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Optics Express

BB84 protocol using rotationally symmetric states and a Fresnel cone

Katherine Stevens, Amy McWilliam, Rair Macêdo, Sonja Franke‐Arnold

Published Jun 11, 2026• 0 citations
Publisher

Abstract

BB84 is one of the most prominent protocols for quantum key distribution (QKD), and the prototype for all protocols relying on Heisenberg's uncertainty relation to provide security. Photon polarization remains a chosen degree of freedom to implement QKD protocols, as its weak interaction with the environment creates stability during propagation. Generally, polarization-based QKD implementation requires a shared coordinate reference frame between the sender and receiver to maintain the assignment of the mutually unbiased bases. While this is easily realized for stationary systems, it proves challenging for handheld and satellite-to-satellite communication. The use of rotationally symmetric states, including some classes of vector beams, has been proposed to remove the need for a shared reference frame; however, most of these systems are wavelength dependent, thereby limiting available bandwidth. Here, we demonstrate a classical, proof-of-principle BB84 protocol using rotationally symmetric vector beams as the mutually unbiased basis, and a measurement system employing a Fresnel cone. Our results demonstrate that it can yield an error rate of 1.1%. This system is reference frame invariant and can be implemented in a wavelength-independent manner. We expect our technique to be suitable for implementing QKD in scenarios where the sender and receiver's coordinate systems rotate with respect to each other, such as with satellite or handheld communication, while still maintaining large bandwidth capabilities.

DOI
10.1364/oe.585793

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BB84 is one of the most prominent protocols for quantum key distribution (QKD), and the prototype for all protocols relying on Heisenberg's uncertainty relation to provide security. Photon polarization remains a chosen degree of freedom to implement QKD protocols, as its weak interaction with the environment creates stability during propagation. Generally, polarization-based QKD implementation requires a shared coordinate reference frame between the sender and receiver to maintain the assignment of the mutually unbiased bases. While this is easily realized for stationary systems, it proves challenging for handheld and satellite-to-satellite communication. The use of rotationally symmetric states, including some classes of vector beams, has been proposed to remove the need for a shared reference frame; however, most of these systems are wavelength dependent, thereby limiting available bandwidth. Here, we demonstrate a classical, proof-of-principle BB84 protocol using rotationally symmetric vector beams as the mutually unbiased basis, and a measurement system employing a Fresnel cone. Our results demonstrate that it can yield an error rate of 1.1%. This system is reference frame invariant and can be implemented in a wavelength-independent manner. We expect our technique to be suitable for implementing QKD in scenarios where the sender and receiver's coordinate systems rotate with respect to each other, such as with satellite or handheld communication, while still maintaining large bandwidth capabilities.
Quantum Key Distribution (QKD) is a cutting-edge field that leverages the principles of quantum mechanics to enable secure communication between parties involved. Single-photon quantum emitters offer remarkable on-demand photon emission, near-unitary indistinguishability, and low multiphoton generation, thereby enhancing the performance of QKD protocols. Standard approaches in which the polarization degree-of-freedom is exploited are limited by the precise alignment between the communicating parties. To overcome this obstacle, the Orbital Angular Momentum (OAM) of light represents a suitable candidate for encoding the information, as it allows the implementation of rotational-invariant photonic states that remove the need for a fixed physical reference frame between the communicating parties. Here, we demonstrate an alignment-free BB84 implementation using on-demand single photons from a quantum-dot emitter at 925 nm. Time-to-spatial demultiplexing and Q -plates encode rotationally invariant spin–orbit states that we transmit over a 2 m free-space link while rotating the receiver between 0 ∘ and 90 ∘ . The source exhibits g (2) (0)≈0.03; the measured QBER remains (4.04±0.02)% and is essentially independent of the relative angle. A simple security model tailored to sub-Poissonian emission, which explicitly incorporates g (2) (0), yields a positive asymptotic secret fraction and an effective QBER threshold of ∼9.6% under our conditions. These results validate rotationally invariant QKD with an on-demand single-photon source and outline its scalability to long-distance scenarios.
Quantum key distribution (QKD) can generate secure key bits between remote users employing the features of quantum physics. However, a shared reference frame is necessary for QKD systems in most scenarios. A reference-frame-independent (RFI) scheme can tolerate the reference frame drifting between legitimate remote users, which is significant in the operation of relative moving terminals such as satellites and aircraft. We design and experimentally demonstrate an RFI-BB84-QKD system by joint encoding with the polarization and orbital angular momentum states of the photons. We use self-compensating fiber Sagnac interferometers to perform high-speed polarization modulation, and q-plates to passively manipulate the rotation-invariant photon states, which makes the system feasible for high-speed operation using off-the-shelf components.
Quantum key distribution (QKD) is a secure key-transmitting method based on quantum mechanics to deliver private keys for encryption. Satellite QKD is a promising technique that overcomes the limited transmission distance in optical-fibre-based systems. To enable polarisation encoded QKD, polarisation reference-frame mismatches between the satellite and a receiving optical ground station (OGS) have to be compensated. We developed and implemented a compensation method for a BB84 protocol designed QKD receiver by an additional set of three waveplates (HWP, QWP, QWP). In simulations and laboratory demonstrations, we show the robustness under conditions that we expect on our future satellite downlink mission. As a result, we expect good compensation quality for a wide range of signal to noise ratios and satellite rotation frequencies by requiring only a few signal photons of 2000 of two non-orthogonal polarisation states, respectively, to measure the reference-frame mismatch used for one compensation sequence.
Quantum Key Distribution (QKD) provides a secure way of generating shared cryptographic keys between a sender (Alice) and a receiver (Bob). The original BB84 protocol uses a two-dimensional polarization basis, limiting the information content of a single photon to 1 bit. Using the transverse position of single photons as one basis and the Fourier space as a second basis, one can construct a pair of mutually unbiased higher-dimensional bases. This improves not only the security of the protocol, but also the key generation rate. We present experimental results with a Spatial-Light-Modulator-based encoding scheme employing two nearly orthogonal alphabets with on the order of 103symbols each and an information content of about 10 bit.
Polarization-entangled photon-based quantum key distribution (QKD) has seen notable advancements, requiring users to share a common frame of reference that might lead to a significant technical overhead of constant monitoring of their frame of reference. In this work, we characterize and demonstrate hybrid entangled photon pairs for their utilization in rotational alignment-free QKD applications. By employing vortex half-wave retarders that have an azimuthally varying fast axis with a topological charge of q=12, we generate high brightness rotationally invariant hybrid entangled photons and show their resilience against the misalignment of the frame of reference. We demonstrate high fidelity (>92%) entanglement and depict a low quantum bit error rate (QBER) of ∼5−6% (lower than the threshold value of 11%) at a significantly high angle of misalignment θ>45°), in contrast to the polarization-entangled photon pairs that suffer from the degradation of entanglement quality due to a rotational misalignment between the reference frame of communicating entities. The rotationally invariant hybrid photon pairs with robust entanglement properties offer a significant advantage for secure and reliable quantum communication, making them lucrative candidates for applications such as satellite-to-satellite and ground-to-satellite QKD networks. We also show the reliability and stability of the entangled photon source over a long period (measured over 6 h) by demonstrating the BBM92 protocol with a raw key rate of ∼2.8 kbps and a QBER of ∼5% in a single-pass configuration. The performance metrics of our quantum source, measured with conventional avalanche photodiodes (SPADs, quantum efficiency ∼60%, dark counts ∼40 cps), are among the best values reported so far with these detectors.
We study a reference frame independent (RFI) quantum key distribution (QKD) protocol using six states for Alice and only four states for Bob, while previous RFI protocols require a six state analyzer for Bob. Our protocol can generate a secure key for any possible phase of the entangled state provided the variation is small compared to the measurement rate, as shown by our numerical key rate analysis. We perform a proof-of-principle experiment using polarization entangled photon pairs. In the presence of a varying rotational phase, we obtain a consistently low error rate of less than 4%, indicating the feasibility of this protocol for QKD. Our RFI protocol is hence beneficial but not limited to applications in a satellite or mobile free-space QKD, where a communication node must limit the resources and restrict the number of measured states to four instead of six.