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arXiv:2004.02691 · Physical Review A

Improved heralded schemes to generate entangled states from single photons

F. V. Gubarev, I. V. Dyakonov, M. Yu. Saygin, G. I. Struchalin, Stanislav S. Straupe, S. P. Kulik

Published Jul 2, 2020• 39 citations
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Abstract

We present a semianalytical methodology to construct optimal linear-optical circuits for the heralded production of three-photon Greenberger-Horne-Zeilinger (3-GHZ) and two-photon Bell states. We provide a detailed description and analysis of the resulting optical schemes, which deliver success probabilities of 1/54 and 2/27 for dual-rail encoded 3-GHZ and Bell-state generation, respectively. Our results improve the known constructive bounds on the success probabilities for 3-GHZ states and are of particular importance for a ballistic quantum computing model [M. Gimeno-Segovia et al., Phys. Rev. Lett. 115, 020502 (2015)], for which these states provide an essential resource.

DOI
10.1103/physreva.102.012604

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We present a semianalytical methodology to construct optimal linear-optical circuits for the heralded production of three-photon Greenberger-Horne-Zeilinger (3-GHZ) and two-photon Bell states. We provide a detailed description and analysis of the resulting optical schemes, which deliver success probabilities of 1/54 and 2/27 for dual-rail encoded 3-GHZ and Bell-state generation, respectively. Our results improve the known constructive bounds on the success probabilities for 3-GHZ states and are of particular importance for a ballistic quantum computing model [M. Gimeno-Segovia et al., Phys. Rev. Lett. 115, 020502 (2015)], for which these states provide an essential resource.
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.
High-dimensional multipartite entanglement plays a crucial role in quantum information science. However, existing schemes for generating such entanglement become complex and costly as the dimension of quantum units increases. In this Letter, we overcome the limitation by proposing a significantly enhanced linear optical heralded scheme that generates the d-level N-partite Greenberger-Horne-Zeilinger (GHZ) state with single-photon sources and linear operations. Our scheme requires dN photons, which is the minimal required photon number, with substantially improved success probability from previous schemes. It employs linear optical logic gates compatible with any qudit encoding system and can generate generalized GHZ states with installments of beam splitters. With efficient generations of high-dimensional resource states, our work opens avenues for further exploration in high-dimensional quantum information processing.
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 dual-rail encoded 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 work marks an important step for the future fault-tolerant photonic quantum computing, leading to the acceleration of building a large-scale optical quantum computer.
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.
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.
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.