Probabilistic shaped 128-APSK CV-QKD transmission system over optical fibres.

In this Letter we present a discrete modulated, continuous variables quantum key distribution implementation using two probabilistically shaped, 128-symbol, amplitude and phase shift keying constellations. At Bob's detection side, a polarization diverse, true heterodyne receiver architecture is implemented for symbol recovery. We demonstrate experimentally that our system is capable of achieving security against collective attacks, while using accessible, telecom-grade material, and of functioning for an indefinitely long period of time at distances in excess of 185 km, in the asymptotic regime.

Quantum Oblivious Transfer: A Short Review.

Quantum cryptography is the field of cryptography that explores the quantum properties of matter. Generally, it aims to develop primitives beyond the reach of classical cryptography and to improve existing classical implementations. Although much of the work in this field covers quantum key distribution (QKD), there have been some crucial steps towards the understanding and development of quantum oblivious transfer (QOT). One can show the similarity between the application structure of both QKD and QOT primitives. Just as QKD protocols allow quantum-safe communication, QOT protocols allow quantum-safe computation. However, the conditions under which QOT is fully quantum-safe have been subject to intense scrutiny and study. In this review article, we survey the work developed around the concept of oblivious transfer within theoretical quantum cryptography. We focus on some proposed protocols and their security requirements. We review the impossibility results that daunt this primitive and discuss several quantum security models under which it is possible to prove QOT security.

Polarization based discrete variables quantum key distribution via conjugated homodyne detection.

Optical homodyne detection is widely adopted in continuous-variable quantum key distribution for high-rate field measurement quadratures. Besides that, those detection schemes have been being implemented for single-photon statistics characterization in the field of quantum tomography. In this work, we propose a discrete-variable quantum key distribution (DV-QKD) implementation that combines the use of phase modulators for high-speed state of polarization (SOP) generation, with a conjugate homodyne detection scheme which enables the deployment of high speed QKD systems. The channel discretization relies on the application of a detection threshold that allows to map the measured voltages as a click or no-click. Our scheme relies also on the use of a time-multiplexed pilot tone-quantum signal architecture which enables the use of a Bob locally generated local oscillator and opens the door to an effective polarization drift compensation scheme. Besides that, our results shows that for higher detection threshold values we obtain a very low quantum bit error rate (QBER) on the sifted key. Nevertheless, due to huge number of discarded qubits the obtained secure key length abruptly decreases. From our results, we observe that optimizing the detection threshold and considering a system operating at 500 MHz symbol generation clock, a secure key rate of approximately 46.9 Mbps, with a sifted QBER of  [Formula: see text] over 40 km of optical fiber. This considering the error correction and privacy amplification steps necessary to obtain a final secure key.

Full polarization random drift compensation method for quantum communication.

Long-term quantum key distribution (QKD) using polarization encoding requires a random drift compensation method. We propose a method to compensate any state of polarization based on the quantum bit error rate (QBER) of two states from two non-orthogonal mutually unbiased bases. The proposed method does not require dedicated equipment, and through a simple but highly efficient feedback loop it compensates the polarization random drift suffered by photons while transmitted over the optical fiber quantum channel. A QBER lower than 2% was observed even considering imperfect single photon detectors. Besides, we verify a 82% secret key rate generation improvement in a finite-key size BB84 implementation for a 40 km fiber-optics quantum channel.

Secret key rate of multi-ring M-APSK continuous variable quantum key distribution.

Discrete modulation continuous variable quantum key distribution (DM-CV-QKD) is highly considered in real implementations to avoid the complexity of Gaussian modulation (GM), which is optimum in terms of the key rate. DM-CV-QKD systems usually consider M-symbol phase shift keying (M-PSK) constellations. However, this type of constellation cannot reach transmission distances and key rates as high as GM, limiting the practical implementation of CV-QKD systems. Here, by considering M-symbol amplitude and phase shift keying (M-APSK) constellations, we can approximate GM. Indeed, considering finite-size effects, 4 ring 64-APSK can reach 52.0 km, only 7.2 km less than GM and 282% the maximum achievable transmission distance for 8-PSK.

Reversal operator to compensate polarization random drifts in quantum communications.

A quantum bit error rate (QBER) based algorithm for polarization random drift compensation is proposed. For a transmission window of 8 ms, for instance in aerial fiber installations, the algorithm overhead is below 1%. In an extreme turbulent situation, where the transmission window is as shorter as 0.8 ms, the overhead is still below 10%. Besides being able to operate smoothly, even in a very extreme situation, the algorithm overhead is also insensitive to the length of the communication system. It is upper layer protocol agnostic, and it is based on the mapping of the QBER on the Poincaré sphere. The algorithm finds the polarization reversal operator, which results in much lower overhead contrary to the blind methods currently used. The algorithm reverts the polarization random drift performing two QBER estimations and applying three rotations, at most. The uncertainty on the two QBER estimations defines an area over the sphere surface that is related with upper-layer protocols QBER threshold.

Reduced-complexity algorithm for space-demultiplexing based on higher-order Poincaré spheres.

We propose a reduced-complexity space-demultiplexing algorithm based on higher-order Poincaré spheres (HoPs) which is modulation format agnostic, free of training sequences and robust to the local oscillator phase fluctuations and frequency offsets. The signal tributaries are space-demultiplexed by calculating and realigning the best fit plane in the HoPs, with the inverse channel matrix being iteratively constructed by sequentially space-demultiplexing all pairs of tributaries. When compared with the previous proposed HoPs-based space-demultiplexing algorithm, results show a complexity reduction gain of 99% along with an improvement of 97% in terms of convergence speed.

Space-demultiplexing based on higher-order Poincaré spheres.

We propose a space-demultiplexing algorithm based on signal analysis in higher-order Poincaré spheres for optical transmission systems supported by space-division multiplexing. This algorithm is modulation format agnostic and does not require training sequences. We show that any arbitrary pair of tributaries signals can be represented in a higher-order Poincaré sphere. In such sphere, the crosstalk between any two tributary signals can be reversed by computing and realigning the best fit plane. Using this procedure for all possible combinations of tributaries the transmitted signal is successfully recovered, with negligible signal-to-noise ratio (SNR) penalties for quadrature phase-shift keying (QPSK) and 16-quadrature amplitude modulation (QAM) constellations, and with a SNR penalty as lower as 0.5 dB for the 64-QAM.

Simplified high-order Volterra series transfer function for optical transmission links.

We develop a simplified high-order multi-span Volterra series transfer function (SH-MS-VSTF), basing our derivation on the well-known third-order Volterra series transfer function (VSTF). We notice that when applying an approach based on a recursive method and considering the phased-array factor, the order of the expression for the transfer function grows as 3 raised to the number of considered spans. By imposing a frequency-flat approximation to the higher-order terms that are usually neglected in the commonly used VSTF approach, we are able to reduce the overall expression order to the typical third-order plus a complex correction factor. We carry on performance comparisons between the purposed SH-MS-VSTF, the well-known split-step Fourier method (SSFM), and the third-order VSTF. The SH-MS-VSTF exhibits a uniform improvement of about two orders of magnitude in the normalized mean squared deviation with respect to the other methods. This can be translated in a reduction of the overall number of steps required to fully analyze the transmission link up to 99.75% with respect to the SSFM, and 98.75% with respect to the third-order VSTF, respectively, for the same numerical accuracy.

Nonlinear compensation with DBP aided by a memory polynomial.

Using digital backpropagation (DBP) based on the split step Fourier method (SSFM) aided by a memory polynomial (MP) model, we demonstrate an improved DBP approach for fiber nonlinearity compensation. The proposed technique (DBP-SSFM&MP) is numerically validated and its performance and complexity are compared against the benchmark DBP-SSFM, considering a single-channel 336 Gb/s PM-64QAM transmission system. We demonstrate that the proposed technique allows to maintain the performance achieved by DBP-SSFM, while decreasing the required number of iterations, by over 60%. For a transmission length of 1600 km we obtain a complexity reduction gain of 50.7% in terms of real multiplications in comparison with the standard DBP-SSFM.

Switching in multicore fibers using flexural acoustic waves.

We propose an in-line wavelength selective core switch for multicore fiber (MCF) transmission systems, based on the acousto-optic effect. A theoretical model addressing the interaction between flexural acoustic waves and the optical signal in MCFs is developed. We show that an optical signal propagating in a particular core can be switched to any other core or distributed over all the cores. By tuning the acoustic wave amplitude, we can adjust the amount of optical power transferred between the cores.

Experimental demonstration of a frequency-domain Volterra series nonlinear equalizer in polarization-multiplexed transmission.

Employing 100G polarization-multiplexed quaternary phase-shift keying (PM-QPSK) signals, we experimentally demonstrate a dual-polarization Volterra series nonlinear equalizer (VSNE) applied in frequency-domain, to mitigate intra-channel nonlinearities. The performance of the dual-polarization VSNE is assessed in both single-channel and in wavelength-division multiplexing (WDM) scenarios, providing direct comparisons with its single-polarization version and with the widely studied back-propagation split-step Fourier (SSF) approach. In single-channel transmission, the optimum power has been increased by about 1 dB, relatively to the single-polarization equalizers, and up to 3 dB over linear equalization, with a corresponding bit error rate (BER) reduction of up to 63% and 85%, respectively. Despite of the impact of inter-channel nonlinearities, we show that intra-channel nonlinear equalization is still able to provide approximately 1 dB improvement in the optimum power and a BER reduction of ~33%, considering a 66 GHz WDM grid. By means of simulation, we demonstrate that the performance of nonlinear equalization can be substantially enhanced if both optical and electrical filtering are optimized, enabling the VSNE technique to outperform its SSF counterpart at high input powers.

Mitigation of intra-channel nonlinearities using a frequency-domain Volterra series equalizer.

We address the issue of intra-channel nonlinear compensation using a Volterra series nonlinear equalizer based on an analytical closed-form solution for the 3rd order Volterra kernel in frequency-domain. The performance of the method is investigated through numerical simulations for a single-channel optical system using a 20 Gbaud NRZ-QPSK test signal propagated over 1600 km of both standard single-mode fiber and non-zero dispersion shifted fiber. We carry on performance and computational effort comparisons with the well-known backward propagation split-step Fourier (BP-SSF) method. The alias-free frequency-domain implementation of the Volterra series nonlinear equalizer makes it an attractive approach to work at low sampling rates, enabling to surpass the maximum performance of BP-SSF at 2× oversampling. Linear and nonlinear equalization can be treated independently, providing more flexibility to the equalization subsystem. The parallel structure of the algorithm is also a key advantage in terms of real-time implementation.

Broadband polarization pulling using Raman amplification.

The Raman gain based polarization pulling process in a copropagating scheme is investigated. We map the degree of polarization, the angle between the signal and pump output Stokes vectors, the mean signal gain and its standard deviation considering the entire Raman gain bandwidth. We show that, in the undepleted regime (signal input power ~ 1 µW), the degree of polarization is proportional to the pump power and changes with the signal wavelength, following the Raman gain shape. In the depleted regime (signal input power ≳ 1 mW), the highest values for the degree of polarization are no more observed for the highest pump powers. Indeed, we show that exists an optimum pump power leading to a maximum degree of polarization.