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

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

Published Jan 1, 2020• 1 citation
Publisher

Abstract

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.

DOI
10.1051/epjconf/202023811004

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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.
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.
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.
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.
We present a high-dimensional quantum key distribution protocol by using N-qudits quantum light states, that is, product states with N photons, each of them in a quantum superposition of dimension d which provides a high dimension dN and accordingly a very high security. We present the implementation of this protocol in different types of optical fibers where the mentioned states undergo perturbations under propagation in optical fibers; such perturbations can be notably reduced in a passive (autocompensation) or active way and importantly the N-qubits present a great robustness against such optical perturbations. Likewise, quantum states also undergo attenuation, that is, some photons are lost under propagation in the optical fibers and then effective N′ (< N)-qudits are obtained which also are used to generate secret keys. In fact, the detection of states combines standard projective measurements along with photon coincidences. Besides, we analyze the security of this high-dimensional protocol under an intercept and resend attack realized by Eve, and the resulting secure key rates are calculated showing a significative increasing with the dimension provided by the number N of photons.
We propose a high-dimensional quantum key distribution (QKD) protocol that employs temporal correlations of entangled photons. The security of the protocol relies on measurements by Alice and Bob in one of two conjugate bases, implemented using dispersive optics. We show that this dispersion-based approach is secure against collective attacks. The protocol, which represents a QKD analog of pulse position modulation, is compatible with standard fiber telecommunications channels and wavelength division multiplexers. We describe several physical implementations to enhance the transmission rate and describe a heralded qudit source that is easy to implement and enables secret-key generation at >4>4>4 bits per character of distilled key across over 200 km of fiber.
An improved DPS-QKD scheme is proposed and demonstrated in this paper. At Alice's site，we use a M-Z interferometer to produce two coherent pulses. At Bob's site，a Faraday-mirrors-based Michelson interferometer is used instead of a M-Z interferometer to auto-compensate for the phase drifts and polarization mode dispersions in the fiber. It enhances the security of the whole system to use the two quantum cryptography protocols (namely the two pulse DPS-QKD scheme associated with the BB84 scheme). It is shown in our experiment that such a system features perfect stability with a quantum bit error rate less than 5% and high key generation rate. This scheme has been implemented successfully during the 80km fiber transmission.