**1. Introduction**

Quantum communication networks provide a unique opportunity of sharing a random sequence of bits between users with guaranteed security not achievable in classical open or special systems with cryptographic protection [1]. This is achieved by means of quantum key distribution (QKD) technology use.

square of the phases difference is characterized, and for the bottom—cosine-squared one. The optimal implementation of the QKD frequency encoding technology and the most clearly cryptography protocol BB84 can be obtained by using AM (Alice) and PM (Bob) (or PM-AM), which was shown in [13]. In the latter works, a broad understanding of frequency encoding principle is used, where to each state of the photons, instead of the phase of the modulating signal at a certain frequency, one or more lateral component frequencies either photon optical

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The symmetric pairs of the PM-PM, AM-AM and meshed AM-PM (PM-AM) are described by known electro-optical modulation and re-modulation schemes, where the first component determines the type of modulation and modulator on the side of Alice, and the other—on the side of Bob. The most important features of this type of QKD system are simplicity of schemes and phase shift matching decisions on both sides of quantum channel, efficient use of its bandwidth and capability to add quantity of subcarriers using one carrier source [15]. From another point of view [16], the smallest value of QBER is achieved in circuits with passive definition of photons states, without re-modulation and using only filter systems based on fiber Bragg gratings (FBG) or arrayed waveguide gratings (AWG) for subcarriers or carrier selection. Thus, we have to analyze as symmetrical systems with re-modulation, so and asym-

Disadvantages of above-described QKD systems are connected mainly with strong carrier and photon subcarrier levels' interaction along the optical fiber and its energy meshing. First, in [17], it was shown that effects of nonlinear phase modulation (NPM) are small on temporally separable sources utilizing symmetric group velocity matching but appreciably change the state of temporally entangled sources with the same group velocity-matching scheme. The largest changes to the state due to NPM occur in long FOCL with long pulse durations and low repetition rates (in limit, it is CW-technology of QKD with frequency coding). Second, in [18], it was shown that most quantum setups use simple attenuation of laser carrier as a source of quantum states. In such cases, average probability of single photon emission per time unit is equal to μ ≈ 0.1. The security condition in this case is no longer strict due to Poisson distribution of photons, so carrier or subcarriers may contain more than one photon. This fact can be easily used by Eve—illegal agent. She successfully can perform undetectable beam splitting or photon number splitting (PNS) attack without changing QBER and receive a part of the key, which can be significant at higher μ. Third, in [15], it was shown that quantum information transfer devices at subcarrier frequencies of modulated radiation required an exact separation of the quantum subcarrier signal and central wavelength. Inadequate extinction of the signal on the main frequency significantly reduces the signal-to-noise ratio of the system and leads to a significant increase in the number of errors in the quantum communication channel. Therefore, the QKD technology with frequency coding, based on the modulation conversion of an optical carrier with its complete or partial suppressing, is the actual problem to improve quantum channel characteristics. Due to the natural symmetry of modulated signals and the highest achievable ratio of the modulation conversions, amplitude-phase modulation with complete or partial suppression of the optical carrier has found a particularly wide application in the systems of microwave photonics [19]. Let us apply microwave photonics principles to design of QKD systems with

metrical ones without re-modulation and only filter selection.

carrier [14] are put into line.

frequency encoding.

Nowadays, there are at least four basic photonic QKD technologies: polarization [2], interferometric [3], differential phase shift [4] and frequency encoding [5]. The polarization technology is based on the features of four photons' fundamental states consideration and encoding, using one conjugate base of circular polarization and one of linear. The main disadvantage of this technology is the inability to maintain the polarization state of the photon along the entire length of fiber optic communication lines (FOCL). Interference technology relies on the use of optical delay lines and balanced interferometers in FOCL transmitter and receiver. The basic requirement for the implementation of this technology is to maintain the phase stroke difference of interferometers when exposed to temperature, vibration and other factors that are hard to realize. A phase technology is an approach based on the methods of differential phase shift, which allows implementing the QKD technology at FOCL lengths over 100 km, although with limited security [6].

The technology of frequency encoding allows determining the ground states of photons through the amplitude value of its carrier frequency, modulated in phase and/or amplitude by radiofrequency (RF) signal and the received high-order sidebands (subcarriers). This technology, based on the modulation conversion of multiphoton optical carrier, is widely used in microwave photonics, in its various classic applications [7–9].

Standard implementation of frequency encoding technology in quantum communication networks can be described as follows [10]. Alice (legal subscriber, transmitter) randomly changes the phase of the RF signal used to modulate the photons, among four discrete values 0;π,…,π/2;3π/2, which form a pair of conjugate bases, and sends it by FOCL quantum channel to Bob (legal subscriber, receiver). Bob modulates receiving photons again, using the same frequency RF signal as Alice, but with its own discrete phases, independent from Alice, from the same paired bases 0;π,…,π/2;3π/2. Along with this, the new order photon sidebands on the Bob's side will interfere with photons' sideband components received from the Alice's side. The interference result will determine the correctness of the adopted phase information and the encoded photon's state. For simplicity, quantum communication channel with sidebands only of first order is considered.

Over the last 20 years, this technology has been substantially modified and improved. Initially, it was used to implement the QKD in hardware, based on the modified cryptographic B92 protocol [11]. In this case, the level of constructive or destructive interference of the two lateral components, obtained by means of phase modulation (PM), was determined as a function of the cosine-squared type from the phase difference between the Alice and Bob signals. In more detailed characteristic consideration, the amplitude modulation (AM) application was used instead of phase technology to implement the QKD in hardware, based on the underlying cryptographic BB84 protocol [12], although the last one in theory was designed earlier than BB92 one. Thus, for the amplitude of the upper lateral components, the function of the sine square of the phases difference is characterized, and for the bottom—cosine-squared one. The optimal implementation of the QKD frequency encoding technology and the most clearly cryptography protocol BB84 can be obtained by using AM (Alice) and PM (Bob) (or PM-AM), which was shown in [13]. In the latter works, a broad understanding of frequency encoding principle is used, where to each state of the photons, instead of the phase of the modulating signal at a certain frequency, one or more lateral component frequencies either photon optical carrier [14] are put into line.

**1. Introduction**

distribution (QKD) technology use.

114 Advanced Technologies of Quantum Key Distribution

with limited security [6].

Quantum communication networks provide a unique opportunity of sharing a random sequence of bits between users with guaranteed security not achievable in classical open or special systems with cryptographic protection [1]. This is achieved by means of quantum key

Nowadays, there are at least four basic photonic QKD technologies: polarization [2], interferometric [3], differential phase shift [4] and frequency encoding [5]. The polarization technology is based on the features of four photons' fundamental states consideration and encoding, using one conjugate base of circular polarization and one of linear. The main disadvantage of this technology is the inability to maintain the polarization state of the photon along the entire length of fiber optic communication lines (FOCL). Interference technology relies on the use of optical delay lines and balanced interferometers in FOCL transmitter and receiver. The basic requirement for the implementation of this technology is to maintain the phase stroke difference of interferometers when exposed to temperature, vibration and other factors that are hard to realize. A phase technology is an approach based on the methods of differential phase shift, which allows implementing the QKD technology at FOCL lengths over 100 km, although

The technology of frequency encoding allows determining the ground states of photons through the amplitude value of its carrier frequency, modulated in phase and/or amplitude by radiofrequency (RF) signal and the received high-order sidebands (subcarriers). This technology, based on the modulation conversion of multiphoton optical carrier, is widely used in

Standard implementation of frequency encoding technology in quantum communication networks can be described as follows [10]. Alice (legal subscriber, transmitter) randomly changes the phase of the RF signal used to modulate the photons, among four discrete values 0;π,…,π/2;3π/2, which form a pair of conjugate bases, and sends it by FOCL quantum channel to Bob (legal subscriber, receiver). Bob modulates receiving photons again, using the same frequency RF signal as Alice, but with its own discrete phases, independent from Alice, from the same paired bases 0;π,…,π/2;3π/2. Along with this, the new order photon sidebands on the Bob's side will interfere with photons' sideband components received from the Alice's side. The interference result will determine the correctness of the adopted phase information and the encoded photon's state. For simplicity, quantum communication channel with sidebands only of first order is considered.

Over the last 20 years, this technology has been substantially modified and improved. Initially, it was used to implement the QKD in hardware, based on the modified cryptographic B92 protocol [11]. In this case, the level of constructive or destructive interference of the two lateral components, obtained by means of phase modulation (PM), was determined as a function of the cosine-squared type from the phase difference between the Alice and Bob signals. In more detailed characteristic consideration, the amplitude modulation (AM) application was used instead of phase technology to implement the QKD in hardware, based on the underlying cryptographic BB84 protocol [12], although the last one in theory was designed earlier than BB92 one. Thus, for the amplitude of the upper lateral components, the function of the sine

microwave photonics, in its various classic applications [7–9].

The symmetric pairs of the PM-PM, AM-AM and meshed AM-PM (PM-AM) are described by known electro-optical modulation and re-modulation schemes, where the first component determines the type of modulation and modulator on the side of Alice, and the other—on the side of Bob. The most important features of this type of QKD system are simplicity of schemes and phase shift matching decisions on both sides of quantum channel, efficient use of its bandwidth and capability to add quantity of subcarriers using one carrier source [15]. From another point of view [16], the smallest value of QBER is achieved in circuits with passive definition of photons states, without re-modulation and using only filter systems based on fiber Bragg gratings (FBG) or arrayed waveguide gratings (AWG) for subcarriers or carrier selection. Thus, we have to analyze as symmetrical systems with re-modulation, so and asymmetrical ones without re-modulation and only filter selection.

Disadvantages of above-described QKD systems are connected mainly with strong carrier and photon subcarrier levels' interaction along the optical fiber and its energy meshing. First, in [17], it was shown that effects of nonlinear phase modulation (NPM) are small on temporally separable sources utilizing symmetric group velocity matching but appreciably change the state of temporally entangled sources with the same group velocity-matching scheme. The largest changes to the state due to NPM occur in long FOCL with long pulse durations and low repetition rates (in limit, it is CW-technology of QKD with frequency coding). Second, in [18], it was shown that most quantum setups use simple attenuation of laser carrier as a source of quantum states. In such cases, average probability of single photon emission per time unit is equal to μ ≈ 0.1. The security condition in this case is no longer strict due to Poisson distribution of photons, so carrier or subcarriers may contain more than one photon. This fact can be easily used by Eve—illegal agent. She successfully can perform undetectable beam splitting or photon number splitting (PNS) attack without changing QBER and receive a part of the key, which can be significant at higher μ. Third, in [15], it was shown that quantum information transfer devices at subcarrier frequencies of modulated radiation required an exact separation of the quantum subcarrier signal and central wavelength. Inadequate extinction of the signal on the main frequency significantly reduces the signal-to-noise ratio of the system and leads to a significant increase in the number of errors in the quantum communication channel. Therefore, the QKD technology with frequency coding, based on the modulation conversion of an optical carrier with its complete or partial suppressing, is the actual problem to improve quantum channel characteristics.

Due to the natural symmetry of modulated signals and the highest achievable ratio of the modulation conversions, amplitude-phase modulation with complete or partial suppression of the optical carrier has found a particularly wide application in the systems of microwave photonics [19]. Let us apply microwave photonics principles to design of QKD systems with frequency encoding.

We present in this chapter the results of the universal QKD system design, based on a tandem electro-optic AMPM-PMAM scheme built on microwave photonics principles applied to photon carrier modulation. It allows us to implement all of the above-mentioned classical symmetrical schemes PM-PM, AM-AM and meshed AM-PM (PM-AM) and also to review the requirements for building a promising tandem AM and phase commutation (PC) scheme with the possibility of implementing a nonclassical asymmetric structure with passive filtering (FBG/AWG) on Bob's side and suppressed carrier.

B92 protocol [11] is the modernization of BB84 protocol and is used to encode one of the two

One of the first PM-PM scheme variants is based on the B92 protocol [22]. Its OptiSystem

the receiving end, Bob modulates the input radiation synchronized with Alice RF signal from

It should be noted that modulation effect is to transfer energy from carrier on the sidebands (subcarriers). Its effectiveness depends on modulation and corresponding phases ΦA and ΦB. Transfer

at maximum when ∆Φ = 0, which indicates the same basis chosen by Alice and Bob (**Figure 2**). Further exchange of information between Alice and Bob allows them to set a secure connection with the implementation of the B92 protocol. The definition of a key with probability

Determination of phase's compliance level in the scheme is actually implemented by the amplitude of the subcarriers. That is also the evidence of these scheme drawbacks, taking into account the small power of optical subcarriers and the presence of noise in the communica-

*<sup>k</sup>*−*<sup>n</sup> expjn<sup>Φ</sup><sup>A</sup> expj*(*k*−*n*)*Φ<sup>B</sup>*

*n*=+∞ *J <sup>n</sup> expjn<sup>Φ</sup><sup>A</sup>*

where, for simplicity of display, the argument of the Bessel's function *J*

efficiency P(ω0 → ω0 ± Ω) is proportional to the function cos<sup>2</sup>

**Figure 1.** Modeling of PM-PM scheme for QKD system with frequency coding.

its sine generator (right) phase Φ=ΦB. At Bob's PM output, one will receive:

*n J*

⟩ in left PM by RF signal from sine generator with frequency Ω

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*n*


(∆Φ/2), where ∆Φ = ΦB−ΦA, and is

is not specified. On

presented in (1) bases.

**2.1. PM-PM schemes**

model is presented in **Figure 1**.



equal to one for Eve is impossible.

tion channel and single photon detector (SPD).

Alice modulates photon |ω0

and phase Φ = ΦA, getting:

The chapter in the main is based on the results of analytical review of [1–19], materials of Morozov et al. [20] and additional and new results of theoretical and experimental researches in QKD theme and miscellaneous applications. Next chapter sections are organized as follows. The second section shows the principles of design of QKD systems with frequency encoding based on the classical approaches; key nodes involved for the implementation of PM-PM, AM-AM and meshed AM-PM (PM-AM) schemes are described; the descriptions of protocol bases and some experimental results are given; the advantages and disadvantages of classical schemes are evaluated, and the ways of its development are discussed. The third section discusses the design of promising universal tandem AMPM-PMAM scheme and its microwave photonic (MWP) basis; version of QKD system with tandem amplitude modulation and phase commutation of photons is proposed; the capabilities of re-modulation and possibilities of re-commutation procedures, or their absent and using only passive filtering structure realizations. In conclusion, the received results are analyzed and the key development challenges for QKD systems with frequency encoding are highlighted.
