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A Survey on Continuous Variable Quantum Key Distribution for Secure Data Transmission: Toward the Future of Secured Quantum-Networks

Mobin Motaharifar

Mobin Motaharifar

Photonics Research Laboratory, Electrical Engineering Dept, Amirkabir University of TechnologyTehran, Iran
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Motaharifar, Mobin
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Mahmood Hasani

Mahmood Hasani

Photonics Research Laboratory, Electrical Engineering Dept, Amirkabir University of TechnologyTehran, Iran
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Hasani, Mahmood
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Hassan Kaatuzian

Hassan Kaatuzian

Photonics Research Laboratory, Electrical Engineering Dept, Amirkabir University of TechnologyTehran, Iran
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Kaatuzian, Hassan
  
May 26, 2025
A Survey on Continuous Variable Quantum Key Distribution for Secure Data Transmission: Toward the Future of Secured Quantum-Networks's Cover Image
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Article Category: Review
Published Online: May 26, 2025
Page range: 175 - 194
Received: Dec 13, 2024
Accepted: Mar 09, 2025
DOI: https://doi.org/10.2478/qic-2025-0009
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© 2025 Mobin Motaharifar et al., published by Sciendo
This work is licensed under the Creative Commons Attribution-NonCommercial-NoDerivatives 4.0 International License.

Figure 1.

(a) An arbitrary coherent state (b) is the amplitude-squeezed state of light and (c) is the phase-squeezed state of light. The quasi-probability of the perpendicular axis displays the Wigner function value.
(a) An arbitrary coherent state (b) is the amplitude-squeezed state of light and (c) is the phase-squeezed state of light. The quasi-probability of the perpendicular axis displays the Wigner function value.

Figure 2.

Illustration of continuous-variable quantum teleportation. An arbitrary coherent state |ψ〉 (top rail) is to be teleported from Alice to Bob. Two infinitely squeezed vacuum states (middle and bottom rails) serve as the shared resource between them. First, these two squeezed states pass through a 50:50 beam splitter (left 50:50 block) to create an entangled EPR-like pair, with one mode held by Alice and the other mode sent to Bob. Next, Alice couples her unknown state |ψ〉 with her half of the entangled pair using another 50:50 beam splitter (right 50:50 block). She then performs homodyne measurements of both the amplitude (x) and phase (p) quadratures on the combined output. The measured values, 〈x〉 and 〈p〉, are sent via a classical channel to Bob, who applies corresponding displacement operations (the X and Z boxes) to his mode. This “corrects” his half of the entangled pair into an identical copy of |ψ〉. The inset (lower box) shows the 50:50 beam splitter’s action, splitting or combining two input modes in equal proportions.
Illustration of continuous-variable quantum teleportation. An arbitrary coherent state |ψ〉 (top rail) is to be teleported from Alice to Bob. Two infinitely squeezed vacuum states (middle and bottom rails) serve as the shared resource between them. First, these two squeezed states pass through a 50:50 beam splitter (left 50:50 block) to create an entangled EPR-like pair, with one mode held by Alice and the other mode sent to Bob. Next, Alice couples her unknown state |ψ〉 with her half of the entangled pair using another 50:50 beam splitter (right 50:50 block). She then performs homodyne measurements of both the amplitude (x) and phase (p) quadratures on the combined output. The measured values, 〈x〉 and 〈p〉, are sent via a classical channel to Bob, who applies corresponding displacement operations (the X and Z boxes) to his mode. This “corrects” his half of the entangled pair into an identical copy of |ψ〉. The inset (lower box) shows the 50:50 beam splitter’s action, splitting or combining two input modes in equal proportions.

Figure 3.

Wigner function of quadrature diagram of Bob and Alice entangled states after going through beamsplitters.
Wigner function of quadrature diagram of Bob and Alice entangled states after going through beamsplitters.

Figure 4.

(a) A modified integrated unit cell inspired by the Mach-Zehnder Cell. It can act as an arbitrary Measurement gate for identifying state’s position or momentum by changing the variable θ of the phase shifter. (b) Bent directional coupler with labeled parameters: Rin and Rout represent the inner and outer bending radii, respectively, while θ indicates the bending angle. The structure is designed to facilitate efficient light coupling between waveguides while minimizing losses and cross-talk effects.
(a) A modified integrated unit cell inspired by the Mach-Zehnder Cell. It can act as an arbitrary Measurement gate for identifying state’s position or momentum by changing the variable θ of the phase shifter. (b) Bent directional coupler with labeled parameters: Rin and Rout represent the inner and outer bending radii, respectively, while θ indicates the bending angle. The structure is designed to facilitate efficient light coupling between waveguides while minimizing losses and cross-talk effects.

Figure 5.

A 3D representation of a Photonic Integrated Circuit (PIC) designed to implement quantum teleportation in a continuous quantum variable circuit. The input states are introduced into the circuit from the left where (a) is with bent directional couplers and (b) is with conventional directional couplers, and at the conclusion (right side), Bob will possess Alice’s initial state of |ψ〉. The two blue cones symbolize homodyne detectors that measure the average value of arbitrary quadrature components. The outcomes of these measurements are utilized as controls for X and Z which are position displacement and momentum displacement, respectively, to recover the state |ψ〉 exactly.
A 3D representation of a Photonic Integrated Circuit (PIC) designed to implement quantum teleportation in a continuous quantum variable circuit. The input states are introduced into the circuit from the left where (a) is with bent directional couplers and (b) is with conventional directional couplers, and at the conclusion (right side), Bob will possess Alice’s initial state of |ψ〉. The two blue cones symbolize homodyne detectors that measure the average value of arbitrary quadrature components. The outcomes of these measurements are utilized as controls for X and Z which are position displacement and momentum displacement, respectively, to recover the state |ψ〉 exactly.

Figure 6.

This is the experimental configuration proposal for a 50-km Continuous Variable Quantum Key Distribution (CV QKD). In this setup, DAQ refers to the data acquisition module, AM is the amplitude modulator, PM stands for the phase modulator, and PBS is the polarizing beam splitter. DPC is the dynamic polarization controller, MVOA denotes the motor variable optical attenuator, and BHD is the balanced homodyne detector.
This is the experimental configuration proposal for a 50-km Continuous Variable Quantum Key Distribution (CV QKD). In this setup, DAQ refers to the data acquisition module, AM is the amplitude modulator, PM stands for the phase modulator, and PBS is the polarizing beam splitter. DPC is the dynamic polarization controller, MVOA denotes the motor variable optical attenuator, and BHD is the balanced homodyne detector.

Figure 7.

(a) A detailed optical setup for generating and measuring squeezed light. An infrared laser (main laser) undergoes second-harmonic generation (SHG) via a nonlinear crystal, converting it into a green pump beam. This pump beam is then used to drive an optical parametric amplifier (OPA), which generates squeezed infrared light. Dichroic and beam splitters direct different frequency components through the system. The output squeezed state is analyzed using homodyne detection, where the interference pattern is recorded by a spectrum analyzer. (b) A conceptual diagram of homodyne detection. The reference field (local oscillator) interferes with the squeezed field at a beam splitter, producing two outputs detected by photodiodes. The difference in photocurrent reveals quadrature noise properties of the squeezed state. (c) and (d) illustrate interactions at beam splitters. (c) represents a standard beam splitter operation where input beams mix and split into new paths. (d) shows dichroic beam splitting, where different wavelength components are separated, enabling selective manipulation of infrared and green light in the experiment.
(a) A detailed optical setup for generating and measuring squeezed light. An infrared laser (main laser) undergoes second-harmonic generation (SHG) via a nonlinear crystal, converting it into a green pump beam. This pump beam is then used to drive an optical parametric amplifier (OPA), which generates squeezed infrared light. Dichroic and beam splitters direct different frequency components through the system. The output squeezed state is analyzed using homodyne detection, where the interference pattern is recorded by a spectrum analyzer. (b) A conceptual diagram of homodyne detection. The reference field (local oscillator) interferes with the squeezed field at a beam splitter, producing two outputs detected by photodiodes. The difference in photocurrent reveals quadrature noise properties of the squeezed state. (c) and (d) illustrate interactions at beam splitters. (c) represents a standard beam splitter operation where input beams mix and split into new paths. (d) shows dichroic beam splitting, where different wavelength components are separated, enabling selective manipulation of infrared and green light in the experiment.

Figure 8.

(a) The chip is being reintroduced, as shown in a micro-graph of the actual device. (b) The provided quantum circuit diagram serves as a comparable representation of the photonic hardware, emphasizing its functional features similar to [69].
(a) The chip is being reintroduced, as shown in a micro-graph of the actual device. (b) The provided quantum circuit diagram serves as a comparable representation of the photonic hardware, emphasizing its functional features similar to [69].
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