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.

Figure 1

Concept of transmission of high-dimensional quantum states in RCF.

Figure 2

Principle of state preparation. The Poincaré sphere presents the transformation of the states.

Figure 3

Experimental setup of high-order quantum cryptography in a RCF. (a) Measurement setup using a SLM for 4 km fiber transmission. Laser wavelength $1550$ nm. (b) Measurement setup using a $q$ plate for 4 and 25 km fiber transmission. IM, intensity modulator; M, mirror; PC, polarization controller; Pol., polarizer; QP, $q$ plate; QWP, quarter-wave plate; SMF, single-mode fiber; SPD, single-photon detector; VOA, variable optical attenuator.

Figure 4

Fiber information. (a) RCF refractive index versus radius. (b) Simulated OAM eigenmodes of the fiber and effective refractive index.

Figure 5

Mode fields of MUBs. (a) MUBs prepared by a $q$ plate with $q=1/2$. (b) MUBs prepared by a $q$ plate with $q=1$. The arrows represent the polarization orientation.

Figure 6

Measured intensity distributions of modes after the fiber. (a) MUBs prepared by a $q$ plate with $q=1/2$. (b) MUBs prepared by a $q$ plate with $q=1$.

Figure 7

Experimental probability-of-detection matrices. (a) Annotated heat map of the probability-of-detection matrix for $\ell =|1|$ with measured QBER of $Q=4.3\mathrm{\%}$. (b) Annotated heat map of the probability-of-detection matrix for $\ell =|2|$ with measured QBER of $Q=6.5\mathrm{\%}$.

Figure 8

Experimental probability-of-detection matrices from the $q$-plate setup for (a) $\ell =|1|$ with 4 km of RCF, (b) $\ell =|2|$ with a 4 km of , and (c) $\ell =|2|$ with 25 km of RCF.