Challenges
Datasets
Workspaces
Papers
Discussions
Leaderboard
Log inSign up
Challenges
Datasets
Workspaces
Papers
Discussions
Leaderboard
Blog
Job Board
Q3AS

© 2026 Aqora Quantum S.A.S.

TermsPrivacyLegal Notice

arXiv:2610.17300

Ghost unitaries for loss-resilient photonic resource-state generation

Kevin J. Randles, Manuel H. Muñoz-Arias, Kevin Thompson

quant-phphysics.opticsSubmitted Oct 12, 2026• Announced Oct 14, 2026• 0 citations
arXivHTMLPDF

Abstract

Entangled few-photon states, such as Bell and Greenberger-Horne-Zeilinger (GHZ) states, are central resources for discrete-variable photonic quantum information processing. In many architectures, these states are generated probabilistically by first heralding single photons from biphoton sources and then interfering them in linear-optical circuits. In this work, we show that the entanglement structure of said biphoton sources can be directly exploited for noise-engineering to deliver higher quality resource states. Using the transpose identity of multi-mode squeezed vacuum states, we introduce "ghost-unitary" implementations in which the target resource-generation interferometer is applied to the heralding modes rather than to the delivered resource modes. When the dominant imperfection is interferometric loss, this relocation converts direct amplitude damping of the output into false-positive heralding events that require both higher-pair emission and photon loss. In the low-squeezing regime, these events are parametrically suppressed, yielding higher-fidelity conditional resource states. We analyze this mechanism for single-qubit states, two-photon NOON states, Bell states, and a family of $n$-qubit GHZ states, as well as for single-qubit teleportation and type-I-fusion-based resource growth. Across these examples, we delineate finite parameter regimes in which ghost-unitary implementations outperform direct implementations, with particular relevance to frequency-bin photonics where active linear-optical transformations can be relatively lossy. We also prove that, in the setting considered here, the direct implementation of the $n$-GHZ family delivers identically damped outputs: equivalent to the ideal state followed by uniform amplitude damping. This extends the known $n=2,3$ cases and provides a structural result of independent interest for photonic quantum information processing.

Comments
17 + 27 pages, 9 + 4 figures, comments welcome

Related papers

Limits of heralded photonic Bell-state generation in the presence of loss

Kevin J. Randles, Manuel H. Muñoz-Arias, Mohan Sarovar

High-quality entangled states of photons underlie quantum information science (QIS) applications across communication, sensing, and computing. In many discrete-variable photonic QIS architectures, large application-ready states (e.g., cluster states, repeater graph states) are constructed via fusion measurements on small entangled seed states, of which Bell states are the fundamental example. The quality of seed-state generation therefore sets a baseline for application performance, making it crucial to understand this process under realistic error mechanisms, particularly in integrated photonics experiments. In this work, we analyze five heralded schemes for generating event-ready photonic Bell states, contrasting their heralding probabilities, fidelities, and error robustness. We develop a hierarchy of error models, progressing from an analytically tractable lumped-loss model to realistic heralded single-photon sources with multiphoton emission errors and finally to integrated frequency-bin implementations with architecture-dependent loss. Across these models, we find that schemes based on higher-order multiphoton interference provide superior fidelity robustness in low-loss implementations, while lower-photon-number schemes can be preferable when probabilistic sources or lossy beamsplitters dominate the resource cost. Our results provide design guidance for integrated discrete-variable quantum photonics, with particular relevance for frequency-bin architectures where active beamsplitter loss can determine the optimal resource-state-generation strategy.

quant-pharXiv:2608.01549•Aug 4, 2026•0 citations

Heralding Higher-Dimensional Bell and Greenberger–Horne–Zeilinger states using multiport splitters

Daniel Bhatti, Stefanie Barz

Abstract One of the most important resources for quantum optical experiments and applications are on-demand highly entangled multiphoton quantum states. A promising way of generating them is heralding entanglement generation at a high rate from letting independent photons interfere. However, such schemes often work for a specific internal degree of freedom of the interfering photons only. Going to higher numbers of entangled photons, the success probabilities decrease while the number of necessary resources, e.g. auxiliary photons and optical elements, increases. To make probabilistic schemes feasible also for larger quantum states, it is therefore important to find resource-efficient generation schemes with high success probabilities. In this work, we introduce easily implementable schemes to herald qubit Greenberger–Horne–Zeilinger (GHZ) states, higher-dimensional Bell states and higher-dimensional three-party GHZ states. Our schemes solely rely on multiphoton interference, i.e. they can be adjusted to work for arbitrary degrees of freedom. Furthermore, they demonstrate high success probabilities and need comparably few auxiliary photons.

arXiv:2408.08473•New Journal of Physics•Feb 21, 2025•8 citations

Beyond Fidelity: Resolving Errors in Photonic Seed State Generation

Sara Bartolucci, Patrick Birchall, Jacob Bulmer +5 more

An important aspect of many linear optical quantum computing architectures is probabilistically generating small dual-rail qubit entangled states, or seed states. While many schemes to achieve this have been discovered, attention has been primarily focused on minimizing input resources and maximizing success probability rather than establishing a detailed understanding of linear-optical error performance. In this work, we develop a framework for resolving sensitivities to physically distinct errors in linear optical state generation, allowing us to identify precise ways in which these errors affect the properties of the output state. We use this framework to identify seed state generators in which destructive many-photon interference prevents detector loss and detector noise from causing a falsely successful heralding event. We show that this effect suppresses errors, for example cutting the effective loss on the output of particular Bell state generators in half relative to a standard scheme. We also present a new Bell state generator in which both detector loss and detector noise do not affect the quality of the output Bell state to first order, and a 4GHZ generator with >75% higher success probability than a standard circuit. In addition we provide some useful identities, bounds and invariants for studying linear optical seed state generation.

quant-pharXiv:2610.26603•Oct 20, 2026•0 citations

Photonic Source of Heralded Greenberger-Horne-Zeilinger States

Huan Cao, L. M. Hansen, Francesco Giorgino +5 more

Generating large multiphoton entangled states is of main interest due to enabling universal photonic quantum computing and all-optical quantum repeater nodes. These applications exploit measurement-based quantum computation using cluster states. Remarkably, it was shown that photonic cluster states of arbitrary size can be generated by using feasible heralded linear optics fusion gates that act on heralded three-photon Greenberger-Horne-Zeilinger (GHZ) states as the initial resource state. Thus, the capability of generating heralded GHZ states is of great importance for scaling up photonic quantum computing. Here, we experimentally demonstrate this required building block by reporting a polarisation-encoded heralded GHZ state of three photons, for which we build a high-rate six-photon source (547±2 Hz) from a solid-state quantum emitter and a stable polarization-based interferometer. The detection of three ancillary photons heralds the generation of three-photon GHZ states among the remaining particles with fidelities up to F=0.7278±0.0106. Our results initiate a path for scalable entangling operations using heralded linear-optics implementations.

arXiv:2308.05709•Physical Review Letters•Mar 28, 2024•58 citations

Heralded Three-Photon Entanglement from a Single-Photon Source on a Photonic Chip

Si Chen, Lichao Peng, Y.-P. Guo +13 more

In the quest to build general-purpose photonic quantum computers, fusion-based quantum computation has risen to prominence as a promising strategy. This model allows a ballistic construction of large cluster states which are universal for quantum computation, in a scalable and loss-tolerant way without feed forward, by fusing many small n-photon entangled resource states. However, a key obstacle to this architecture lies in efficiently generating the required essential resource states on photonic chips. One such critical seed state that has not yet been achieved is the heralded three-photon Greenberger-Horne-Zeilinger (3-GHZ) state. Here, we address this elementary resource gap, by reporting the first experimental realization of a heralded 3-GHZ state. Our implementation employs a low-loss and fully programmable photonic chip that manipulates six indistinguishable single photons of wavelengths in the telecommunication regime. Conditional on the heralding detection, we obtain the desired 3-GHZ state with a fidelity 0.573±0.024. Our Letter marks an important step for the future fault-tolerant photonic quantum computing, leading to the acceleration of building a large-scale optical quantum computer.

Physical Review Letters•Mar 28, 2024•47 citations

Loss and distinguishability effects in heralded entangled state generation with Gaussian resources

Yun-Long Cao, Xiao-Ye Xu, Wiwittawin Sukmas +2 more

The effects of optical loss and photon distinguishability on the heralded generation of entangled states based on Gaussian resources are quantitatively investigated. By incorporating mode-dependent loss and the statistical characteristics of partially distinguishable photons into a phase-space representation, an efficient numerical framework is established to optimize target-state fidelity and success probability, with a specific focus on the enhancement triggered by non-Gaussian operations such as photon addition and subtraction. The numerical optimization results indicate that a non-vacuum post-selection strategy within a dual-rail encoding framework, combined with the simultaneous tuning of squeezing parameters and the interferometer network, effectively suppresses vacuum noise, enabling the generation of high-fidelity Bell, GHZ, and W states under realistic experimental constraints. The results show that introducing non-Gaussian operations can successfully enhance the state generation performance under realistic imperfections analogous to the enhancements observed under ideal conditions. This study demonstrates that experimental imperfections primarily scale down the success probability rather than fundamentally compromising the state fidelity, providing practical design guidelines for scalable state engineering on integrated photonic platforms.

quant-pharXiv:2607.23048•Jul 28, 2026•0 citations
Entangled few-photon states, such as Bell and Greenberger-Horne-Zeilinger (GHZ) states, are central resources for discrete-variable photonic quantum information processing. In many architectures, these states are generated probabilistically by first heralding single photons from biphoton sources and then interfering them in linear-optical circuits. In this work, we show that the entanglement structure of said biphoton sources can be directly exploited for noise-engineering to deliver higher quality resource states. Using the transpose identity of multi-mode squeezed vacuum states, we introduce "ghost-unitary" implementations in which the target resource-generation interferometer is applied to the heralding modes rather than to the delivered resource modes. When the dominant imperfection is interferometric loss, this relocation converts direct amplitude damping of the output into false-positive heralding events that require both higher-pair emission and photon loss. In the low-squeezing regime, these events are parametrically suppressed, yielding higher-fidelity conditional resource states. We analyze this mechanism for single-qubit states, two-photon NOON states, Bell states, and a family of nnn-qubit GHZ states, as well as for single-qubit teleportation and type-I-fusion-based resource growth. Across these examples, we delineate finite parameter regimes in which ghost-unitary implementations outperform direct implementations, with particular relevance to frequency-bin photonics where active linear-optical transformations can be relatively lossy. We also prove that, in the setting considered here, the direct implementation of the nnn-GHZ family delivers identically damped outputs: equivalent to the ideal state followed by uniform amplitude damping. This extends the known n=2,3n=2,3n=2,3 cases and provides a structural result of independent interest for photonic quantum information processing.
High-quality entangled states of photons underlie quantum information science (QIS) applications across communication, sensing, and computing. In many discrete-variable photonic QIS architectures, large application-ready states (e.g., cluster states, repeater graph states) are constructed via fusion measurements on small entangled seed states, of which Bell states are the fundamental example. The quality of seed-state generation therefore sets a baseline for application performance, making it crucial to understand this process under realistic error mechanisms, particularly in integrated photonics experiments. In this work, we analyze five heralded schemes for generating event-ready photonic Bell states, contrasting their heralding probabilities, fidelities, and error robustness. We develop a hierarchy of error models, progressing from an analytically tractable lumped-loss model to realistic heralded single-photon sources with multiphoton emission errors and finally to integrated frequency-bin implementations with architecture-dependent loss. Across these models, we find that schemes based on higher-order multiphoton interference provide superior fidelity robustness in low-loss implementations, while lower-photon-number schemes can be preferable when probabilistic sources or lossy beamsplitters dominate the resource cost. Our results provide design guidance for integrated discrete-variable quantum photonics, with particular relevance for frequency-bin architectures where active beamsplitter loss can determine the optimal resource-state-generation strategy.
Abstract One of the most important resources for quantum optical experiments and applications are on-demand highly entangled multiphoton quantum states. A promising way of generating them is heralding entanglement generation at a high rate from letting independent photons interfere. However, such schemes often work for a specific internal degree of freedom of the interfering photons only. Going to higher numbers of entangled photons, the success probabilities decrease while the number of necessary resources, e.g. auxiliary photons and optical elements, increases. To make probabilistic schemes feasible also for larger quantum states, it is therefore important to find resource-efficient generation schemes with high success probabilities. In this work, we introduce easily implementable schemes to herald qubit Greenberger–Horne–Zeilinger (GHZ) states, higher-dimensional Bell states and higher-dimensional three-party GHZ states. Our schemes solely rely on multiphoton interference, i.e. they can be adjusted to work for arbitrary degrees of freedom. Furthermore, they demonstrate high success probabilities and need comparably few auxiliary photons.
An important aspect of many linear optical quantum computing architectures is probabilistically generating small dual-rail qubit entangled states, or seed states. While many schemes to achieve this have been discovered, attention has been primarily focused on minimizing input resources and maximizing success probability rather than establishing a detailed understanding of linear-optical error performance. In this work, we develop a framework for resolving sensitivities to physically distinct errors in linear optical state generation, allowing us to identify precise ways in which these errors affect the properties of the output state. We use this framework to identify seed state generators in which destructive many-photon interference prevents detector loss and detector noise from causing a falsely successful heralding event. We show that this effect suppresses errors, for example cutting the effective loss on the output of particular Bell state generators in half relative to a standard scheme. We also present a new Bell state generator in which both detector loss and detector noise do not affect the quality of the output Bell state to first order, and a 4GHZ generator with >75% higher success probability than a standard circuit. In addition we provide some useful identities, bounds and invariants for studying linear optical seed state generation.
Generating large multiphoton entangled states is of main interest due to enabling universal photonic quantum computing and all-optical quantum repeater nodes. These applications exploit measurement-based quantum computation using cluster states. Remarkably, it was shown that photonic cluster states of arbitrary size can be generated by using feasible heralded linear optics fusion gates that act on heralded three-photon Greenberger-Horne-Zeilinger (GHZ) states as the initial resource state. Thus, the capability of generating heralded GHZ states is of great importance for scaling up photonic quantum computing. Here, we experimentally demonstrate this required building block by reporting a polarisation-encoded heralded GHZ state of three photons, for which we build a high-rate six-photon source (547±2 Hz) from a solid-state quantum emitter and a stable polarization-based interferometer. The detection of three ancillary photons heralds the generation of three-photon GHZ states among the remaining particles with fidelities up to F=0.7278±0.0106. Our results initiate a path for scalable entangling operations using heralded linear-optics implementations.
In the quest to build general-purpose photonic quantum computers, fusion-based quantum computation has risen to prominence as a promising strategy. This model allows a ballistic construction of large cluster states which are universal for quantum computation, in a scalable and loss-tolerant way without feed forward, by fusing many small n-photon entangled resource states. However, a key obstacle to this architecture lies in efficiently generating the required essential resource states on photonic chips. One such critical seed state that has not yet been achieved is the heralded three-photon Greenberger-Horne-Zeilinger (3-GHZ) state. Here, we address this elementary resource gap, by reporting the first experimental realization of a heralded 3-GHZ state. Our implementation employs a low-loss and fully programmable photonic chip that manipulates six indistinguishable single photons of wavelengths in the telecommunication regime. Conditional on the heralding detection, we obtain the desired 3-GHZ state with a fidelity 0.573±0.024. Our Letter marks an important step for the future fault-tolerant photonic quantum computing, leading to the acceleration of building a large-scale optical quantum computer.
The effects of optical loss and photon distinguishability on the heralded generation of entangled states based on Gaussian resources are quantitatively investigated. By incorporating mode-dependent loss and the statistical characteristics of partially distinguishable photons into a phase-space representation, an efficient numerical framework is established to optimize target-state fidelity and success probability, with a specific focus on the enhancement triggered by non-Gaussian operations such as photon addition and subtraction. The numerical optimization results indicate that a non-vacuum post-selection strategy within a dual-rail encoding framework, combined with the simultaneous tuning of squeezing parameters and the interferometer network, effectively suppresses vacuum noise, enabling the generation of high-fidelity Bell, GHZ, and W states under realistic experimental constraints. The results show that introducing non-Gaussian operations can successfully enhance the state generation performance under realistic imperfections analogous to the enhancements observed under ideal conditions. This study demonstrates that experimental imperfections primarily scale down the success probability rather than fundamentally compromising the state fidelity, providing practical design guidelines for scalable state engineering on integrated photonic platforms.