Reduction of the two-photon temporal distinguishability for measurement-device-independent quantum key distribution.

Measurement-device-independent quantum key distribution (MDI-QKD) has been proven to protect legitimate users from attacks against measurement devices. The MDI-QKD requires that the two photons arriving at the instrument be indistinguishable. Precise time control is required to eliminate the distinguishability due to differences in photon arrival times. In the conventional methods, the time difference between photons is measured at a measuring instrument (Charlie), and a control signal is transmitted to the users (Alice and Bob). However, this method requires a long feedback loop, and the control may become unstable for long-distance transmission. This article proposes a method in which the photon arrival time difference is detected and controlled at Charlie. The reference signal for the time control is generated by an optical frequency comb in synchronization with the quantum signal. Therefore, the quantum signal photons can also be synchronized by synchronizing the reference signal pulses. A proof-of-principle experiment confirmed that the time synchronization accuracy required for protocol execution could be obtained. This proposal simplifies the implementation of the MDI-QKD.

Direct measurement of ultrafast temporal wavefunctions.

The large capacity and robustness of information encoding in the temporal mode of photons is important in quantum information processing, in which characterizing temporal quantum states with high usability and time resolution is essential. We propose and demonstrate a direct measurement method of temporal complex wavefunctions for weak light at a single-photon level with subpicosecond time resolution. Our direct measurement is realized by ultrafast metrology of the interference between the light under test and self-generated monochromatic reference light; no external reference light or complicated post-processing algorithms are required. Hence, this method is versatile and potentially widely applicable for temporal state characterization.

Spatial-light-modulator-based optical-fiber joint switch for few-mode multicore fibers.

To realize simplified cost-efficient optical networks with routing flexibility and scaling potential, a spatial-light-modulator-based optical-fiber joint switch for few-mode multicore fibers is proposed herein, which can route all spatial channels together as a unit. Numerical simulations and experiments were performed, and the results show that the signal paths for a 6-mode 19-core fiber can be simultaneously switched to the target output ports using the proposed method, and the mode-field patterns of the diffracted light can be maintained after joint switching. Further, the maximum port crosstalk can be reduced considerably from -11.6 to -25.1 dB by changing the position of the output port in the proposed method.

State preparation robust to modulation signal degradation by use of a dual parallel modulator for high-speed BB84 quantum key distribution systems.

Security certification of quantum key distribution systems with a practical device is essential for their social deployment. Considering the transmitter, we investigate quantum state generation affected by degraded electrical signals from practical bandwidth-limited devices on high-speed phase-encoding BB84 quantum key distribution systems. The state preparation flaw caused by this degradation undesirably enhances the distinguishability between the two bases for the BB84 protocol and decreases the key generation rate. We propose the state preparation with a dual parallel modulator for increasing the robustness to signal degradation. To verify the effectiveness of the dual parallel modulator, we characterize the generated states using state tomography and estimate the key generation rate based on the Gottesman-Lo-Lütkenhaus-Preskill theory with fidelity derived from the estimated density matrices. Simulation results show that the key generation rate remains unaffected by modulation voltage shifts up to 20%.

Wavefront superposition method for accurate and efficient mode conversion.

A wavefront superposition (WS) method is proposed for accurate and efficient mode conversion in mode-division multiplexing transmission. The WS method converts an input beam to the WS state, which is composed of the conversion target and radiation modes of a few-mode fiber. The appropriate weighting for the modal component of the WS state enables more efficient conversion than the conventional method in which the output beam consists only of the conversion target. Further, since the components of the radiation modes in the output are eliminated by the mode-filtering property of the few-mode fiber, no modal crosstalk occurs in the WS method. We examine the conversion performance of the WS method by a numerical simulation for the mode-multiplexing numbers 3, 6, 10, and 15. The WS method shows a 2.4 dB higher efficiency than the conventional method, while maintaining an extremely low modal crosstalk (less than -80 dB), even when the number of multiplexed modes is 15.

Virtual phase conjugation based optical tomography for single-shot three-dimensional imaging.

We propose a virtual phase conjugation (VPC) based optical tomography (VPC-OT) for realizing single-shot optical tomographic imaging systems. Using a computer-based numerical beam propagation, the VPC combines pre-modulation and post-demodulation of the probe beam's wavefront, which provides an optical sectioning capability for resolving the depth coordinates. In VPC-OT, the physical optical microscope system and VPC are coupled using digital holography. Therefore, in contrast to conventional optical tomographic imaging (OTI) systems, this method does not require additional elements such as low-coherence light sources or confocal pinholes. It is challenging to obtain single-shot three-dimensional (3D) tomographic images using a conventional OTI system; however, this can be achieved using VPC-OT, which employs both digital holography and computer based numerical beam propagation. In addition, taking into account that VPC-OT is based on a complex amplitude detection using digital holography, this method allows us to simultaneously obtain quantitative phase contrast images. Using an objective lens with a numerical aperture (NA) of 0.8, we demonstrate a single-shot 3D imaging of frog blood cells with a depth resolution of 0.94 µm.

Volume holographic spatial mode demultiplexer with a dual-wavelength method.

Volume holographic demultiplexers (VHDMs) provide spatial mode demultiplexing using simple optical systems. However, applying VHDM to practical optical communication systems is difficult, as typical holographic media have no sensitivity in the infrared region, which includes optical transmission bands. In this paper, we propose a VHDM scheme combined with a dual-wavelength method (DWM). Using the DWM, VHDMs are able to perform mode demultiplexing in the optical transmission bands. We experimentally demonstrated the basic operation of our proposal using experiments performed at an 850-nm wavelength. In addition, we performed numerical simulations to investigate the application of VHDM to the C-band.

Intensity fluctuation of a gain-switched semiconductor laser for quantum key distribution systems.

Security certification of quantum key distribution (QKD) systems under practical conditions is necessary for social deployment. This article focused on the transmitter, and, in particular, investigated the intensity fluctuation of the optical pulses emitted by a gain-switched semiconductor laser used in QKD systems implementing decoy-BB84 protocol. A large intensity fluctuation was observed for low excitation, showing strong negative correlation between the adjacent pulses, which would affect the final key rate. The fluctuation decreased and the correlation disappeared as excitation increased. Simulation with rate equations successfully reproduced the experimental results and revealed that the large fluctuation originates from an intrinsic instability of gain-switched lasers driven periodically at a rate comparable to the inverse of carrier lifetime, as in GHz-clock QKD systems. Methods for further reduction of the intensity fluctuation were also discussed.

Analog Quantum Error Correction with Encoding a Qubit into an Oscillator.

To implement fault-tolerant quantum computation with continuous variables, Gottesman-Kitaev-Preskill (GKP) qubits have been recognized as an important technological element. However, the analog outcome of GKP qubits, which includes beneficial information to improve the error tolerance, has been wasted, because the GKP qubits have been treated as only discrete variables. In this Letter, we propose a hybrid quantum error correction approach that combines digital information with the analog information of the GKP qubits using a maximum-likelihood method. As an example, we demonstrate that the three-qubit bit-flip code can correct double errors, whereas the conventional method based on majority voting on the binary measurement outcome can correct only a single error. As another example, we show that a concatenated code known as Knill's C_{4}/C_{6} code can achieve the hashing bound for the quantum capacity of the Gaussian quantum channel (GQC). To the best of our knowledge, this approach is the first attempt to draw both digital and analog information to improve quantum error correction performance and achieve the hashing bound for the quantum capacity of the GQC.

Virtual interferogram-generation algorithm for robust complex amplitude measurement using two interferograms.

We propose a virtual interferogram-generation algorithm using two interferograms. This algorithm can measure a complex amplitude of a signal beam with high accuracy even when its intensity is greater than the intensity of a reference beam. Unlike the conventional algorithm that uses two interferograms, our algorithm can compute measurements when the phase shift of interferograms in not equal to π/2. Our method generates two phase-shifted holograms in a computer by capturing the intensities of two signal beams, two reference beams, and two interferograms. The complex amplitude of a signal beam is calculated by four interference patterns, two holograms, and two interferograms. The proposed algorithm can drastically suppress the calculation error caused by the smaller value between the intensity of the reference beam and can choose the most suitable phase shift.

Reference-free holographic diversity interferometry via iterative measurements for high accuracy phase detection.

To obtain a phase distribution without the use of an optical path besides an object beam, a reference-free holographic diversity interferometry (RF-HDI) has been proposed. Although the RF-HDI can generate an internal reference beam from the object beam, the method has a problem of measurement accuracy due to insufficient power of the internal reference beam. To solve the problem, we newly propose a RF-HDI via iterative measurements. Our method improves the measurement accuracy by utilizing iterative measurements and feedback of each obtained phase image to the measurement system. In the experiment, the phase image, which has a random pattern, can be measured as an object beam with a higher accuracy than in the conventional RF-HDI. To support this result, we also evaluated the wavefront accuracy and optical power efficiency of an internal reference beam in this method. As a result, we verified that our method enables us to generate an internal reference beam that has the wavefront of a near single plane wave and a higher power efficiency than the conventional RF-HDI. In addition, our method can be applied to measurement for the modal content in an optical fiber, atmosphere turbulence, etc., where it is difficult to prepare an external reference beam with a high coherency.

Two-channel algorithm for single-shot, high-resolution measurement of optical wavefronts using two image sensors.

We propose a two-channel holographic diversity interferometer (2ch-HDI) system for single-shot and highly accurate measurements of complex amplitude fields with a simple optical setup. In this method, two phase-shifted interference patterns are generated, without requiring a phase-shifting device, by entering a circularly polarized reference beam into a polarizing beam splitter, and the resulting patterns are captured simultaneously using two image sensors. However, differences in the intensity distributions of the two image sensors may lead to serious measurement errors. Thus, we also develop a two-channel algorithm optimized for the 2ch-HDI to compensate for these differences. Simulation results show that this algorithm can compensate for such differences in the intensity distributions in the two image sensors. Experimental results confirm that the combination of the 2ch-HDI and the calculation algorithm significantly enhances measurement accuracy.

Spatial cross modulation method using a random diffuser and phase-only spatial light modulator for constructing arbitrary complex fields.

We propose a spatial cross modulation method using a random diffuser and a phase-only spatial light modulator (SLM), by which arbitrary complex-amplitude fields can be generated with higher spatial resolution and diffraction efficiency than off-axis and double-phase computer-generated holograms. Our method encodes the original complex object as a phase-only diffusion image by scattering the complex object using a random diffuser. In addition, all incoming light to the SLM is consumed for a single diffraction order, making a diffraction efficiency of more than 90% possible. This method can be applied for holographic data storage, three-dimensional displays, and other such applications.

Digital phase conjugate mirror by parallel arrangement of two phase-only spatial light modulators.

In a conventional digital phase conjugation system, only the phase of an input light is time-reversed. This deteriorates phase conjugation fidelity and restricts application fields to specific cases only when the input light has uniformly-distributed scattered wavefront. To overcome these difficulties, we present a digital phase conjugate mirror based on parallel alignment of two phase-only spatial light modulators (SLMs), in which both amplitude and phase of the input light can be time-reversed. Experimental result showed that, in the phase conjugation through a holographic diffuser with diffusion angle of 0.5 degree, background noises decrease to 65% by our digital phase conjugation mirror.

Modified E91 protocol demonstration with hybrid entanglement photon source.

We report on an experimental demonstration of the modified Ekert 91 protocol of quantum key distribution using a hybrid entanglement source with two different degrees of freedoms, a 1550 nm time-bin qubit and 810 nm polarization qubit. The violation of the Clauser-Horne-Shimony-Holt inequality could be demonstrated for the entanglement between the polarization qubit in free space and the time-bin qubit through 20 km fiber transmission. The secure key rate in our system is estimated 70-150 bps.

Mode demultiplexer using angularly multiplexed volume holograms.

This study proposes a volume holographic demultiplexer (VHDM) for extracting the spatial modes excited in a multimode fiber. A unique feature of the demultiplexer is that it can separate a number of multiplexed modes output from a fiber in different directions by using multi-recorded holograms without beam splitters, which results in a simple configuration as compared with that using phase plates instead of holograms. In this study, an experiment is conducted to demonstrate the basic operations for three LP mode groups to confirm the performance of the proposed VHDM and to estimate the signal-to-crosstalk noise ratio (SNR). As a result, an SNR of greater than 20 dB is obtained.

Selective multimode excitation using volume holographic mode multiplexer.

We propose a mode multiplexer based on volume holograms to realize a simple and efficient mode-division-multiplexed transmission system that supports a large number of modes. Selective multiexcitation of three spatial modes into a conventional multimode fiber is experimentally demonstrated. This device could potentially multiplex 10 or more modes. Future perspectives of the mode multiplexer for application in mode-division multiplexing are also discussed.

High-speed wavelength-division multiplexing quantum key distribution system.

A high-speed quantum key distribution system was developed with the wavelength-division multiplexing (WDM) technique and dedicated key distillation hardware engines. Two interferometers for encoding and decoding are shared over eight wavelengths to reduce the system's size, cost, and control complexity. The key distillation engines can process a huge amount of data from the WDM channels by using a 1 Mbit block in real time. We demonstrated a three-channel WDM system that simultaneously uses avalanche photodiodes and superconducting single-photon detectors. We achieved 12 h continuous key generation with a secure key rate of 208 kilobits per second through a 45 km field fiber with 14.5 dB loss.

Holographic diversity interferometry for optical storage.

This study proposes holographic diversity interferometry (HDI), a system that combines information from spatially dispersed plural image sensors to reconstruct complex amplitude distributions of light signals. HDI can be used to generate four holographic interference fringes having different phases, thus enabling optical phase detection in a single measurement. Unlike conventional phase-shifting digital holography, this system does not require piezoelectric elements and phase shift arrays. In order to confirm the effectiveness of HDI, we generated optical signals having multilevel phases and amplitudes by using two SLMs and performed an experiment for detection and demodulation with HDI.

Ultra fast quantum key distribution over a 97 km installed telecom fiber with wavelength division multiplexing clock synchronization.

We demonstrated ultra fast BB84 quantum key distribution (QKD) transmission at 625 MHz clock rate through a 97 km field-installed fiber using practical clock synchronization based on wavelength-division multiplexing (WDM). We succeeded in over-one-hour stable key generation at a high sifted key rate of 2.4 kbps and a low quantum bit error rate (QBER) of 2.9%. The asymptotic secure key rate was estimated to be 0.78- 0.82 kbps from the transmission data with the decoy method of average photon numbers 0, 0.15, and 0.4 photons/pulse.