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- Chinese Optics Letters
- Vol. 18, Issue 8, 082701 (2020)

Abstract

Quantum internet connects quantum computers with quantum communication channels^{[1,2]}, facilitating the transmission of information carried by qubits. Recently, free-space quantum communication has had tremendous advancement^{[3]}. On the other hand, fiber-based quantum communication is a natural candidate for the realization of transmitting quantum information in the metropolitan scale. This is because of its compatibility with an established fiber network for classical communication^{[4–12]}.

To obtain the full knowledge of the transmission process over the fiber channel is quintessential for the security and reliability of quantum communication systems. A method for reconstructing the quantum process is known as quantum process tomography (QPT)^{[13]}. Based on the method, we can fully describe the channels and understand the possible errors during transmission^{[14–16]}. A time-bin qubit is a promising quantum information carrier over fiber networks [e.g., intercity quantum teleportation^{[17,18]} and quantum key distribution (QKD)^{[19–21]}] because it is easy to prepare, is polarization independent, and stable in the fiber. However, to the best of our knowledge, there are no tests of QPT in a fiber network based on time-bin qubits encoded in weakly coherent states, let alone in an installed metropolitan telecommunication fiber network^{[14,15,22–24]}. Here, we carry out tomographic protocols based on time-bin encoding to characterize an installed commercial fiber network between the two campuses of Nanjing University. The physical distance between the two campuses is about 30.5 km. We use a fiber loop (about 61 km in total with a loss of 28.02 dB) to guide the photon back to the Gulou Campus at Nanjing University. By doing so, we double the attenuations of the signal, which enables us to characterize our QKD system under various operating conditions and provides important metrics of our system with high-transmission loss. Full reconstruction of the channel helps us better understand the channel conditions. To verify the reliability of the QPT experiment, we then implement a field trial of coherent one way (COW) QKD^{[20]} with continuous and autonomous feedback control over 12 h. We obtain the averaged quantum bit error rates (QBERs) of 0.25% and visibilities of 99.2%, respectively, matching well with the QPT results. Such a technique can be used as a standardized method for the calibration of quantum fiber networks in the future. The COW protocol can be naturally extended to a three-state protocol for considering the coherent attacks, which has been studied both theoretically and experimentally^{[25–27]}.

An aerial map of the Nanjing University quantum network, identifying the locations of Alice and Bob, is shown in Fig. ^{[21]}, where a phase shifter (PS) is employed to determine the relative phase information of the two time bins. For COW QKD, Bob can decode the qubits at setup Bob1 with a 90:10 beam splitter to passively route most of the photons for arrival time measurements. The remaining 10% are fed into an FMI for measuring the phase coherence. Photons are then transmitted to node B and detected by SSPDs with 80% detection efficiency; the corresponding electronic signals return to node A through coaxial cables and are collected by a field programmable gate array (FPGA) with 156 ps resolution. Note that the three-state protocol can also be implemented in this setup^{[26]}. To optimize the visibility, we develop a real-time proportional-integral-derivative (PID) feedback system, where a thermal PS is used to compensate the phase drifts of the interferometer per 0.47 s with the error count rate in the monitor line as the feedback. The mean photon number of 0.29 per pulse is optimized by considering the measured transmission loss and the detection efficiency according to the security proof by Branciard *et al*.^{[28]}.

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Figure 1.Schematics of the experimental setup in the Nanjing University optical fiber network. Node A and node B are located in the Zhongying Tang Building and the Electron Microscope Building, respectively, in the Gulou Campus. Node C is located in the Fundamental Laboratory Building in the Xianlin Campus. These nodes are separated by distances of 0.2 km and 30.5 km. Fiber is installed along the yellow line. Abbreviations of components: IM, intensity modulator; IM bias, intensity modulator bias; AMP, amplifier; PM, phase modulator; PBS, polarization beam splitter; BS, beam splitter; PC, polarization controller; EPC, electrical polarization controller; DWDM, dense wavelength division multiplexer; SynLs, synchronized laser; FM, Faraday rotation mirror; PS, phase shifter; SSPD, superconducting single-photon detector; PD, power detector; APD, avalanche photodiode FPGA; field programmable gate array; VDC, variable direct current. Imagery©2020 Google. Map data from Google, Maxar Techonologies, CNES/Airbus.

To characterize the performance of the quantum system, we perform single-qubit quantum-state tomography (QST) on the quantum states transmitted over the 61.1 km looped back fiber. We create photons in, and project them onto, well-defined time-bin states, such as $|0\rangle $, $|1\rangle $, $|\pm \rangle =1/\sqrt{2}(|0\rangle \pm |1\rangle )$, and $|\pm i\rangle =1/\sqrt{2}(|0\rangle \pm i|1\rangle )$, where $|0\rangle $ ($|1\rangle $) stands for the quantum state of the photon being an early (late) temporal mode. The density matrices of the six final output states reconstructed by QST are shown in Fig.

Figure 2.Characterization of the quantum channel. (a) Density matrices of output time-bin-encoded states. (b) State fidelities of the six output states to the ideal states. (c), (d) Real and imaginary parts of the process matrices for the quantum channel with a fidelity of

Figure ^{[16]}. In Fig.

Having established this high-quality quantum system, we proceed to perform QKD by employing the COW protocol^{[20,28–34]}. The coherent pulses chopped by Alice are either empty or have a mean photon number $\mu =0.29$. Each logical bit of information is defined by the position of a non-empty pulse in neighboring bins, for example, $\mu $-0 for a logical “0” or 0-$\mu $ for a logical “1”. Decoy sequences $\mu $-$\mu $ are sent to prevent photon-number-splitting attacks^{[28]}. To obtain the key, Bob measures the arrival time of the photons on his data line, detectors in Bob1 of Fig.

Fiber Links | Length | Total Attenuation | Time | Temperature | |
---|---|---|---|---|---|

A-B | 0.2 | 12.95 | 10 pm, Jun. 09 to 10 am, Jun. 10 | 12 h | 22–31°C |

B-C | 30.5 |

Table 1. Characteristics of Our System under Test

Figure ^{[34–37]}.

Figure 3.A 12 h continuous operation of the Nanjing quantum network with excellent system parameters: quantum bit error rate (blue, left vertical axis) and (red, right vertical axis) for COW protocol.

Figure *et al*.^{[28]}, it has been shown to be an upper bound under the assumption of collective attacks (i.e., Eve interacts with each individual state using the same strategy). We calculate the key rate in the infinite key scenario. As the channel attenuation increases, the number of counts decreases, and the dark count rates (DCRs) of the SSPDs (about ${10}^{-7}\text{\hspace{0.17em}}\text{\hspace{0.17em}}{\mathrm{ns}}^{-1}$) become a major component of QBER; thus, the SKR decreases exponentially. With the high visibility and negligible DCRs, our system can tolerate more channel loss, which means a wider area network.

Figure 4.Field trial SKR as a function of attenuation. Green and red pentagrams are our SKR on the network.

With these field tests of our network for quantum communications, we have fully evaluated the quality of the system via both quantum state and process tomography techniques. The QPT technique can be a standardized method for calibrating the quantum fiber networks in the future. We have extended a high security key rate per pulse for the COW protocol over the installed commercial fiber network with a real-time feedback control. Our results pave the way for the high-performance quantum network with metropolitan fibers.

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Peiyu Zhang, Liangliang Lu, Fangchao Qu, Xinhe Jiang, Xiaodong Zheng, Yanqing Lu, Shining Zhu, Xiao-Song Ma. High-quality quantum process tomography of time-bin qubit’s transmission over a metropolitan fiber network and its application[J]. Chinese Optics Letters, 2020, 18(8): 082701

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