**3. Tandem АМPМ-PМАМ structure of QKD system with frequency encoding**

#### **3.1. Serial and parallel microwave photonic AMPM one port units**

The general model shown in **Figure 7** for a single-port parallel system, where either intensity or phase modulation (or both simultaneously in parallel) can be applied, can represent all the former examples from the point of view of traditional simple microwave photonic (MWP) links.

The impact of all intermediate optical components of quantum channel placed between the electro-optical (EO) and the optoelectronic (OE) conversion stages can be united into an optical transfer function H(ω) (in our case, its FBG as filter for carrier, fiber of channel with losses and so on). Authors of [26], in order to classify these systems, use the term 'filtered MWP links' (FMWPL).

Universal Microwave Photonics Approach to Frequency-Coded Quantum Key Distribution http://dx.doi.org/10.5772/intechopen.71974 123

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

modulation is used.

modulation transform.

in the next section.

**encoding**

links.

links' (FMWPL).

{


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

the filtering implemented in the second variant of PM-PM scheme [14].

⎨ ⎪ ⎩

122 Advanced Technologies of Quantum Key Distribution


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 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 re-

Replacing status |+;1⟩ and |+;2⟩ to '1' and |+;1⟩ and |−;1⟩ to '0', Alice and Bob will get an exact

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

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

**3. Tandem АМPМ-PМАМ structure of QKD system with frequency** 

The general model shown in **Figure 7** for a single-port parallel system, where either intensity or phase modulation (or both simultaneously in parallel) can be applied, can represent all the former examples from the point of view of traditional simple microwave photonic (MWP)

The impact of all intermediate optical components of quantum channel placed between the electro-optical (EO) and the optoelectronic (OE) conversion stages can be united into an optical transfer function H(ω) (in our case, its FBG as filter for carrier, fiber of channel with losses and so on). Authors of [26], in order to classify these systems, use the term 'filtered MWP

**3.1. Serial and parallel microwave photonic AMPM one port units**

match of the sent qubits. This ensures an exact match of QKD protocol to BB84.

<sup>⎧</sup> <sup>⎪</sup>


+*Ω*

−*Ω*

. (5)

<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*

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

> 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 channel will change frequency.

> 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 method.

> 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 synchronizing channel.

> **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].

**Figure 9.** The spectrums of initial AM radiation (a) and output ones from amplitude MZM (b), operating in 'zero' point, and AMPM system based on tandem amplitude and phase MZM (c).

by AMPM method (**Figure 9c**). If these oscillations expose the amplitude detector, the frequency of their envelopes will be different in two times.

Orthogonal polarization controllers, allowing carrier amplitude modulation and controlling the modulator transmission index, when no modulation is needed, can be installed at MZM 1AM input and output. Amplitude and phase modulation parameters are controlled by generator of radiofrequency signals GRFS 1 (A or P) with angular frequency Ω ≪ ω and selectable phase Ф of a pair of conjugate bases 0;π or π/2;3π/2. A source of DC bias serves to select the operating point of the MZM 1 AM modulation characteristics, providing amplitude modulation at zero, quarter-wave and half-wave operating points by submitting to its corresponding 0, Uπ/2 or Uπ input voltage, where Uπ—half-wave voltage of modulator. The modulation factors of MZM 1AM and MZM 1PM are selected to ensure their operation in the linear range. Thus, the radiation at the output port in classical schemes will be limited by components in the range from ω to ω ± 2 Ω, and the filter on FBG2 additionally selects ω [15]. The setting of FMWPL provides the opportunity to work with and without amplitude and phase modula-

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125

Bob's side—receiver, based on receiving part of single-port serial FMWPL, consists of MZM 2PM, MZM 2AM, filter units (FBG1/AWG) and the block of SPD for emission registration at frequencies ω, ω ± Ω and ω ± 2 Ω (for classical schemes, half part of SPD is shown) and ω, ω ± Ω/2, and ω ± 3 Ω/2 (for advanced schemes, half part of SPD is shown). A more detailed

tion of photons. In latter, the DC voltage put in MZM 1PM for its opening.

**Figure 10.** Functional scheme of АМPМ-PМАМ QKD system with frequency encoding.

As seen from **Figure 9**, the difference frequency between two frequency components of radiation is equal to the frequency 2 Ω or modulating waveforms. Components of higher harmonics can be ignored because of the smallness of their amplitudes.

We obtained the doubled narrowing of the difference frequency if compared to classical schemes of modulation applicable in practice and using a single-amplitude MZM, operating in the 'zero' point of the modulation characteristics [29].

#### **3.2. Tandem АМPМ-PМАМ scheme**

Functional scheme of tandem AMPM-PMAM QKD system with frequency encoding is presented in **Figure 10**.

Alice's side—transmitter, based on a transmitting part of a single-port serial type FMWPL, consists of low-power single mode (frequency) continuous wave laser diode (SM CW LD) simulator of single photons with carrier frequency ω, amplitude Mach-Zehnder modulator (MZM 1AM) and phase Mach-Zehnder modulator (MZM 1PM).

Universal Microwave Photonics Approach to Frequency-Coded Quantum Key Distribution http://dx.doi.org/10.5772/intechopen.71974 125

**Figure 10.** Functional scheme of АМPМ-PМАМ QKD system with frequency encoding.

by AMPM method (**Figure 9c**). If these oscillations expose the amplitude detector, the fre-

**Figure 9.** The spectrums of initial AM radiation (a) and output ones from amplitude MZM (b), operating in 'zero' point,

As seen from **Figure 9**, the difference frequency between two frequency components of radiation is equal to the frequency 2 Ω or modulating waveforms. Components of higher harmon-

We obtained the doubled narrowing of the difference frequency if compared to classical schemes of modulation applicable in practice and using a single-amplitude MZM, operating

Functional scheme of tandem AMPM-PMAM QKD system with frequency encoding is pre-

Alice's side—transmitter, based on a transmitting part of a single-port serial type FMWPL, consists of low-power single mode (frequency) continuous wave laser diode (SM CW LD) simulator of single photons with carrier frequency ω, amplitude Mach-Zehnder modulator

quency of their envelopes will be different in two times.

and AMPM system based on tandem amplitude and phase MZM (c).

in the 'zero' point of the modulation characteristics [29].

**3.2. Tandem АМPМ-PМАМ scheme**

124 Advanced Technologies of Quantum Key Distribution

sented in **Figure 10**.

ics can be ignored because of the smallness of their amplitudes.

(MZM 1AM) and phase Mach-Zehnder modulator (MZM 1PM).

Orthogonal polarization controllers, allowing carrier amplitude modulation and controlling the modulator transmission index, when no modulation is needed, can be installed at MZM 1AM input and output. Amplitude and phase modulation parameters are controlled by generator of radiofrequency signals GRFS 1 (A or P) with angular frequency Ω ≪ ω and selectable phase Ф of a pair of conjugate bases 0;π or π/2;3π/2. A source of DC bias serves to select the operating point of the MZM 1 AM modulation characteristics, providing amplitude modulation at zero, quarter-wave and half-wave operating points by submitting to its corresponding 0, Uπ/2 or Uπ input voltage, where Uπ—half-wave voltage of modulator. The modulation factors of MZM 1AM and MZM 1PM are selected to ensure their operation in the linear range. Thus, the radiation at the output port in classical schemes will be limited by components in the range from ω to ω ± 2 Ω, and the filter on FBG2 additionally selects ω [15]. The setting of FMWPL provides the opportunity to work with and without amplitude and phase modulation of photons. In latter, the DC voltage put in MZM 1PM for its opening.

Bob's side—receiver, based on receiving part of single-port serial FMWPL, consists of MZM 2PM, MZM 2AM, filter units (FBG1/AWG) and the block of SPD for emission registration at frequencies ω, ω ± Ω and ω ± 2 Ω (for classical schemes, half part of SPD is shown) and ω, ω ± Ω/2, and ω ± 3 Ω/2 (for advanced schemes, half part of SPD is shown). A more detailed filter pack description will be given below when discussing the variants of QKD scheme implementation.

devices LSIPD-A75-FA, using filters based on FBG2. The modulation frequency was 4.2 GHz. **Figure 12** shows signal spectrograms in destructive and constructive interference on the lat-

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127

Thus, it was shown that AMPM-PMAM system could be implemented, for example, as PM-PM QKD scheme with frequency encoding based on classical approaches. It should be highlighted that in classical approaches transfer efficiency P(ω → ω ± Ω) at low modulation coefficients does not reach high values. The main energy is concentrated at the carrier frequency, and the proportion of energy of the side components is very small. Then, in order to compensate NPM, we have to extract carrier, so the efficiency of photon registration on subcarriers is very small also. This factor gave us additional arguments to implement modulation transformation of photon carrier based on Il'in-Morozov's method [24, 25]. The procedures are concluded in amplitude modulation and phase commutation (PC) of optical carrier with its suppression and full

Let us evaluate the possibility of perspective AMPC-PCAM system implementation in two variants. First is symmetrical structure with amplitude modulation and phase commutation at the Alice's side and amplitude re-modulation and phase re-commutation on the Bob's side. Second is variant, in which the asymmetric structure of the QKD with amplitude modulation and phase commutation on the Alice's side and only passive filtering based on the FBG1/

The operation of AMPC-PCAM QKD system with frequency encoding is based on amplitudephase modulation conversion of the photon carrier realized with the procedures described by Il'in-Morozov's method and its implementations on one or two modulators [29, 30]. Variants of constructive AM interference are shown in **Figure 13** in the case of constructive PC on Alice

**Figure 12.** The spectrogram of the signal in destructive (a) and constructive (b) interference on the lateral frequencies

eral frequencies ω ± Ω.

energy transfer in subcarriers.

and Bob sides.

ω ± Ω in PM-PM scheme implementation.

AWG on the side of Bob are implemented.

**3.4. Estimation of possibility AMPC-PCAM scheme implementation**

Special synchronization channel from Alice to Bob [15] serves to transmit information about a modulating signal at frequency Ω, which allows to use on Bob's side radiofrequency modulating signal with the same frequency as Alice and control it with local GRFS 2 (A or P). MZM 2AM and MZM 2PM Bob's modulators are controlled analogously to Alice's ones.

## **3.3. AMPM-PMAM system implementation for classical QKD schemes**

General view of the AMPM-PMAM experimental setup is presented in **Figure 11**.

For amplitude modulation, an amplitude modulator JDSU APE microwave analog is used with operating frequencies band over 4.2 GHz and a half-wave voltage of 3.3 V. The size of the modulator reaches a length of 120 mm and a width of 15 mm. Irregularity of frequency response in the range of 0.13–20 GHz is 7 dB. For the phase modulation, the phase modulator JDSU APE with the working frequency band above 10 GHz was used. The sizes of phase modulator are close to the dimensions of the intensity modulator. It does not require the input (bias) of the operating point.

The range of wavelengths includes an operating wavelength of 1550 nm. Losses of both types of modulators are about 3 dB. Maximum input power is up to 200 mW. As far as the small signal approaches, we are interested in the power of 1 mW, the use of which does not result in nonlinear effects in an optical fiber such as stimulated Mandelstam-Brillouin or Raman scattering [20].

Let us consider the modeling implementation of PM-PM scheme. Laser radiation from the Alice's side, as the source of which the laser optical spectrum analyzer was used, allowing realization of low-power laser analogue, arrived on the MZM 1AM in an open state and a phase modulator MZM 1PM. Further on across the bay of optical fiber SMF-28 of 2 km length, the radiation was received on the Bob's side, where it was re-modulated within the MZM 2PM (MZM 2AM was open) and recorded in the optical spectrum analyzer and photodetector

**Figure 11.** General view of the AMPM-PMAM experimental setup.

devices LSIPD-A75-FA, using filters based on FBG2. The modulation frequency was 4.2 GHz. **Figure 12** shows signal spectrograms in destructive and constructive interference on the lateral frequencies ω ± Ω.

filter pack description will be given below when discussing the variants of QKD scheme

Special synchronization channel from Alice to Bob [15] serves to transmit information about a modulating signal at frequency Ω, which allows to use on Bob's side radiofrequency modulating signal with the same frequency as Alice and control it with local GRFS 2 (A or P). MZM

For amplitude modulation, an amplitude modulator JDSU APE microwave analog is used with operating frequencies band over 4.2 GHz and a half-wave voltage of 3.3 V. The size of the modulator reaches a length of 120 mm and a width of 15 mm. Irregularity of frequency response in the range of 0.13–20 GHz is 7 dB. For the phase modulation, the phase modulator JDSU APE with the working frequency band above 10 GHz was used. The sizes of phase modulator are close to the dimensions of the intensity modulator. It does not require the input

The range of wavelengths includes an operating wavelength of 1550 nm. Losses of both types of modulators are about 3 dB. Maximum input power is up to 200 mW. As far as the small signal approaches, we are interested in the power of 1 mW, the use of which does not result in nonlinear effects in an optical fiber such as stimulated Mandelstam-Brillouin or Raman

Let us consider the modeling implementation of PM-PM scheme. Laser radiation from the Alice's side, as the source of which the laser optical spectrum analyzer was used, allowing realization of low-power laser analogue, arrived on the MZM 1AM in an open state and a phase modulator MZM 1PM. Further on across the bay of optical fiber SMF-28 of 2 km length, the radiation was received on the Bob's side, where it was re-modulated within the MZM 2PM (MZM 2AM was open) and recorded in the optical spectrum analyzer and photodetector

2AM and MZM 2PM Bob's modulators are controlled analogously to Alice's ones.

General view of the AMPM-PMAM experimental setup is presented in **Figure 11**.

**3.3. AMPM-PMAM system implementation for classical QKD schemes**

implementation.

126 Advanced Technologies of Quantum Key Distribution

(bias) of the operating point.

**Figure 11.** General view of the AMPM-PMAM experimental setup.

scattering [20].

Thus, it was shown that AMPM-PMAM system could be implemented, for example, as PM-PM QKD scheme with frequency encoding based on classical approaches. It should be highlighted that in classical approaches transfer efficiency P(ω → ω ± Ω) at low modulation coefficients does not reach high values. The main energy is concentrated at the carrier frequency, and the proportion of energy of the side components is very small. Then, in order to compensate NPM, we have to extract carrier, so the efficiency of photon registration on subcarriers is very small also.

This factor gave us additional arguments to implement modulation transformation of photon carrier based on Il'in-Morozov's method [24, 25]. The procedures are concluded in amplitude modulation and phase commutation (PC) of optical carrier with its suppression and full energy transfer in subcarriers.

Let us evaluate the possibility of perspective AMPC-PCAM system implementation in two variants. First is symmetrical structure with amplitude modulation and phase commutation at the Alice's side and amplitude re-modulation and phase re-commutation on the Bob's side. Second is variant, in which the asymmetric structure of the QKD with amplitude modulation and phase commutation on the Alice's side and only passive filtering based on the FBG1/ AWG on the side of Bob are implemented.

#### **3.4. Estimation of possibility AMPC-PCAM scheme implementation**

The operation of AMPC-PCAM QKD system with frequency encoding is based on amplitudephase modulation conversion of the photon carrier realized with the procedures described by Il'in-Morozov's method and its implementations on one or two modulators [29, 30]. Variants of constructive AM interference are shown in **Figure 13** in the case of constructive PC on Alice and Bob sides.

**Figure 12.** The spectrogram of the signal in destructive (a) and constructive (b) interference on the lateral frequencies ω ± Ω in PM-PM scheme implementation.

**4.** implementation of an asymmetric system with a totally passive data filtering sent by Alice,

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**Figure 14** shows the output spectrum of AMPC procedure, which can be described as twofrequency symmetrical radiation with fully suppressed carrier and fractional harmonics nΩ/2

In this case, we can decrease NPM (carrier is absent) in FOLC and increase signal-to-noise ratio, because we can register photon by envelope amplitude on difference frequency Ω, which lies in SPD spectrum region with minimum level of noises. The point about separation

Thus, if we realize full re-modulation of Alice's phases in phases on Bob's side, we get spectrum, as shown in **Figure 12b**, after Bob's PM, and, as shown in **Figure 12a**, after Bob's AM. Therefore, the carrier is present, but only in receiver, not in quantum channel, and its

Analysis shows that we can realize classical symmetrical QKD scheme with modulation and re-modulation. To do this, we are going to select the two bases for frequency-encoding the photon states in AMPC of asymmetrical type without re-modulation/re-commutation and


<sup>⎧</sup>

The state |+;1⟩ is the unmodulated photon transmitted from SM CW LD, through the open Alice's modulators. The state |−;1⟩ is amplitude-modulated photon (frequency of modulation is Ω; 'zero' operating point of MZM 1 AM; absence of phase commutation). The state |+;2⟩

**Figure 14.** The output spectrum of AMPC procedure for propagation in FOLC: frequency encoding of second |−; 1⟩ and

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

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

+3*Ω*/2 <sup>−</sup> \_\_1 √ \_\_ <sup>2</sup> |1⟩*<sup>ω</sup>*<sup>0</sup>

−3*Ω*/2

(6)

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


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

on the of Bob's side without re-modulation or re-commutation.

Let us make the first three statements plain.

filter necessity is a question.

explain the order they are received.

third |+; 2⟩ photon states is shown.

(here n = 1 for **Figure 14a** and n = 2 for **Figure 14b**).

influence on channel characteristics is minimized. Let us clarify the last from above four statements.

{

⎪ ⎨ ⎪ ⎩

**Figure 13.** Variants of constructive interference with the coincidence of the parameters AM and PC on the side of Alice and Bob: the results of AM (a) and PC (b) at the output of modulators on the side of Alice; the results of PC (c) and AM (d) at the output of modulators on the side of Bob.

To simulate the scheme and carry out the project evaluations, the modeling principles of single-port modulation radio photon of serial link type proposed by us in [29, 31, 32] and photonic simulation of electro-optic modulators [33] were used.

The implementation of Il'in-Morozov's method for the modulation conversion P(ω → ω ± nΩ), where n is the number of subcarriers, will provide:


**4.** implementation of an asymmetric system with a totally passive data filtering sent by Alice, on the of Bob's side without re-modulation or re-commutation.

Let us make the first three statements plain.

**Figure 14** shows the output spectrum of AMPC procedure, which can be described as twofrequency symmetrical radiation with fully suppressed carrier and fractional harmonics nΩ/2 (here n = 1 for **Figure 14a** and n = 2 for **Figure 14b**).

In this case, we can decrease NPM (carrier is absent) in FOLC and increase signal-to-noise ratio, because we can register photon by envelope amplitude on difference frequency Ω, which lies in SPD spectrum region with minimum level of noises. The point about separation filter necessity is a question.

Thus, if we realize full re-modulation of Alice's phases in phases on Bob's side, we get spectrum, as shown in **Figure 12b**, after Bob's PM, and, as shown in **Figure 12a**, after Bob's AM. Therefore, the carrier is present, but only in receiver, not in quantum channel, and its influence on channel characteristics is minimized.

Let us clarify the last from above four statements.

To simulate the scheme and carry out the project evaluations, the modeling principles of single-port modulation radio photon of serial link type proposed by us in [29, 31, 32] and

01 1

**Figure 13.** Variants of constructive interference with the coincidence of the parameters AM and PC on the side of Alice and Bob: the results of AM (a) and PC (b) at the output of modulators on the side of Alice; the results of PC (c) and AM

1

Wa

 1.55 avelength (µm) *b*

1.5501

1.5501

Wa

 1.55 avelength (µm) *d*

Power (a.u.)

 0 3

0.20.3

0.40.5

00.1

1.5499

0

00.1

 0 1

 0 2

0.2

Power (a.u.)

The implementation of Il'in-Morozov's method for the modulation conversion P(ω → ω ± nΩ),

**1.** high-efficiency optical carrier transfer into subcarrier left and right components (up to 0.6– 0.8 amplitude for each of them), high level of spectral purity under the optimal conversion

**2.** NPM decreasing (carrier is absent), to exclude spectrum filter, which separates carrier and sidebands, to increase signal-to-noise ratio, because we can register photon by envelope amplitude on difference frequency Ω, which lies in SPD spectrum region with minimum

**3.** synthesis of whole number subcarriers (n ≥ 1) and fractional ones (n/2, for n ≥ 1) that will improve the cryptographic protection level of the communication system, in case of Eve

parameters (only first or additionally third number subcarriers are existing);

photonic simulation of electro-optic modulators [33] were used.

1.55 0

µm)

discoveries the frequency of synchronization channel;

where n is the number of subcarriers, will provide:

level of noises;

1.5499

 1.55 1 Wavelength ( *a* 

128 Advanced Technologies of Quantum Key Distribution

1.5501 µm)

 1.55 Wavelength ( *c*

(d) at the output of modulators on the side of Bob.

1.5499

Power (a.u.)

0 0.1 0.2 0.3

Power (a.u.)

0 0.1 0.2 0.3 0.4 0.5

Analysis shows that we can realize classical symmetrical QKD scheme with modulation and re-modulation. To do this, we are going to select the two bases for frequency-encoding the photon states in AMPC of asymmetrical type without re-modulation/re-commutation and explain the order they are received.

$$\begin{aligned} &\text{isymmetrical type without re-modulation/re-commutation and received.}\\ &\text{ received:}\\ &\left\{ \begin{array}{rcl} \left| \begin{array}{l} \left| \mathrel{+} \ 1 \end{array} \right. \right. \right. = & \left| \begin{array}{l} \left| \mathrel{+} \ 1 \end{array} \right. \\ &\left\{ \begin{array}{l} \left| \left- \mathrel{-} \ 1 \end{array} \right. \right. \right. =& \left| \begin{array}{l} \left| \ 1 \end{array} \right. \\ &\left\{ \begin{array}{l} \left| \mathrel{+} \ 2 \end{array} \right. \right. \right. \right. \left. \right. \right. \end{aligned} \\ &\left\{ \begin{array}{l} \left| \left+ \text{-} \ 2 \end{array} \right. \right. =& \frac{1}{\sqrt{2}} \left| \begin{array}{l} \left| \ 1 \end{array} \right. \right. \right. \\ &\left\{ \begin{array}{l} \left| \left- \text{-} \end{array} \right. \right. \right. \end{aligned} \end{aligned} \tag{6}$$

The state |+;1⟩ is the unmodulated photon transmitted from SM CW LD, through the open Alice's modulators. The state |−;1⟩ is amplitude-modulated photon (frequency of modulation is Ω; 'zero' operating point of MZM 1 AM; absence of phase commutation). The state |+;2⟩

**Figure 14.** The output spectrum of AMPC procedure for propagation in FOLC: frequency encoding of second |−; 1⟩ and third |+; 2⟩ photon states is shown.

is full tandem amplitude-modulated and phase-commutated photon (quadrature operating point of MZM 1 AM; amplitude modulation coefficient m = 0.59; phase commutation 0/π with frequency Ω/2 in MZM 1 PM). The state |−;2⟩ is described by lateral components obtained at the same parameters of amplitude modulation, but MZM 1 PM had phase commutation 0/π with frequency 3 Ω/2. The parameter control of the amplitude modulation and phase commutation is performed by GRFS 1A and 1P with a corresponding change in functions.

**Acknowledgements**

**Author details**

Oleg G. Morozov<sup>1</sup>

Tatarstan, Russia

**References**

Il'daris M. Gabdulkhakov<sup>2</sup>

2 PJSC «Tattelecom», Kazan, Russia

10.1049/el:19970427

10.1364/OE.16.018790

10.1117/12.923121

("Asymmetry", base task no. 8.6872.2017/8.9).

\*Address all correspondence to: microoil@mail.ru

DOI: 10.1103/RevModPhys.81.1301

1993;**23**:383-388. DOI: 10.1209/0295-5075/23/6/001

\*, Airat J. Sakhabutdinov<sup>1</sup>

Ministry of Education and Science of Russian Federation supported this work: state R&D task to Kazan National Research Technical University n.a. A.N. Tupolev—Kazan Aviation Institute

1 Kazan National Research Technical University n.a. A.N. Tupolev-KAI, Kazan, Republic of

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Optics Letters. 2001;**26**(18):1427-1429. DOI: 10.1364/OL.26.001427

, Gennady A. Morozov<sup>1</sup>

Universal Microwave Photonics Approach to Frequency-Coded Quantum Key Distribution

and

http://dx.doi.org/10.5772/intechopen.71974

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Frequency encoding of second |−; <sup>1</sup>⟩ and third |+; <sup>2</sup>⟩ photon states is presented in **Figure 14b** and **a**, respectively. As can be seen from last paragraph and in **Figure 14**, all four photons states can be passively allocated through a system of filters tuned respectively to frequencies ω0 →|+;1⟩, ω0 ± Ω/2→|+;2⟩, ω0 ± Ω→|−;1⟩, ω0 ± 3 Ω/2→|−;2⟩. Thus, AMPC-FBG/AWG asymmetric system can be constructed as shown in **Figure 10**, but without modulators on Bob's side.
