Wavelength conversion for single-photon polarization qubits through continuous-variable quantum teleportation

We investigate continuous variable (CV) quantum teleportation using relevant classes of non-Gaussian states of the radiation field as entangled resources. First, we introduce the class two-mode squeezed symmetric superposition of Fock states, including finite truncations of twin-beam Gaussian states as special realizations. These states depend on a set of free independent parameters that can be adjusted for the optimization of teleportation protocols, with an enhancement of the success probability of teleportation both for coherent and Fock input states. We show that the optimization procedure reduces the entangled resources to truncated twin beam states, which thus represents an optimal class of non-Gaussian resources for quantum teleportation. We then introduce a further class of two-mode non-Gaussian entangled resources, in the form of squeezed cat-like states. We analyze the performance and the properties of such states when optimized for (CV) teleportation, and compare them to the optimized squeezed Bell-like states introduced in a previous work [12]. We discuss how optimal resources for teleportation are characterized by a suitable balance of entanglement content and squeezed vacuum affinity. We finally investigate the effects of thermal noise on the efficiency of quantum teleportation. To this aim, a convenient framework is to describe noisy entangled resources as linear superpositions of non-Gaussian state and thermal states. Although the presence of the thermal component strongly reduces the teleportation fidelity, noisy non-Gaussian states remain preferred resources when compared to noisy twin-beam Gaussian states.

The possibility to perform broad wavelength generation and conversion is of great interest in classical and quantum optics. With the introduction of integrated nonlinear silicon photonics, these tasks have been made even more viable thanks to the combination of the high nonlinear refractive index of silicon with the high confinement provided by the photonic waveguides. Exploiting this platform, several solutions for wavelength conversion have been investigated, for both optical processing [1] and applications in the Mid Infrared (MIR) [2]. The possibility to perform broad and controllable wavelength generation can be exploited also for creating integrated sources of quantum states of light based on single photons [3] or correlated photon pairs [4]. Both the generation and conversion can be accomplished by means of Four Wave Mixing (FWM). FWM is a nonlinear optical process in which two pump photons at frequency are converted into signal and idler photons at frequencies and ω/ respectively (with ω I /ω S ). In the particular case of wavelength conversion, FWM is stimulated by a seed wave at the same wavelength of the signal (idler) that will be converted to the wavelength of the idler (signal). FWM has to satisfy the energy conservation, according to which the relation ω P + ω P = ω S + ω I holds, and its efficiency is ruled by the phase matching condition. This latter condition is related to the phase mismatch among the waves involved in the FWM process, that is evaluated as Δk = k p + k p −k S −k I , where k P , k S , k I are the wavevectors for the pump, the signal and the idler, respectively. When Δk = 0, the phase matching condition is fulfilled and the efficiency of FWM is maximized. What is important for wavelength generation and conversion is the spectral position of the phase matching condition, which determines the wavelength at which the maximum efficiency of the conversion or generation process is achieved. Because of this, techniques for the control of the phase matching condition have been developed, focusing on the possibility to tailor the Group Velocity Dispersion (GVD) through a proper engineering of the waveguide geometry [5]. While these techniques consider only the first order waveguide mode, here we propose to exploit the higher order modes propagating inside a multimode waveguide. The dispersion of the higher order modes can be used to tune the spectral position of the phase matching condition for the FWM process, achieving controllable and large spectral translation in both Stimulated Four Wave Mixing (sFWM) and Spontaneous Four Wave Mixing (SFWM).

We propose a scheme to generate entanglement between a single-photon qubit in the polarization basis and a coherent state of light. The required resources are a superposition of coherent states, a polarization entangled photon pair, beam splitters, the displacement operation, and four photodetectors. Even when realistic detectors with a limited efficiency are used, an arbitrarily high fidelity can be obtained by adjusting a beam-splitter ratio and the displacement amplitude at the price of reducing the success probability. Our analysis shows that high fidelities may be obtained using on-off detectors with low efficiencies and available resource states under current technology.

Quantum teleportation has achieved significant progress in the optical frequency domain but faces persistent challenges, including high transmission losses and limited transmittance. In contrast, the microwave frequency domain offers distinct advantages, such as reduced absorption losses, lower energy consumption, and compatibility with superconducting quantum technologies. To overcome the limitations of optical quantum teleportation, this study presents a microwave-based continuous-variable quantum teleportation (CVQT) scheme designed for open-air environments at room temperature. The proposed approach employs microwave two-mode squeezed states, with entanglement enhanced through quantum scissors operations to mitigate environmental degradation. Numerical simulations demonstrate that the maximum transmission distance of microwave entangled states for CVQT is about 200 m at room temperature. The results also indicate that the microwave CVQT scheme achieves lower attenuation and higher fidelity over short distances compared to optical frequency CVQT under similar weather conditions. Moreover, microwave quantum states exhibit reduced sensitivity to weather-induced variations, highlighting their robustness and practicality for open-air quantum communication applications.

Summary form only given. The concept of quantum teleportation of continuous variables was suggested by Vaidman [see Phys. Rev. A, vol. 49, p. 1473, 1994]. The protocol for this kind of teleportation was elaborated and demonstrated experimentally by Kimble with collaborators [see Science, vol. 282, p. 706, 1998]. In this scheme the state being teleported is that of a single transverse mode of the electromagnetic field with finite frequency bandwidth. We describe the quantum teleportation scheme that allows one to teleport the quantum state of the wavefront of an electromagnetic wave. In other words we propose teleportation of the quantum state of a spatially multimode electromagnetic field.

One of many fiber nonlinear effects is a four-wave mixing (FWM) phenomenon that is resonant when the phase matching condition is satisfied. It only occurs for particular combinations of fiber dispersion and signal frequencies. In particular, phase matching is achieved for signals with very similar frequencies propagating near the zero dispersion wavelength of the fiber. The FWM is a very unpleasant transmission phenomenon in a transparent optical network, but it could be used for building all-optical devices such as wavelength converters, parametric amplifiers, optical demultiplexers, chromatic dispersion compensators, as well as signal to noise regenerators. At the process of device optimization or network planning it is important to know the fiber nonlinear coefficient (NLC). This measurement can be efficiently taken by the observation of FWM in a particular optical fiber. Besides fiber NLC measurement, FWM also enables the measurement of some other important fiber parameters, such as zero dispersion wavelength, chromatic dispersion and polarisation mode dispersion.

The progress in quantum operations of continuous-variable (CV) schemes can be reduced to that in CV quantum teleportation. The fidelity of quantum teleportation of an optical setup is limited by the finite degree of quantum correlation that can be prepared with a pair of finitely squeezed states. Reports of improvement of squeezing level have appeared recently, and we adopted the improved methods in our experimental system of quantum teleportation. As a result, we teleported a coherent state with a fidelity $F=0.83\ifmmode\pm\else\textpm\fi{}0.01$, which is better than any other figures reported to date, to our knowledge. In this paper, we introduce a measure ${n}_{s}$, the number of teleportations expected to be carried out sequentially. Our result corresponds to ${n}_{s}=5.0\ifmmode\pm\else\textpm\fi{}0.4$. It suggests that our improvement would enable us to proceed toward more advanced quantum operations involving multiple steps.

Polarisation encoding is widely used in fibre-based Quantum Key Distribution (QKD), but random birefringence in optical fibres causes the transmitted states to drift, requiring active compensation at the receiver. Electronic Polarisation Controllers (EPCs) are commonly used for this purpose, yet the relationship between their control voltages and the resulting polarisation transformation is highly nonlinear and difficult to model. While optimisation algorithms are frequently employed to align and stabilise polarisation states, their comparative performance has not been systematically studied in realistic QKD settings. In this work, we benchmark four optimisation algorithms for electronic polarisation control, using both a numerical model and a 50 km fibre-based experimental setup. We evaluate each algorithm in terms of convergence time, failure rate, and stability, under both initial alignment and continuous drift compensation scenarios. Coordinate Descent achieved the fastest average alignment time (2.1 ms in simulation; 34.6 s experimentally), while Simulated Annealing delivered perfect reliability. We further propose a hybrid control strategy that combines fast initial alignment with high-reliability realignment. This approach was validated over a continuous 2 h QKD simulation with real fibre drift, demonstrating robust polarisation control without manual intervention. Our results provide guidance for algorithm selection in practical QKD deployments and suggest a pathway to resilient, autonomous polarisation tracking in long-distance quantum networks.

We propose an optical parametric diffuser (OPD), a novel optical wavelength conversion device for wide wavelength band optical sampling systems. The OPD is made by using a multiple quantum well (MQW) structure with different band gap materials. Our aim is to achieve wavelength conversion of wider than 30 THz using the OPD and we simulated the wavelength conversion by four-wave mixing (FWM) for pico-second order optical pulses into the OPD. Experimental results indicated a conversion efficiency of -10 dB at a wavelength conversion frequency of 10 THz. To confirm this simulation result, we fabricated a basic OPD and measured the characteristics of wavelength conversion. These measurements gave a conversion efficiency of -22 dB (approx. -16 dB for the basic OPD itself) at a wavelength conversion frequency of 5 THz. Comparison of the simulation and experimental results suggested the possibility of high wavelength conversion efficiency even above 20 THz conversion frequency by optimizing the OPD structure.

Future optical networks may require both wavelength conversion and bit shape regeneration in an all-optical domain. The possibility of pulse reshaping while providing wavelength conversion may support new demands over medium and large distances links (Kelly, 2001). Indeed, during propagation the optical data signal suffers deterioration due to the amplified spontaneous emission (ASE) from optical amplifiers, pulse distortion from intrinsic dispersion, crosstalk, and attenuation. All-optical regenerators may be important components for the restoration of these signals, providing complexity and cost reductions with the avoidance of optoelectronic conversions. The regeneration could be 2R (reamplification and reshaping) or 3R, which also provide retiming to solve jitter (Simon et al., 2008). Several 3R regenerators using the semiconductor optical amplifier (SOA) have been proposed, such as cascaded SOAs setups (Funabashi et al., 2006) or SOA based MachZehnder interferometers (MZI) (Fischer et al., 1999). However for small and medium distances systems, where the signal amplitude noise and distortions form the main problem and where jitter has fewer magnitudes, the simpler 2R processes can be adequate to keep signal quality (Simon et al., 1998). In addition, the SOA is a helpful device for both 2R-regeneration (Ohman et al., 2003) and wavelength conversion (Durhuus et al., 1996). Several techniques for 2R-regeneration based on SOAs have been proposed and tested, for example by using four-wave mixing (FWM) (Simos et al., 2004), cross-gain modulation (XGM) (Contestabile et al., 2005), integration within MZI (Wang et al., 2007), multimode interferometric SOA (Merlier et al., 2001), cross-phase modulation (XPM) with filtering (Chayet et al., 2004), and feed forward technique (Conforti et al., 1999). However, these techniques require complex designs and involve critical operation points, even the simplest ones based on XGM features. In addition, most of these techniques are not capable of wavelength conversion and regeneration simultaneously. Recently a regenerator based on cross-gain modulation was proposed using one SOA for wavelength conversion (in a counter-propagating mode) and another deeply saturated SOA (synchronized by an optical delay line) to achieve cross-gain compression (Contestabile 2005). This efficient approach has similarities with the all-optical feed-forward techniques. In addition, this regenerator could not done wavelength conversion if the wavelength of the

We have developed a depolarization technique to achieve polarization-insensitive wavelength conversion using four-wave mixing in an optical fiber. A maximum conversion efficiency of -11.79 dB was achieved over a 3 dB bandwidth of 26 nm in a 100-m-long dispersion-flattened photonic crystal fiber. The polarization-dependent conversion efficiency was less than 0.38 dB and the measured power penalty for a 10 Gbit/s NRZ signal was 1.9 dB. The relation between the conversion efficiency and the degree of polarization of the pump was also formulated.

Future high capacity wavelength division multiplexed (WDM) optical networks will rely on transmitting signals with information encoded on both the amplitude and phase of multiple optical carriers. To optimise the efficiency of these networks, they are likely to employ some level of wavelength switching [1], and a key function required by wavelength switching is wavelength conversion [1]. Wavelength conversion of phase modulated signals in wavelength switched optical networks will need to be undertaken using a coherent nonlinear process, such as four-wave mixing (FWM) in a semiconductor optical amplifier (SOA) [2] employing a fast wavelength tuneable pump laser to ensure an optical channel can be dynamically routed to different wavelengths. A crucial issue that is likely to have a major impact on the wavelength conversion of such high capacity signals using FWM is the phase noise transfer to the converted signal. A detailed study of FWM wavelength converted continuous-wave signals in [3] showed that the phase noise transfer from the pump to the idler, increased the linewidth of the idler by a factor of 4 relative to the pump. Such a large line broadening is highly detrimental to the detection of phase-encoded signals, especially since the tuneable lasers that exhibit small wavelength switching times (<;50 ns) and would be employed in wavelength switched networks tend to have linewidths of the order of a few MHz [4]. Therefore estimating the linewidth limits that enable FWM wavelength conversion using this scheme is vital to select a tuneable pump laser with suitable linewidth.

Four-wave mixing (FWM) in semiconductor optical amplifiers (SOAs) has several important features, such as, high speed and high FWM conversion efficiency as well as optical demultiplexing (DEMUX) (Mecozzi et al., 1995; Mecozzi & Mrk, 1997; Das et al., 2000). The are several applications of FWM in SOAs for all-optical devices, such as, wavelength converters (Vahala et al., 1996), optical samplers (Inoue & Kawaguchi, 1998), optical phase conjugators (Kikuchi & Matsumura, 1998) and optical multiplexers/demultiplexers (Kawanishi et al., 1997; Kawanishi et al., 1994; Morioka et al., 1996; Uchiyama et al., 1998; Tomkos et al., 1999; Kirita et al., 1998; Buxens et al., 2000) have been demonstrated for optical communication systems. When a pulse of a time-multiplexed signal train (for example, a probe pulse) and a pump pulse are injected simultaneously into an SOA, gain and refractive index in the SOA are modulated and an FWM signal is generated by the modulations. Thus, we can obtain a demultiplexed signal as an FWM signal at the output of SOA. All-optical demultiplexing has been experimentally demonstrated up to 200 Gbit/s (Morioka et al., 1996). Tomkos et al., (Tomkos et al., 1999) suggested a number of ways to improve the performance of the dual-pump demultiplexer at 40 Gbit/s as follows; adjustment of the input wavelengths at the peak gain wavelength of the SOA under saturation conditions, the use of higher pump power at the input of the device, or/and the use of pulsed pumps with short pulsewidths. For the higher bit-rate, the overlap of the input to the FWM signal pulses may appear both in the time and spectral domain. The pattern effect may also appear in the FWM signal due to the slow components of the optical nonlinearities in SOAs (Saleh & Habbab, 1990). These effects degrade the usefulness of the FWM in SOAs as a practical DEMUX device in optical network/ communication systems. Therefore, it is very important to analysis the optical DEMUX characteristics based on FWM in SOAs for the ultrafast multi-bit input optical pulses.

Nondegenerate four-wave mixing in semiconductor optical amplifiers was studied both as a spectroscopic tool for probing semiconductor dynamics and as a wavelength conversion technique. Four-wave mixing spectra were measured at detuning frequencies ranging from GHz to THz rates and ultrasfast intraband mechanisms having relaxation time constants of 650 fs and less than 100 fs were revealed in the measurements. Cross-polarization four-wave mixing was also measured to study the inter quantum-well carrier transport process in quantum-well amplifiers. In addition, broadband wavelength conversion using four-wave mixing in semiconductor optical amplifiers was investigated. Results concerning the conversion efficiency over spans up to 65 nm, as well as a demonstration of wavelength conversion with gain are presented. The issue of converted signal-to-background noise in this process is also addressed.

Satellite-based quantum communication is critical in establishing a global quantum network for its ability to achieve thousand-kilometer-level tasks without the requirement of quantum relay. The free-space channel, however, is affected by diffraction, regular refraction, and atmospheric turbulence, which induce random wandering and broadening of the transmitted beam, resulting in the transmittance of fluctuation. In such a scenario, the ability to predict the unknown situation has become a problem worth considering. In this paper, we suggest a machine learning (ML) assisted prediction of continuous-variable quantum teleportation (CVQT) over satellite-ground channel. We apply the prediction algorithm, which involves <inline-formula xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink"><tex-math notation="LaTeX">$k$</tex-math></inline-formula> -nearest neighbor (KNN) algorithm and decision tree (DT) algorithm, to the squeezing parameter and the satellite altitude. Numerical analysis shows that the predicted parameter can reflect the actual derivation and calculation under certain circumstances within the allowable range of error. Moreover, we apply the prediction algorithm to the case affected by the fluctuating parameter transmittance. The results show that the ML-assisted prediction results are consistent with the actual data when zenith angles, turbulence strengths, and wavelengths are taken into account. It demonstrates the high identifying accuracy without increasing the complexity of the system.