quantum Physics, University of Science and Technology of China, Hefei 230026, China

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Keywords Entanglement distribution  Multiuser  Telecom-band

1 Introduction Quantum entanglement is a potential resource for many quantum information processes, such as quantum communication [1], quantum dense coding [2], quantum cryptography based on entanglement [3, 4], and quantum teleportation [5]. Quantum entanglement in various systems has been investigated [6, 7]. In the regime of quantum communication, generally, there is a server to distribute the quantum entanglement to remote users and can adapt the quantum entanglement to different users. There are some experiments that have realized one-to-one entanglement distribution [8, 9], but up to now there is no experiments that realize multiuser-to-multiuser entanglement distribution. Furthermore, according to realistic demand, users need not to share the entanglement at any time [10], so we can realize the multiuser-to-multiuser quantum entanglement distributor based on wavelength-division multiplexing (WDM). In order to realize distribution of entanglement, the loss of transmission must be very low, so usually the telecom-band entangled photon-pair sources are preferred due to their low transmission loss of 0.2 dB/km in commercial optical fiber. The most simple and operable approach to prepare entangled photon pair is using the spontaneous parametric down-conversion (SPDC) process in nonlinear crystal, such as beta-barium borate (BBO) and periodically poled lithium niobate (PPLN). Entangled photon pairs are conventionally prepared in polarization degree of freedom [11, 12], spatial mode [13], time bin [14, 15], orbital angular momentum [16, 17], or hybrid entanglement [18]. Due to the fact that the polarization freedom is more convenient to

Sci. Bull. (2015) 60(12):1128–1132

operate and measure, we choose the polarization freedom as qubit state space. Polarization-entangled photon pairs prepared by SPDC have been studied in a large range of fields and for a long time [19, 20]. The majority of experiments about quantum communication and quantum cryptography involved entanglement employ periodically poled crystal, for its high efficiency and brightness. However, temperature-controlled crystal is critical but troublesome. Moreover, the method is difficult to be applied to multiphoton scheme. Here, we adopt beamlike type-II SPDC [21, 22], in which photon pairs in e-ray and o-ray rings are emitted as two separate circular beams rather than as two diverging cones when the phase-matching angle is decreased from collinear phase-matching angle. Beamlike type-II SPDC has an important advantage that nearly all emitted photon pairs could be collected by small apertures lie in beams exit direction. As a result, beamlike type-II SPDC shows better photon-pair collection efficiency than conventional type-I [23] and type-II [24] SPDC. However, this is not enough. To prepare polarization-entangled twophoton state, a two-crystal geometry must be employed with the second crystal rotated 180° around the pump direction. This scheme was first proposed by Kim [25].

2 Entanglement distribution We take advantage of nonlinear crystal and wavelengthdivision multiplexing system to set up the entanglement distributor. The pump laser should have broadband compared to wavelength-division multiplexing channel bandwidth (1 nm). Here, we use pump laser with a bandwidth of 9 nm to improve the average fidelity of output. By SPDC, we can prepare 1.55 lm EPR photon pairs. Then, one photon is coupled into any one channel of the WDM. The other photon also is coupled into any one channel of the other WDM (eight channels but only four channels we used). The outputs of the two WDMs are guided into two avalanche photodiodes. Due to the fact that crystal’s phase

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match condition can be met in a wide range of wavelength from broadband sources, the output photon in any channel of one WDM still should be entangled with the output photon in any channel of the other WDM, which constitutes a four-by-four quantum network in two locations (Fig. 1). In our experiment, a mode-locked Ti:sapphire laser is used with a duration of 140 fs, a repetition rate of 76 MHz, and the central wavelength around 777 nm. The light power of the laser is up to 1.5 W. The laser is focused by a lens of 100 mm focus length on two 1-mm-thick BBO crystals which are both cut at h = 27.9°, and their optical axes lie in the horizontal plane. The latter crystal is rotated 180° around the pump direction, so the two crystals generate the photon pairs in polarization state H1V2 for BBO1 and V1H2 for BBO2, where H and V correspond to horizontal and vertical polarization state. However, by now, there is obviously no entanglement, because the photon pairs generated by the two crystals could be distinguished spatially and temporally. To overlap the two wave packets, we need to insert spatial and time compensation in the optical path. For the purpose of spatial compensation, we place a 3.2-mm-thick LiNbO3 crystal with cutting angle of h = 45° in two paths. We also inserted two YVO4 crystals of thickness of 0.124 and 0.149 mm in path 1 and 2 separately to compensate the temporal separation between H and V polarizations caused by birefringence in BBO and LiNbO3 crystals and produce the anti-symmetry 1 Bell state w ¼ pffiffiffi ðH1 V2  V1 H2 Þ. To efficiently couple 2 photons into single-mode fibers, two lens of 100 mm focal length are used as a collimator before each fiber coupler. A tilted QWP (quarter-wave plate) and a HWP (half-wave plate) are placed in path 1 to adjust the phase between H and V polarization and exchange the polarization in path 1 so that we can prepare any one of the Bell states [24]. Two polarization analyzers composed of a QWP, a HWP, and a PBS (polarizing beamsplitter) are placed separately before single-photon detectors D1 and D2 to measure the output states. A long-pass filter and an interference filter

Fig. 1 (Color online) Configuration of multiuser-to-multiuser entanglement distribution. Entanglement is distributed to two remote cities via telecom-band fiber. Any of the users located at city A can share the entanglement with any of the users located at city B by WDM and timedivision multiplexing (TDM)

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(IF) centered at 1550 nm (FWHM = 9 nm) are also inserted in both paths to filter the noises. Through singlemode fiber, the photons are coupled into WDMs, whose outputs are guided into single-photon detectors D1 and D2, which could detect photon pairs, and then, the single and coincidence counts of D1 and D2 can be recorded by coincidence and counting units (Fig. 2). To characterize the property of the source, we firstly remove the WDMs to reconstruct the density matrix of our twophoton entangled state by quantum state tomography [26] and then get the value of the fidelity and concurrence [27, 28] both to be about 90 % (raw data). Then, we put back the WDMs, remove the IFs, and perform the tomography measurement at each of the four-by-four combinations. We also test 16 Clauser–Horne–Shimony–Holt (CHSH) inequalities violation. All of the data are given in Tables 1, 2, and 3. The tables consist of 16 entries via the combination of two same WMDs. Either WDM has four ports, whose centered wavelengths are at 1551.72 nm (A1, B1), 1553.33 nm (A2, B2), 1554.94 nm (A3, B3), 1556.55 nm (A4, B4), respectively, and each port’s bandwidth is 1 nm. By combining any two ports from two different WDMs. According to the tables, we can see all of concurrences exceed 95 % after subtracting the accidental coincidences, and all CHSH inequalities values are also greater than 2, which demonstrate the nonlocality of the two distant nodes. So, any two users located at two nodes, respectively, can implement a large number of quantum information processes based on quantum entanglement distributed by the source.

Table 2 The concurrences after the subtraction of the accidental coincidences Sub concur

A1

A2

A3

A4

B1

0.994

0.961

0.987

0.973

B2

0.983

0.987

0.990

0.986

B3

0.999

0.999

0.982

0.953

B4

0.979

0.997

0.987

0.952

All of the concurrences exceed 95 %, which indicate high entanglement degree after entanglement distribution

For example, quantum secret key distribution based on entanglement [3] requires quantum bit error ratio (QBER) to be not greater than 11 %. Our fiber-based broadband sources also can be used to extract the quantum key. In the H/V measurement basis, the average of the QBER is 6.2 % (raw data), and each of the QBER is less than 11 %. Meanwhile, the average of QBER in the D=Dþ measure1 ment basis is 7.1 % (raw data), where D ¼ pffiffiffi ðH þ V Þ 2 1 and Dþ ¼ pffiffiffi ðH  V Þ, and each of the QBER is still less 2 than 11 %. According to Koashi and Preskill [29], the quantum key can be generated. We also estimate the secret key rates according to the formula given by Ma et al. [30]. The QBER and key rates are given in the Tables 4 and 5, respectively. Therefore, our sources not only can generate the quantum secret key but also can distribute them into multiusers in fiber-based quantum network.

Fig. 2 (Color online) Experiment setup to prepare 1.55 lm polarization-entangled photon pairs. BBO is nonlinear crystals used to produce photon pairs. LiNbO3 and YVO4 crystals are for spatial and time compensations, respectively Table 1 Value of the raw concurrences with the error bar given in the parentheses Raw concur

A1

A2

A3

A4

B1

0.782 (0.042)

0.833 (0.033)

0.865 (0.033)

0.861 (0.022)

B2

0.842 (0.027)

0.870 (0.031)

0.865 (0.017)

0.835 (0.036)

B3 B4

0.868 (0.037) 0.760 (0.033)

0.887 (0.036) 0.872 (0.034)

0.852 (0.018) 0.869 (0.027)

0.827 (0.037) 0.826 (0.022)

The concurrences decrease is derived from severe photon loss

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Table 3 S values of CHSH inequality with standard deviation (All of the quantities S are greater than 2, which suggests the nonlocality) CHSH

A1

A2

A3

A4

B1

2.193 (0.042)

2.426 (0.040)

2.395 (0.038)

2.504 (0.036)

B2

2.264 (0.039)

2.461 (0.036)

2.468 (0.036)

2.546 (0.036)

B3

2.409 (0.036)

2.505 (0.036)

2.564 (0.035)

2.532 (0.036)

B4

2.449 (0.035)

2.490 (0.036)

2.492 (0.036)

2.479 (0.039)

Table 4 16 QBERs (all of them are less than 11 %, so that secret key rates can be extracted from them) QBER

A1

A2

A3

A4

B1

0.081

0.072

0.057

0.07

B2

0.077

0.069

0.049

0.055

B3

0.066

0.049

0.058

0.06

B4

0.06

0.05

0.055

0.057

Table 5 Key rates of 16 configurations (all of configuration are able to extract security keys) Key rates

A1

A2

A3

A4

B1

20.74

43.52

73.8

46.55

B2

31.72

45.24

95.62

77.26

B3

51.16

88.52

70.66

66.43

B4

67.38

84.73

75.25

69.85

3 Entanglement transmission in optical fibers In addition, to describe the long-distance transmission of our entangled photon source, we further demonstrate the evolution of entanglement concurrence with the transmission distance of photon pairs increasing gradually in standard optical fibers. The setup is shown in Fig. 3, and

fibers are put into the single-photon detectors. We measure the entanglement concurrence after different length of fiber evolution, and the data are shown in Fig. 4. It is shown that the raw entanglement concurrence remarkably decreases as the transmission length of fibers increase, but the entanglement concurrence after subtracting the accidental coincidence almost remains unchanged. The main reason for the raw entanglement concurrence decreasing is photons loss. The main loss mechanism is naturally optical fiber loss, and the other serious loss mechanism is due to the dispersion. The coincidence gate width of our single-photon detectors is fixed at 1 ns; however, the transmission in long fibers results in huge wave packet broadening, which may be far greater than the detector gate width so as to filter out most of the photons, the result is that the dark counts cannot be neglected, and the accidental coincidence becomes severe and degrades the raw entanglement concurrence. Comparing our source with previous experiments [8], we can see that the brightness of Lim’s source is slightly brighter than ours, but our source is particularly suitable for multinode network. Armed with this source, we can prepare multiphoton entangled states and then distribute these photons to multinodes. It is reported that eight-photon GHZ state has been demonstrated by this source [31]. We can also change the multiphoton entangled state so that the source can be used in various different quantum network protocols.

we generate polarization-entangled photon pairs w ¼ 1 pffiffiffi ðH1 V2  V1 H2 Þ first and then put the photon pairs into 2 standard communication optical fibers. Photons out of

Fig. 3 (Color online) The polarized entanglement photon pairs go through different length fibers, and the fiber length of two paths is exactly the same

Fig. 4 (Color online) The entanglement concurrence after different length of fiber evolution. The dashed line marked stars represents the raw entanglement concurrence, and the other one represents the entanglement concurrence after subtracting background

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With rapid development and a series of breakthroughs in the field of quantum memory in recent years, in principle, we can use our sources in cooperation with quantum memory to realize entanglement distribution between any two users who are located in remote cities. This is very important to quantum communication. We also can coherently transform the telecom photons to visible photons with frequency conversion technique by waveguide or bulk crystal. The visible photons can interface with matter qubit, which is the basis of hybrid quantum network. So, with these sources in hand, we can further carry out a series of experiments toward quantum network and quantum communication.

4 Conclusions In summary, we establish a four-by-four quantum network which provides quantum entanglement to any two nonlocal users so that they can implement a series of quantum information process. We also evaluate the concurrence which describes the quantum entanglement quantitatively and test the CHSH-type Bell inequality violation that signifies the nonlocal property. Finally, we also estimate the QBER and secret key rates of the source and indicate that it is perfectly suitable to distribute the quantum secret key to different users. Acknowledgments This work was supported by the National Natural Science Foundation of China (61327901, 61490711, 11274289, 11325419, 11374288 and 11104261), the National Basic Research Program of China (2011CB921200), the Strategic Priority Research Program (B) of the Chinese Academy of Sciences (XDB01030300), the National Science Fund for Distinguished Young Scholars (61225025), and the Fundamental Research Funds for Central Universities (WK2470000011). Conflict of interest of interest.

The authors declare that they have no conflict

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