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arXiv:2009.13915 · Physical Review A

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

Jesús Liñares, Xesús Prieto-Blanco, Daniel Balado, Gabriel M. Carral

Published Apr 12, 2021• 10 citations
arXivHTMLPDF

Abstract

We present a communication system based on quantum degenerate four-wave mixing for achieving fully autocompensating high-dimensional quantum cryptography. We prove that random phase shifts and couplings (cross-talking) among $2N$ optical modes (spatial and polarization modes), represented by arbitrary $\mathrm{SU}(2N)$ transformations and due to mechanical and thermal perturbations, imperfections, and so on, are autocompensated after a single round trip between Alice and Bob. Bob uses a source of single photons or, alternatively, attenuated coherent states and thus autocompensated 1-qudit states are received by Bob for using them with high-dimensional quantum key distribution (QKD) protocols that provide larger secret key rates for large $N$. A security study is also presented for this autocompensating quantum cryptography system, where it is found that the secure key rate increases with respect to nonautocompensated links for decoy-state QKD in the case of collective attacks. This plug-and-play system can be used in both optical fiber and free-space communication systems.

DOI
10.1103/physreva.103.043710

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We present a communication system based on quantum degenerate four-wave mixing for achieving fully autocompensating high-dimensional quantum cryptography. We prove that random phase shifts and couplings (cross-talking) among 2N2N2N optical modes (spatial and polarization modes), represented by arbitrary SU(2N)\mathrm{SU}(2N)SU(2N) transformations and due to mechanical and thermal perturbations, imperfections, and so on, are autocompensated after a single round trip between Alice and Bob. Bob uses a source of single photons or, alternatively, attenuated coherent states and thus autocompensated 1-qudit states are received by Bob for using them with high-dimensional quantum key distribution (QKD) protocols that provide larger secret key rates for large NNN. A security study is also presented for this autocompensating quantum cryptography system, where it is found that the secure key rate increases with respect to nonautocompensated links for decoy-state QKD in the case of collective attacks. This plug-and-play system can be used in both optical fiber and free-space communication systems.
Quantum cryptographic key distribution (QKD) uses extremely faint light pulses to carry quantum information between two parties (Alice and Bob), allowing them to generate a shared, secret cryptographic key. Autocompensating QKD systems automatically and passively compensate for uncontrolled time-dependent variations of the optical fibre properties by coding the information as a differential phase between orthogonally polarized components of a light pulse sent on a round trip through the fibre, reflected at mid-course using a Faraday mirror. We have built a prototype system based on standard telecom technology that achieves a privacy-amplified bit generation rate of ~1000 bits s -1 over a 10 km optical fibre link. Quantum cryptography is an example of an application that, by using quantum states of individual particles to represent information, accomplishes a practical task that is impossible using classical means.
High-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.
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.
Summary form only given. Quantum cryptography, or quantum key distribution (QKD), invented by Bennett and Brassard is a method for creating shared, assuredly secret, cryptographic key data over unsecured optical links. Security is guaranteed by the fundamental quantum properties of light. We describe our system in great detail, and report recent improvements and results obtained in generating error-corrected, privacy-amplified photographic key data over a 10-km single-mode fiber link. Bob transmits two orthogonally-polarized phase coherent pulses.
Abstract Single photon or biphoton states propagating in optical fibers or in free space are affected by random perturbations and imperfections that disturb the information encoded in such states and accordingly quantum key distribution is prevented. We propose three different systems for autocompensating such random perturbations and imperfections when a measurement-device-independent protocol is used. These systems correspond to different optical fibers intended for space division multiplexing and supporting collinear modes, polarization modes or codirectional modes such as few-mode optical fibers and multicore optical fibers. Accordingly, we propose different Bell-states measurement devices located at Charlie system and present simulations that confirm the importance of autocompensation. Moreover, these types of optical fibers allow the use of several transmission channels, which compensates the reduction of the bit rate due to losses.