High-dimensional entangled states are of significant interest in quantum science as they increase the information content per photon and can remain entangled in the presence of significant noise. The authors develop the analytical theory and show experimentally that the noise tolerance of high-dimensional entanglement can be significantly increased by a modest increase in the size of the Hilbert space. For example, doubling the size of a Hilbert space with a local dimension of d = 300 leads to a reduction in the threshold detector efficiencies required for entanglement certification by two orders of magnitude. This work is developed in the context of spatial entanglement in the few-photon limit, but it can easily be translated to photonic states entangled in different degrees of freedom. The authors also demonstrate that knowledge of a single parameter, the signal-to-noise ratio, precisely links measures of entanglement to a range of experimental parameters quantifying noise in a quantum communication system, enabling accurate predictions of its performance. This work serves to answer a simple question: “Is high-dimensional photonic entanglement robust to noise?” Here, the authors show that the answer is more nuanced than a simple “yes” or “no” and involves a complex interplay between the noise characteristics of the state, channel, and detection system.
High-dimensional entangled states are of significant interest in quantum science as they increase the information content per photon and can remain entangled in the presence of significant noise. The authors develop the analytical theory and show experimentally that the noise tolerance of high-dimensional entanglement can be significantly increased by a modest increase in the size of the Hilbert space. For example, doubling the size of a Hilbert space with a local dimension of d = 300 leads to a reduction in the threshold detector efficiencies required for entanglement certification by two orders of magnitude. This work is developed in the context of spatial entanglement in the few-photon limit, but it can easily be translated to photonic states entangled in different degrees of freedom. The authors also demonstrate that knowledge of a single parameter, the signal-to-noise ratio, precisely links measures of entanglement to a range of experimental parameters quantifying noise in a quantum communication system, enabling accurate predictions of its performance. This work serves to answer a simple question: “Is high-dimensional photonic entanglement robust to noise?” Here, the authors show that the answer is more nuanced than a simple “yes” or “no” and involves a complex interplay between the noise characteristics of the state, channel, and detection system.
Photons offer the potential to carry large amounts of information in their spectral, spatial, and polarisation degrees of freedom. While state-of-the-art classical communication systems routinely aim to maximize this information-carrying capacity via wavelength and spatial-mode division multiplexing, quantum systems based on multi-mode entanglement usually suffer from low state quality, long measurement times, and limited encoding capacity. At the same time, entanglement certification methods often rely on assumptions that compromise security. Here we show the certification of photonic high-dimensional entanglement in the transverse position-momentum degree-of-freedom with a record quality, measurement speed, and entanglement dimensionality, without making any assumptions about the state or channels. Using a tailored macro-pixel basis, precise spatial-mode measurements, and a modified entanglement witness, we demonstrate state fidelities of up to 94.4% in a 19-dimensional state-space, entanglement in up to 55 local dimensions, and an entanglement-of-formation of up to 4 ebits. Furthermore, our measurement times show an improvement of more than two orders of magnitude over previous state-of-the-art demonstrations. Our results pave the way for noise-robust quantum networks that saturate the information-carrying capacity of single photons.
The field of high-dimensional quantum photonics involves the use of multimode photonic degrees-of-freedom such as the spatial, temporal, or spectral structure of light to encode multi-level quantum states. Recent years have seen rapid progress in the development of methods to generate, manipulate, and distribute such quantum states of light and their use in a range of quantum technology applications that offer practical advantages over conventional qubit-based approaches. High-dimensional quantum states of light encoded in photonic time-bins, frequency-bins, transverse-spatial modes, waveguide paths, and temporal modes have enabled noise-robust fundamental tests of quantum mechanics, error-resilient and high-capacity quantum communication protocols, andas well as efficient approaches for quantum information processing, to name just a few examples. However, research in this field has progressed fairly independently, with little exchange across different photonic degrees-of-freedom or between experiment and theory and no comprehensive comparison between degrees-of-freedom. This roadmap aims to bridge this gap by surveying progress in each area and identifying shared challenges and opportunities that cut across two or more photonic degrees-of-freedoms. We review early work and state-of-the-art experimental techniques under development for high-dimensional quantum states encoded in single and entangled photons, as well as theoretical tools for their measurement and certification. We outline the main outstanding challenges for theory and each experimental degree-of-freedom, identifying promising future directions of research that may enable these to be overcome. We end by discussing interconnections and shared challenges centered around their distribution, measurement, and manipulation, with a view towards their integration into next-generation quantum technology platforms and applications.
Many quantum communication protocols rely on the distribution of entanglement between the different participating parties. One example is quantum key distribution (QKD), an application that has matured to commercial use in recent years. However, difficulties remain, especially with noise resilience and channel capacity in long-distance communication. One way to overcome these problems is to use high-dimensional entanglement, which has been shown to be more robust to noise and enables higher secret-key rates. It is therefore important to have access to certifiable high-dimensional entanglement sources to confidently implement these advanced QKD protocols. Here we develop a method for certifying high-dimensional time-bin entanglement in fiber-loop systems. In these systems, entanglement creation and detection can utilize the same physical components, and the number of time bins, and thus the entanglement dimension, can be adapted without making physical changes to the setup. Our certification method builds on previous proposals for the certification of angular-momentum entanglement in photon pairs. In particular, measurements in only two experimentally accessible bases are sufficient to obtain a lower bound on the entanglement dimension for both two- and multiphoton quantum states. Numerical simulations show that the method is robust against typical experimental noise effects and works well even with limited measurement statistics, thus establishing time-bin encoded photons as a promising platform for high-dimensional quantum-communication protocols.
High-dimensional photonic entanglement holds significant promise for advancing quantum communication, computation, and metrology. For example, large-alphabet quantum communication protocols are known to benefit from enhanced noise resilience and information capacity via multi-bit time-bin encoding. Yet, characterizing high-dimensional entangled states is challenging, as full state tomography becomes prohibitively costly and often requires unrealizable measurements. Here, we demonstrate a scan-free method to characterize high-dimensional entanglement in the time-frequency domain. Our reconstruction achieves a record 5.70±0.07 ebits and a fidelity of 65.4±0.4% with the maximally entangled state of local dimension 1021, certifying the presence of 668-dimensional entanglement. We further prove the attainability of a secure key rate of 15.6 kB/s in a composable finite-size, entanglement-based protocol, and show that in continuous operation, the setup can quickly approach asymptotic key rates. Using commercial telecom components and state-of-the-art low-jitter single-photon detectors, our scalable architecture offers a practical path towards high-rate, noise-resilient quantum communication testbeds.
Photonic entanglement is a fundamental resource in quantum information processing and its distribution between distant parties is a key challenge in quantum communications. Optical satellite links allow transmitting entangled photons over longer distances than currently possible on ground and could provide a path towards global quantum communication networks. The majority of current photonic free-space quantum communication systems, including two recent quantum satellite experiments, use two-dimensional polarization encoding, where each photon can carry at most a single bit of quantum information. Encoding additional qubits in the high-dimensional spatio-temporal degrees of freedom could not only increase channel capacities but also improve robustness with respect to noise and eavesdropping in quantum cryptography. Here, we give an overview of our efforts towards exploiting high-dimensional entanglement in long-distance free-space quantum communications. We report on the results of a first feasibility study, in which we used polarization / energy-time hyperentanglement to increase the dimensionality of the state space and transmit genuine 4-dimensional entanglement via an intra-city free-space link. We discuss how we intend to extend this approach to applications in noise-tolerant large-alphabet quantum key distribution via free-space links, and, ultimately, experiments with satellites.
Certifying quantum behavior from classically accessible data is essential for secure communication and scalable quantum technologies. While powerful certification methods such as Bell nonlocality and quantum steering exist, their implementation typically requires entanglement or additional assumptions, and experimental demonstrations mainly focus on low-dimensional systems. In minimal prepare-and-measure scenarios, where a sender encodes information into quantum states and a receiver performs a single measurement, robust certification becomes particularly challenging, especially in the presence of noise and in higher-dimensional Hilbert spaces. Here, we propose, design, and experimentally implement a protocol that certifies quantumness between two distant parties without the need for preshared resources or measurement incompatibility. The experiments are carried out using the orbital angular momentum degrees of freedom of single photons, chosen for providing increased dimensionality that is scalable. We demonstrate the robustness of the protocol through rank-stability analysis of the observed correlations, which enables the certification of non-classicality even in the presence of noise. Our results provide a practical route to validate high-dimensional quantum communication systems and open new possibilities for secure and dimension-efficient quantum information processing.