Sukhjit P. Singh, Elnaz Bazzazi, Diego N. Bernal-García, Simon White, Hassan Jamal Latief, Alison Goldingay, Sven Rogge, Sergei Slussarenko, Farzad Ghafari, Emanuele Polino, Nora Tischler
quant-phSubmitted Dec 9, 2025• Announced Dec 10, 2025• 0 citations• Revised Jul 30, 2026 (v2)
Entangled states of photons form the foundation of quantum communication, computation, and metrology. Yet their generation remains fundamentally constrained: in the absence of intrinsic photon-photon interactions, the generation of such states is inherently probabilistic rather than deterministic. The prevalent technique of post-selection verifies the creation of an entangled state by detecting and thus destroying it. Heralding offers a solution in which measuring ancillary photons in auxiliary modes signals the state generation without the need to measure it. Here, we introduce and experimentally demonstrate a scheme to generate a three-mode two-photon NOON state, where the detection of a single photon in one heralding mode signifies the presence of the state in three target modes. We validate the generated state by estimating a fidelity of 0.823 +/- 0.018 with respect to an ideal three-mode NOON state and certifying genuine multipartite entanglement. By virtue of the high success probability and small resource overhead of our scheme, our work provides a theoretical and experimental stepping stone for entangled multi-mode state generation, which is realizable with current technology. These multi-mode entangled states represent a key direction for linear optical quantum information that is complementary to multi-qubit state encoding.
Entangled states of photons form the foundation of quantum communication, computation, and metrology. Yet their generation remains fundamentally constrained: in the absence of intrinsic photon-photon interactions, the generation of such states is inherently probabilistic rather than deterministic. The prevalent technique of post-selection verifies the creation of an entangled state by detecting and thus destroying it. Heralding offers a solution in which measuring ancillary photons in auxiliary modes signals the state generation without the need to measure it. Here, we introduce and experimentally demonstrate a scheme to generate a three-mode two-photon NOON state, where the detection of a single photon in one heralding mode signifies the presence of the state in three target modes. We validate the generated state by estimating a fidelity of 0.823 +/- 0.018 with respect to an ideal three-mode NOON state and certifying genuine multipartite entanglement. By virtue of the high success probability and small resource overhead of our scheme, our work provides a theoretical and experimental stepping stone for entangled multi-mode state generation, which is realizable with current technology. These multi-mode entangled states represent a key direction for linear optical quantum information that is complementary to multi-qubit state encoding.
We present the first experimental realisation of a heralded three-mode, two-photon NOON state—an essential ingredient for quantum metrology, quantum communication, and distributed quantum information protocols. Our approach is based on a linear-optical architecture that uses only three single-photon inputs interfaced with a four-mode interferometer, yet can theoretically reach a success probability of 25%. A heralding photon unambiguously signals the preparation of the desired state, thereby bypassing the major scalability bottlenecks inherent to conventional post-selection methods. The produced state exhibits a fidelity exceeding 80%, confirming genuine tripartite entanglement. Both the protocol and its experimental implementation constitute a substantial step forward for the fields of quantum optics and quantum information science.
Entangled states of photons form the backbone of many quantum technologies. Due to the lack of effective photon-photon interactions, the generation of these states is typically probabilistic. In the prevailing but fundamentally limited generation technique, known as postselection, the target photons are measured destructively in the generation process. By contrast, in the alternative approach-heralded state generation-the successful creation of a desired state is verified by the detection of ancillary photons. Heralded state generation is superior to postselection in several critical ways: it enables free usage of the prepared states, allows for the success probability to be arbitrarily increased via multiplexing, and provides a scalable route to quantum information processing using photons. Here, we review theoretical proposals and experimental realisations of heralded entangled photonic state generation, as well as the impact of realistic experimental errors. We then discuss the wide-ranging applications of these states for quantum technologies, including resource states in linear optical quantum computing, entanglement swapping for repeater networks, fundamental physics, and quantum metrology.
Large-scale quantum networking systems will inevitably require methods to overcome photon loss. While the no-cloning theorem forbids perfect and deterministic amplification of unknown quantum states, probabilistic heralded amplification schemes offer a viable path forward. Yet, for over a decade, successful multi-photon state amplification has remained out of reach, despite the fundamental importance of such states in achieving quantum advantage in optical applications. Here, we experimentally demonstrate a high-fidelity and post-selection-free amplifier for multi-photon states. We achieve heralded amplification of states with up to two photons in a single optical mode, with over a hundredfold intensity gain, and verify the coherence-preserving operation of our scheme. Our approach is scalable to higher photon numbers and enables noiseless amplification of complex multi-photon quantum states, with applications in large-scale quantum communication systems, distributed quantum metrology, and information processing.
We propose a heralded entanglement generation scheme based on Gaussian sources enhanced by photon addition and subtraction operations. By combining single-mode squeezing, linear interferometers, and conditional photon-number measurements on ancillary modes, our model can probabilistically generate dual-rail encoded Bell, GHZ, and W states. We systematically optimize the squeezing parameters and interferometer settings to maximize both the heralding success probability and the fidelity with the target states. Our results show that photon addition and subtraction significantly enhance the non-classicality of the output states and improve generation performance, while maintaining computational efficiency comparable to single-photon source models. We further analyze the robustness of the scheme under parameter perturbations and find that its performance remains stable under realistic experimental imperfections. This work provides a versatile and experimentally feasible framework for scalable heralded entanglement generation using Gaussian resources with non-Gaussian operations.
Generation of highly non-classical quantum states of light is essential for optical quantum information processing and quantum metrology. Given the lack of sufficiently strong nonlinear interactions between optical fields, the commonly employed optical quantum-state preparation schemes are conditional, based on nonlinearity induced by heralding photon number measurement on a part of a multimode squeezed Gaussian state. Development and optimization of such probabilistic quantum-state engineering schemes represents one of the central challenges in current quantum optics. As technology advances and experiments progress to detection of higher numbers of photons, the maximization of the heralding probability becomes essential to ensure sufficiently high state-preparation rates. Here, we show that for the conditional quantum state preparation schemes based on Gaussian states and photon number measurements the maximization of the heralding probability can be formulated as finding solution to a system of polynomial equations, which offers an efficient way to find the optimal configuration and allows us to apply techniques dedicated specifically to solving such systems of equations. Our approach can seamlessly incorporate bounds on the available single-mode quadrature squeezing, which is highly experimentally relevant. We mainly consider generation of finite superpositions of Fock states but show that the approach can be straightforwardly extended to generation of squeezed superpositions of Fock states. We focus on Gaussian states with vanishing coherent displacements, hence the conditionally generated states have well defined photon number parity. We illustrate our general methodology through examples of generation of single-mode states with two and three heralding modes, and generation of two-mode states with two heralding modes.
We investigated the heralded generation of two-qubit dual-rail-encoded states by programmable linear optics. Two types of scheme generating the states from four single photons, which is the minimum possible to accomplish the task, were considered. The schemes have different detection patterns heralding successful generation events; namely, one-mode heralding, in which the two auxiliary photons are detected in one mode, and two-mode heralding, in which single photons are detected in each of the two modes simultaneously. We show that the dependencies of the schemes' success probabilities on the target state's degree of entanglement are essentially different. In particular, one-mode heralding yields greater efficiency for highly entangled states if the programmable interferometers can explore the full space of the unitary transfer matrices. The reverse is the case for weakly entangled states, where two-mode heralding is better. We found a minimal decomposition of the scheme with two-mode heralding that is programmed by one variable phase shift. We infer that the linear optical schemes designed specifically for the generation of two-qubit states are more efficient than schemes implementing known linear optical gate--based circuits. Our results reveal a substantial reduction of physical resources needed to generate some types of nonmaximally entangled multiqubit states used in quantum computing.