High-dimensional Quantum Cryptography Research Articles

Orbital Angular Momentum in Fibers

Orbital angular momentum (OAM) of light beams with helical phase front, as an alternative spatial dimension resource of photons, has attracted extensive attention over the past decades. Very recently, OAM in fibers has facilitated rapid development of various fiber-based applications, such as optical communications, optical manipulation, optical sensing, optical imaging, nonlinear optics, and quantum science. Comprehensive and in-depth understanding of OAM in fibers is of great interest to researchers in this area. Here, we give a tutorial overview of OAM in fibers. We first introduce the basic theories, including the eigenmode analysis method, mode coupling theory, and spin-orbit mapping of light in fibers. We then give a detailed classification of OAM fibers and discuss versatile spatial mode bases in fibers. After that, we review various OAM fiber designs, including conventional single-mode fibers, conventional multi-mode fibers, ring-core fibers, air-core fibers, photonic crystal fibers, negative-curvature hollow-core fibers, multi-core fibers, active fibers (e.g., erbium-doped fibers), etc. Besides, we describe the state-of-the-art commercial fiber manufacturing processes as well as testing and characterization methods for OAM fibers. We also review various active and passive OAM fiber devices. Moreover, we introduce several typical advanced applications based on OAM fibers, such as capacity scaling fiber-optic communications, remote vectorial Doppler velocimetry, super-resolution optical imaging, and high-dimensional quantum cryptography. Finally, we briefly discuss future challenges and prospects of OAM in fibers.

Quantum Sampling for Finite Key Rates in High Dimensional Quantum Cryptography

It has been shown recently that the framework of quantum sampling, as introduced by Bouman and Fehr, can lead to new entropic uncertainty relations highly applicable to finite-key cryptographic analyses. Here we revisit these so-called sampling-based entropic uncertainty relations, deriving newer, more powerful, relations and applying them to source-independent quantum random number generators and high-dimensional quantum key distribution protocols. Along the way, we prove several interesting results in the asymptotic case for our entropic uncertainty relations. These sampling-based approaches to entropic uncertainty, and their application to quantum cryptography, hold great potential for deriving proofs of security for quantum cryptographic systems, and the approaches we use here may be applicable to an even wider range of scenarios.

High-Dimensional Quantum Cryptography with Hybrid Orbital-Angular-Momentum States through 25 km of Ring-Core Fiber: A Proof-of-Concept Demonstration

Quantum cryptography provides the inherent security for transmitting confidential information across free space or a fiber link. However, a high secure-key rate is still a challenge for a quantum-cryptography system. High-dimensional quantum cryptography, which can tolerate much higher channel noise, is a prospective way to share a higher secure-key rate between legitimate users, and has received substantial attention over the last decade. In particular, orbital angular momentum (OAM) can provide an abundant resource for high-dimensional quantum cryptography. Furthermore, combining spin angular momentum (SAM) with OAM can increase the encoding alphabet. Here we verify a prepare-and-measure quantum-cryptography scheme based on four-dimensional SAM-OAM hybrid states over kilometer-scale ring-core fibers. The measured quantum-bit error rates are $4.3\mathrm{%}$ for 4 km of fiber and $16.3\mathrm{%}$ for 25 km of fiber. The scheme simplifies the process of state preparation and measurement, with a compact and scalable setup.

Fully autocompensating high-dimensional quantum cryptography by quantum degenerate four-wave mixing

We present a bidirectional quantum communication system based on optical phase conjugation for achieving fully autocompensating high-dimensional quantum cryptography. We prove that random phase shifts and couplings among 2N spatial and polarization optical modes described by SU(2N) transformations due to perturbations are autocompensated after a single round trip between Alice and Bob. Bob can use a source of single photons or, alternatively, coherent states and then Alice attenuates them up to a single photon level, and thus non-perturbated 1-qudit states are generated for high-dimensional QKD protocols, as the BB84 one, of a higher security.

Full-field mode sorter using two optimized phase transformations for high-dimensional quantum cryptography

High-dimensional encoding schemes have emerged as a novel way to perform quantum information tasks. For high dimensionality, temporal and transverse spatial modes of photons are the two paradigmatic degrees of freedom commonly used in such experiments. Nevertheless, general devices for multi-outcome measurements are still needed to take full advantage of the high-dimensional nature of encoding schemes. We propose a general full-field mode sorting scheme consisting of only up to two optimized phase elements based on evolutionary algorithms that allows for joint sorting of azimuthal and radial modes. We further study the performance of our scheme through simulations in the context of high-dimensional quantum cryptography, where sorting in different mutually unbiased bases and high-fidelity measurement schemes are crucial.

Autocompensating high-dimensional quantum cryptography by phase conjugation in optical fibers

We present a system based on phase conjugation in optical fibers for autocompensating highdimensional quantum cryptohraphy. Phase changes and coupling effects are auto-compensated by a single loop between Alice and Bob. Bob uses a source of coherent states and next Alice attenuate them up to a single photon level and thus 1-qudit states are generated for implementing a particular QKD protocol, for instance the BB84 one, together with decoy states to detect eavesdropping attacks.

Phase and polarization autocompensating N-dimensional quantum cryptography in multicore optical fibers

Space division multiplexing based on multicore fibers (MCFs) is an optimum candidate to further increase the data bandwidth in optical communications, and its interest for spatial high-dimensional quantum cryptography has increased in the last few years. However, the main shortcoming lies in the appearance of phases and polarization acquired independently in each spatial mode after a long propagation, which prevents implementing efficient quantum key distribution (QKD) protocols with spatial optical modes. In this work, we propose a method for achieving phase, polarization, and time delay autocompensating for N-dimensional QKD in MCFs by using strong coherent states coming from the Bob system. These coherent states make N trips between Alice and Bob and undergo N suitable optical transformations before Alice attenuates such states for producing 1-qudit states. Likewise, passive random-projective-measurement integrated devices are presented as well, in order to measure 1-qudit states. Finally, we analyze the behavior of the system under a cryptoghraphic attack, such as, e.g., the phase-remapping attack, in order to assess the strength of our system.

Holographic Silicon Metasurfaces for Total Angular Momentum Demultiplexing Applications in Telecom

The simultaneous processing of orbital angular momentum (OAM) and polarization has recently acquired particular importance and interest in a wide range of fields ranging from telecommunications to high-dimensional quantum cryptography. Due to their inherently polarization-sensitive optical behavior, Pancharatnam–Berry optical elements (PBOEs), acting on the geometric phase, have proven to be useful for the manipulation of complex light beams with orthogonal polarization states using a single optical element. In this work, different PBOEs have been computed, realized, and optically analyzed for the sorting of beams with orthogonal OAM and polarization states at the telecom wavelength of 1310 nm. The geometric-phase control is obtained by inducing a spatially-dependent form birefringence on a silicon substrate, patterned with properly-oriented subwavelength gratings. The digital grating structure is generated with high-resolution electron beam lithography on a resist mask and transferred to the silicon substrate using inductively coupled plasma-reactive ion etching. The optical characterization of the fabricated samples confirms the expected capability to detect circularly-polarized optical vortices with different handedness and orbital angular momentum.

Total angular momentum sorting in the telecom infrared with silicon Pancharatnam-Berry transformation optics.

Parallel sorting of orbital angular momentum (OAM) and polarization has recently acquired paramount importance and interest in a wide range of fields ranging from telecommunications to high-dimensional quantum cryptography. Due to their inherently polarization-sensitive optical response, optical elements acting on the geometric phase prove to be useful for processing structured light beams with orthogonal polarization states by means of a single optical platform. In this work, we present the design, fabrication and test of a Pancharatnam-Berry optical element in silicon implementing a log-pol optical transformation at 1310 nm for the realization of an OAM sorter based on the conformal mapping between angular and linear momentum states. The metasurface is realized in the form of continuously variant subwavelength gratings, providing high-resolution in the definition of the phase pattern. A hybrid device is fabricated assembling the metasurface for the geometric-phase control with multi-level diffractive optics for the polarization-independent manipulation of the dynamic phase. The optical characterization confirms the capability to sort orbital angular momentum and circular polarization at the same time.

Phase auto-compensating high-dimensional quantum cryptography in elliptical-core few-mode fibres

ABSTRACTHigh-dimensional quantum cryptography through optical fibres with several spatial modes requires an efficient quantum key distribution (QKD). However, optical modes acquire different phases and lags due to modal dispersion and random fluctuations, and a modal crosstalk appears under propagation. At present, special optical fibres for spatial multiplexing are being proposed in order to reduce notably the modal crosstalk, however, arbitrary relative phases and lags between modes are always present, which prevents getting an efficient phase encoding QKD. In this work, we take advantage of elliptical-core few-mode optical fibres presenting a very low modal crosstalk and propose an exact phase auto-compensating method by making photons travel several times the path between Alice and Bob (rounds) and by using appropriate modal inversions in each round trip. In order to make clear the proposed phase auto-compensating method, we study in detail a four-dimensional BB84 QKD case with single photon states excited in both polarization and spatial LP modes.

Generalized optical angular momentum sorter and its application to high-dimensional quantum cryptography.

The orbital angular momentum (OAM) carried by optical beams is a useful quantity for encoding information. This form of encoding has been incorporated into various works ranging from telecommunications to quantum cryptography, most of which require methods that can rapidly process the OAM content of a beam. Among current state-of-the-art schemes that can readily acquire this information are so-called OAM sorters, which consist of devices that spatially separate the OAM components of a beam. Such devices have found numerous applications in optical communications, a field that is in constant demand for additional degrees of freedom, such as polarization and wavelength, into which information can also be encoded. Here, we report the implementation of a device capable of sorting a beam based on its OAM and polarization content, which could be of use in works employing both of these degrees of freedom as information channels. After characterizing our fabricated device, we demonstrate how it can be used for quantum communications via a quantum key distribution protocol.

High-dimensional quantum cloning and applications to quantum hacking.

Attempts at cloning a quantum system result in the introduction of imperfections in the state of the copies. This is a consequence of the no-cloning theorem, which is a fundamental law of quantum physics and the backbone of security for quantum communications. Although perfect copies are prohibited, a quantum state may be copied with maximal accuracy via various optimal cloning schemes. Optimal quantum cloning, which lies at the border of the physical limit imposed by the no-signaling theorem and the Heisenberg uncertainty principle, has been experimentally realized for low-dimensional photonic states. However, an increase in the dimensionality of quantum systems is greatly beneficial to quantum computation and communication protocols. Nonetheless, no experimental demonstration of optimal cloning machines has hitherto been shown for high-dimensional quantum systems. We perform optimal cloning of high-dimensional photonic states by means of the symmetrization method. We show the universality of our technique by conducting cloning of numerous arbitrary input states and fully characterize our cloning machine by performing quantum state tomography on cloned photons. In addition, a cloning attack on a Bennett and Brassard (BB84) quantum key distribution protocol is experimentally demonstrated to reveal the robustness of high-dimensional states in quantum cryptography.

High-dimensional quantum cryptography with twisted light

Quantum key distribution (QKD) systems often rely on polarization of light for encoding, thus limiting the amount of information that can be sent per photon and placing tight bounds on the error rates that such a system can tolerate. Here we describe a proof-of-principle experiment that indicates the feasibility of high-dimensional QKD based on the transverse structure of the light field allowing for the transfer of more than 1 bit per photon. Our implementation uses the orbital angular momentum (OAM) of photons and the corresponding mutually unbiased basis of angular position (ANG). Our experiment uses a digital micro-mirror device for the rapid generation of OAM and ANG modes at 4 kHz, and a mode sorter capable of sorting single photons based on their OAM and ANG content with a separation efficiency of 93%. Through the use of a seven-dimensional alphabet encoded in the OAM and ANG bases, we achieve a channel capacity of 2.05 bits per sifted photon. Our experiment demonstrates that, in addition to having an increased information capacity, multilevel QKD systems based on spatial-mode encoding can be more resilient against intercept-resend eavesdropping attacks.