3. Design of a hybrid quantum-classical network

In this section, we discuss the design challenges to optimize a hybrid quantum-classical network. More specifically, we discuss all the excess noise contributions, expressed as shotnoise-units (SNUs) [18, 32] may come from the imperfect modulation, laser phase noise, laser line width, local oscillator fluctuations and coherent detector imbalance [33].

### 3.1. Transmitter design

2.2. Phase noise cancelation algorithm

26 Telecommunication Networks - Trends and Developments

to be measured with high precision.

<sup>ι</sup>Ið Þ<sup>t</sup> <sup>∝</sup> ffiffiffi 2

<sup>ι</sup>Qð Þ<sup>t</sup> <sup>∝</sup> ffiffiffi 2

<sup>ι</sup>Sð Þ<sup>t</sup> <sup>∝</sup> <sup>2</sup> ffiffiffi 2

> <sup>þ</sup> <sup>2</sup> ffiffiffi 2

Mathematically, they can be expressed as in Eqs. (9) and (10).

<sup>þ</sup> AI Qð Þ cos ð Þ <sup>ω</sup> <sup>þ</sup> <sup>ω</sup><sup>1</sup> � <sup>ω</sup>LO <sup>t</sup> <sup>þ</sup> <sup>φ</sup>1<sup>t</sup> � <sup>φ</sup>2<sup>t</sup> � � <sup>þ</sup> nI

<sup>þ</sup> AI Qð Þsin ð Þ <sup>ω</sup> <sup>þ</sup> <sup>ω</sup><sup>1</sup> � <sup>ω</sup>LO <sup>t</sup> <sup>þ</sup> <sup>φ</sup>1<sup>t</sup> � <sup>φ</sup>2<sup>t</sup> � � <sup>þ</sup> nQ

4 � �

quadrature components can be expressed as in Eqs. (12) and (13).

<sup>p</sup> nI cos ð Þ <sup>ω</sup> � <sup>ω</sup>LO <sup>t</sup> <sup>þ</sup> <sup>φ</sup>1<sup>t</sup> � <sup>φ</sup>2<sup>t</sup> <sup>þ</sup>

<sup>þ</sup> <sup>2</sup> ffiffiffi 2

h i

<sup>p</sup> cos ½ Þ <sup>ω</sup> � <sup>ω</sup>LO <sup>t</sup> <sup>þ</sup> <sup>φ</sup>1<sup>t</sup> � <sup>φ</sup>2<sup>t</sup> <sup>þ</sup>

<sup>p</sup> sin ½ Þ <sup>ω</sup> � <sup>ω</sup>LO <sup>t</sup> <sup>þ</sup> <sup>φ</sup>1<sup>t</sup> � <sup>φ</sup>2<sup>t</sup> <sup>þ</sup>

photocurrents, as in Eqs. (9) and (10), that is, i2

the final result can be depicted as in Eq. (11).

<sup>p</sup> AI tð Þ cos <sup>ω</sup>1<sup>t</sup> � <sup>π</sup>

Conventionally, in order to receive and process the weak quantum signals, a high-level local oscillator is required at the receiver. It is very vital to select the local oscillator with narrow line width so that the laser fluctuations cannot contribute to the overall system's excess noise that may damage the recovery of quantum signals. Furthermore, it will help the coherent receiver to have a low complex digital signal processing (DSP) module, that is, phase noise cancelation (PNC) algorithm, as explained in detail in Figure 2 [25]. For the efficient performance of the PNC module, it is essential that the photocurrents of the in phase and quadrature signals have

π

π

where nI and nQ describe the in phase and quadrature components of the additive phase noise that needs to be remunerated. We have implemented the phase noise cancelation (PNC) algorithm [25]. By combining the squares of the in phase and quadrature component of

I(t) + i2

4 � �

<sup>p</sup> AQ tð Þ cos <sup>ω</sup>1<sup>t</sup> � <sup>π</sup>

The final step in the DSP module is to down-convert the RF signal. The resultant in phase and

Figure 2. Schematic of the digital signal processing (phase noise cancelation) module for quantum receiver.

π 4

n h io

<sup>4</sup> � AI tð Þ cos ð Þ <sup>ω</sup> <sup>þ</sup> <sup>ω</sup><sup>1</sup> � <sup>ω</sup>LO <sup>t</sup> <sup>þ</sup> <sup>φ</sup>1<sup>t</sup> � <sup>φ</sup>2<sup>t</sup> � �

<sup>4</sup> � AI tð Þ cos ð Þ <sup>ω</sup> <sup>þ</sup> <sup>ω</sup><sup>1</sup> � <sup>ω</sup>LO <sup>t</sup> <sup>þ</sup> <sup>φ</sup>1<sup>t</sup> � <sup>φ</sup>2<sup>t</sup> � �

Q(t), and mitigating the DC component,

þ nQ sin ð Þ ω � ωLO t þ φ1t � φ2t þ

(9)

(10)

π 4

(11)

The design of the simplified QTTH network with m-PSK (where m = 4, 8, 16, etc.) modulationbased quantum transmitter (Alice) and LLO-based coherent receiver (Bob) is as shown in Figure 1. At Alice, a narrow line width laser is modeled at the wavelength of 1550 nm having a line width of approximately <5 kHz allowing it to maintain low phase noise regime. A pseudorandom binary sequence (PRBS) of length 231–1 is programmed for single channel transmission and delay decorrelated duplicates copies are generated for the multichannel transmission. Furthermore, we execute pulse shaping at the transmitter according to the Nyquist criterion to generate intersymbol interference (ISI) free signals. Subsequently, 1 GBaud 4-PSK (four state phase-shift keying) signal is generated after the radio frequency (RF) signals are modulated with the help of an electro-optical I/Q modulator, where RF frequency is kept at 2 GHz. The modulation variance is applied with the help of a variable optical attenuator (VOA) prior to the quantum channel, that is, based on the optical fiber.

#### 3.2. Quantum channel

For most of our numerical and experimental investigations, we have used two standard types of fibers, namely, standard single mode fiber (SSMF) and pure silica core fiber (PSCF). The physical parameters of the fibers are given in Table 2. These are the commercial fibers and deployed heavily around the globe for short and long range transmissions. Therefore, these fibers can be used to benchmark the hybrid quantum-classical optical networks.

#### 3.3. Classical coherent receiver

A standard commercially available coherent receiver has been modeled. The receiver module (Bob) consists of a 90� optical hybrid and 20 GHz balanced photodiodes. The gain of TIA,


Table 2. Physical characteristics of the fiber at 1550 nm.

responsivity and noise equivalent power (NEP) of the receiver at 1550 nm are 4 K.V/W, 0.8 A/ W and 22 pW/pHz, respectively. For our analysis, we have kept the high-power laser at the receiver, that is, integral part of Bob in order to avoid any eavesdropping or hacking on the reference signal. That is why, it is termed as local local oscillator (LLO). The LLO photon level is considered as 1 <sup>10</sup><sup>8</sup> photon per pulse. A phase noise cancelation (PNC) [25] based algorithm is implemented to minimize the excess noise as shown in Figure 2(c). The PNC stage has two square operators for in phase and quadrature operators of the light signal, and a digital DC cancelation stage, assisted by a down-converter. The comprehensive implementation of the PNC module is described in Section 2.2 [25].

> give efficient performance, they have high electronic noise that is not beneficial for quantum signals, that is, impacting the high secure key rates. The ADC requirements [24] in terms of

> Figure 3. Performance comparison of classical data transmission: (a) averaged SNR with respect to m-PSK signals at different FEC levels and (b) SNR penalty with respect to ADC resolution for different baud rates for m-PSK signals.

Recent Progress in the Quantum-to-the-Home Networks http://dx.doi.org/10.5772/intechopen.80396 29

Since the noise equivalent power (NEP) determines electronic noise of the coherent receiver and digital post processing unit, it is important to choose a TIA and ADC with lower NEP values for low aggregate electronic noise to shot noise ratio (ESR). Furthermore, as the NEP of the TIA is amplified by the TIA itself (gain amplifiers), it governs the total electronic noise. However, the ESR negligibly changes as the bandwidth of the detector is increased. This is because of the fact that both electronic and shot noise variances linearly increase with the bandwidth, so it is advantageous to use the receivers having 1–20 GHz bandwidth. Since, 20 GHz receivers are easily commercially available so we have modeled them for our investigations. Furthermore, the quantum channel includes the standard SMF and VOA to model the channel loss. The variance of the excess noise is largely due to the bias fluctuation of the I/Q modulator and timing jitter of the Bob, that is, receiver modules. It is estimated that the excess noise can be limited to be as small as 0.01 [25] below the zero key rate threshold. After

bandwidth and sampling rate (Ts/2) are enlisted in Table 3.

Table 3. Summary of the ADC minimum requirements to process the m-PSK signals.

4. Numerical analysis and discussions

4.1. Point-to-point QKD network

#### 3.4. Characterization of coherent receiver

As a first step, we investigated the coherent receiver to detect the m-PSK signals as it is well known that the specific modulation formats require a very particular optical signal-to-noise ratio (OSNR) in order to be detected at a bit error rate (BER) threshold. After the modulation stage, the 4-PSK and 8-PSK signals, back-to-back signals are detected at the coherent receiver and normalized signal-to-noise ratio (Eb/N0, the energy per bit to noise power spectral density ratio) is plotted against BER. The results are plotted in Figure 3(a). The BER threshold is set to be 3.8 103 (Q-factor of <sup>≈</sup> 8.6 dB), corresponding to a 7% overhead, that is, hard-decision forward error correction (HD-FEC). While soft-decision FEC (SD-FEC) level of BER 2.1 102 (Q-factor of ≈ 6.6 dB) can also be used corresponding to 20% overheard. From the results, we can depict that the minimum of 10 dB and 6 dB Eb/N0 values is required for the 8-PSK and 4- PSK signals at HD-FEC. While this limit can further be reduced to smaller values but at the cost of 20% overheard in data rates, that is, SD-FEC.

We have summarized the ADC requirements to detect the m-PSK signals. The results are as shown in Figure 3(b). The ADC resolution (bits) is analyzed with respect to the SNR penalty for 1- and 4 GBaud m-PSK modulated signals. From the results, it is clear that 6–8 bit ADC can be installed in the network to recover the noisy m-PSK signals at diverse baud rates while keeping the SNR penalty ≈ 1 dB. Despite the well-known fact that high-resolution ADC can

Figure 3. Performance comparison of classical data transmission: (a) averaged SNR with respect to m-PSK signals at different FEC levels and (b) SNR penalty with respect to ADC resolution for different baud rates for m-PSK signals.


Table 3. Summary of the ADC minimum requirements to process the m-PSK signals.

give efficient performance, they have high electronic noise that is not beneficial for quantum signals, that is, impacting the high secure key rates. The ADC requirements [24] in terms of bandwidth and sampling rate (Ts/2) are enlisted in Table 3.
