**2.2. AM-AM schemes**

A second version of the PM-PM scheme [14] was proposed for elimination of given drawbacks. It is based on nonlinear interaction of the RF signal and the photon in the electro-optic

**Figure 2.** Constructive ∆Φ = 0 (a) and destructive ∆Φ = π/2 (b), ∆Φ = 3π/2 (c), ∆Φ = π (d) interferences on the output of

set prior to sideband SPD, which reflects the carrier at the corresponding receiver, transmit-

+ \_\_1 <sup>2</sup> |1⟩*<sup>ω</sup>*<sup>0</sup>

− \_\_1 <sup>2</sup> |1⟩*<sup>ω</sup>*<sup>0</sup>


√ \_\_ <sup>2</sup> |1⟩*<sup>ω</sup>*<sup>0</sup> <sup>+</sup>*<sup>Ω</sup>* <sup>−</sup> \_\_1 <sup>2</sup> |1⟩*<sup>ω</sup>*<sup>0</sup> −*Ω* 

<sup>+</sup>*<sup>Ω</sup>* <sup>+</sup> \_\_1 <sup>2</sup> |1⟩*<sup>ω</sup>*<sup>0</sup> −*Ω* 

<sup>+</sup>*<sup>Ω</sup>* <sup>−</sup> \_\_1 √ \_\_ <sup>2</sup> |1⟩*<sup>ω</sup>*<sup>0</sup> −*Ω* frequency is

. (4)

modulator and implements a more advanced BB84 protocol. Notch filter on ω0

ting all the remaining subcarriers on ω0 ± Ω and ω0 ± 2 Ω frequencies.


<sup>|</sup>−; <sup>1</sup>⟩ <sup>=</sup> \_\_1 √ \_\_ <sup>2</sup> |1⟩*<sup>ω</sup>*<sup>0</sup>

For BB84 protocol realization, two bases are set as following:

{

⎧ ⎪ ⎨ ⎪ ⎩

Bob's PM, when Alice's ΦA = 0.

118 Advanced Technologies of Quantum Key Distribution

The first AM-AM scheme is based on BB84 protocol [23]. Its OptiSystem model is presented in **Figure 3**, and constructive and destructive interferences are shown in **Figure 4**.

It should be noted that the modulator on the of Alice's side is modulated according to the law cos(Ωt + ΦA), and on the Bob's side according to sin(Ωt + ΦB). Transfer efficiency P(ω0 → ω0 ± Ω) in this case is proportional to function cos2 (∆Φ/2) and sin<sup>2</sup> (∆Φ/2) for the upper and lower side bands, respectively, at ΦA = π/2 and ΦB = 3π/2. Determination of phase's compliance level in the scheme is also implemented by the amplitude of the lateral components.

## **2.3. Meshed AM-PM (PM-AM) schemes**

AM-PM or PM-AM scheme implementation intuitively appears to be based on the principles set out, respectively, for AM-AM and PM-PM schemes. One of its OptiSystem model is presented in **Figure 5**.

Determination of phase's compliance level in the scheme is also implemented by the amplitude of the lateral components (**Figure 6**).

It should be noted that we have some conflicting information about the possibility [13] and impossibility [23] of meshed AM-PM (PM-AM) scheme realization as for protocol BB84, so

**Figure 3.** Modeling of AM-AM scheme for QKD system with frequency coding.

**Figure 4.** Constructive ∆Φ = π (a) and destructive ∆Φ = π/2 (b), ∆Φ = 3π/2 (c); ∆Φ = 0 (d) interferences on the output of Bob's PM, when Alice's ΦA = 3π/2.

and B92 one. Taking into account that the definition of truth in these statements is not the aim of our chapter, let us consider some results of practical experiments for AM-AM schemes based on acoustic-optical modulators [16], which show us second attempt to implement QKD

**Figure 6.** Constructive ∆Φ = 0 (a) and destructive ∆Φ = π/2 (b), ∆Φ = 3π/2 (c), ∆Φ = π (d) interferences on the output of

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There is a nonelectro-optical solution of AM-AM scheme based on acousto-optic modulation

In the case of Bragg diffraction, all orders of diffracted radiation except the first become negligibly small, and the frequency offset depends from the direction of laser radiation and sound

system without re-modulation.

Bob's PM, when phase of Alice's AM ΦA = 0.

wave propagation.

**2.4. Acousto-optic modulation for AM-AM schemes**

on Alice's side as well as on Bob's side [16].

For BB84 protocol, two bases are set:

**Figure 5.** Modeling of AM-PM scheme for QKD system with frequency coding.

Universal Microwave Photonics Approach to Frequency-Coded Quantum Key Distribution http://dx.doi.org/10.5772/intechopen.71974 121

**Figure 6.** Constructive ∆Φ = 0 (a) and destructive ∆Φ = π/2 (b), ∆Φ = 3π/2 (c), ∆Φ = π (d) interferences on the output of Bob's PM, when phase of Alice's AM ΦA = 0.

and B92 one. Taking into account that the definition of truth in these statements is not the aim of our chapter, let us consider some results of practical experiments for AM-AM schemes based on acoustic-optical modulators [16], which show us second attempt to implement QKD system without re-modulation.

#### **2.4. Acousto-optic modulation for AM-AM schemes**

There is a nonelectro-optical solution of AM-AM scheme based on acousto-optic modulation on Alice's side as well as on Bob's side [16].

In the case of Bragg diffraction, all orders of diffracted radiation except the first become negligibly small, and the frequency offset depends from the direction of laser radiation and sound wave propagation.

For BB84 protocol, two bases are set:

**Figure 4.** Constructive ∆Φ = π (a) and destructive ∆Φ = π/2 (b), ∆Φ = 3π/2 (c); ∆Φ = 0 (d) interferences on the output of

**Figure 5.** Modeling of AM-PM scheme for QKD system with frequency coding.

Bob's PM, when Alice's ΦA = 3π/2.

120 Advanced Technologies of Quantum Key Distribution

$$\begin{cases} \left| +; \left\{ \begin{array}{c} \left| \right\rangle \end{array} \right\} \right| = \left| \left\{ \mathbf{1} \right\} \right\rangle\_{\omega\_{\circ} \circ \Omega} \\ \left| -; \left\{ \mathbf{1} \right\} \right\rangle = \left| \left\{ \mathbf{1} \right\} \right\rangle\_{\omega\_{\circ} \circ \Omega} \end{cases}$$

$$\begin{cases} \left| +; \left\{ \begin{array}{c} \mathbf{2} \end{array} \right\} = \frac{1}{\sqrt{2}} \left| \left\{ \mathbf{1} \right\} \right\rangle\_{\omega\_{\circ} \circ \Omega} + \frac{1}{\sqrt{2}} \left| \left\{ \mathbf{1} \right\} \right\rangle\_{\omega\_{\circ} \circ \Omega} \right. \\ \left| -; \left\{ \begin{array}{c} \mathbf{2} \end{array} \right\} \right| = \frac{1}{\sqrt{2}} \left| \left\{ \mathbf{1} \right\} \right\rangle\_{\omega\_{\circ} \circ \Omega} - \frac{1}{\sqrt{2}} \left| \left\{ \mathbf{1} \right\} \right\}\_{\omega\_{\circ} \circ \Omega} \end{cases} \tag{5}$$

The features of FMWPL are evaluated in terms of figures of merit set: the radiofrequency link gain, the noise figure and the spurious free dynamic range [27]. These metrics have been

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In principle, the interest was focused on intensity-modulated direct detection (IMDD) pointto-point links with direct or external modulation, and models were developed detailed description of the effects of the electronic biasing circuits and impedance matching networks [27]. Paper [28] reciprocally considers the inclusion of an arbitrary optical filter, acting as an FM discriminator, for the particular case of directly modulated FMDD links if synchronizing

For the AMPM feature analysis, classical generalized scheme of single-port FMWPL was converted from parallel to serial circuit type (**Figure 8**) in order to implement Il'in-Morozov's

On the basis of studies carried out in this section, the feasibility of AMPM scheme realized on the amplitude, and phase MZM was theoretically demonstrated. We carried out equations for the calculation of the AMPM scheme output spectrum [29]. The spectrum consists mainly from two components, if phase of PM triggered on π in the minimum of envelope of amplitude-modulated carrier. The difference frequency is equal to modulating one in syn-

**Figure 9** shows the spectrums of the original quasi-harmonic oscillations of the amplitudemodulated signals structure (**Figure 9a**) and the two frequency structure with partly suppressed carrier obtained by MZM AM in 'zero' point (**Figure 9b**) and fully suppressed carrier

**Figure 8.** Schematic representation of a general serial single-port filtered MWP link [28].

computed for a wide variety of configurations in [26].

**Figure 7.** Schematic representation of a general parallel single-port filtered MWP link [25].

channel will change frequency.

method.

chronizing channel.

The first pair of states |+;1⟩ and |−;1⟩ can be identified without re-modulation, using the filter block consisted from FBG or AWG, tuned on the frequencies ω0 ± Ω or one of them, similar to the filtering implemented in the second variant of PM-PM scheme [14].

The second pair of states |+;2⟩ and |−;2⟩ is transmitted with the help of modulation on Alice's side. If we use filters without re-modulation on Bob's side, the error can occur, because both photosensors with ω0 ± Ω filters will trigger. The given states are determined uniquely if remodulation is used.

Replacing status |+;1⟩ and |+;2⟩ to '1' and |+;1⟩ and |−;1⟩ to '0', Alice and Bob will get an exact match of the sent qubits. This ensures an exact match of QKD protocol to BB84.

Certain difficulty, associated with spatial alignment of used devices as on Alice's so and Bob's sides, characterizes using of acousto-optic modulators in QKD system implementation with frequency encoding. Search for ways to implement bases, described in (5), with the help of electro-optic modulation, led us to use Il'in-Morozov's method [24, 25] for the photon carrier modulation transform.

Il'in-Morozov's method belongs to the methods with full or partial suppression of optical carrier. The theoretical justification for this application and synthesized conjugated bases is obtained by amplitude-phase modulation according to Il'in-Morozov's method we consider in the next section.
