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Non-Hermitian Entanglement Filter

Mahmoud A. Selim, Max Ehrhardt, Yuqiang Ding, Hediyeh M. Dinani, Armando Pérez-Leija, Qi Zhong, Şahin Kaya Özdemir, Matthias Heinrich, Alexander Szameit, Demetrios N. Christodoulides, Mercedeh Khajavikhan

Published Jan 1, 2025• 0 citations
Publisher

Abstract

We experimentally demonstrate a fully integrated photonic entanglement filter based non-Hermitian anti-parity-time (APT) symmetry. Our filter exhibits near-unity fidelity and scalability across photon-number subspaces.
DOI
10.1364/cleo_fs.2025.ff138_1

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ABSTRACT Non‐Hermitian systems have attracted increasing attention in recent years, particularly those exhibiting Parity‐Time (PT) symmetry. Quantum metrology establishes the ultimate attainable bounds for parameter estimation in both Hermitian and non‐Hermitian systems. However, comparatively little is known about non‐Hermitian systems with anti‐Parity‐Time (APT) symmetry. In this work, we investigate the theoretical bounds on quantum parameter estimation precision for an APT‐symmetric system governed by the Bogoliubov–de Gennes (BdG) Hamiltonian. We explicitly derive the expression for the quantum Fisher information (QFI) and compare the attainable precision limits for both multiplicative and non‐multiplicative parameters in the BdG Hamiltonian. Our analysis of the effective QFI reveals that quantum parameter estimation precision can be significantly enhanced as the system approaches the exceptional point with unbroken APT symmetry, where Heisenberg scaling becomes achievable. We also examine how the effective QFI depends on the choice of initial states. Furthermore, we demonstrate that entanglement in multi‐particle initial state can provide an additional enhancement to the QFI. The ratio of limit of parameter estimation precision of the entangled state to the greatest one we have found over all the tensor product states is 1.22, which is greater than 1. Our analysis of two‐particle states confirms that entanglement in the initial state can further increase the QFI, highlighting it as a valuable quantum resource. These findings lay a theoretical foundation for future experimental explorations of parameter estimation in APT‐symmetric non‐Hermitian systems.

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Preserving entanglement in the presence of decoherence remains a major challenge for quantum technologies. Recent proposals have employed photonic filters based on anti-parity-time symmetry to recover certain entangled states, but these approaches require intricate, symmetry-constrained waveguide architectures and precise bath engineering. In this work, we show that such strict non-Hermitian symmetry constraints are not necessary for entanglement filtering. Instead, we identify post-selection and the emergence of dark states-arising naturally through destructive interference in simple photonic settings-as the essential mechanisms. By avoiding the need for special bath engineering or non-Hermitian symmetries, our approach significantly simplifies the design and architecture, enhances universality, and extends applicability beyond previously studied dimer configurations. We demonstrate this concept using minimal waveguide network designs, offering a broadly accessible route to robust entanglement filtering.
Entanglement is a key resource for quantum computing, sensing, and communication, but it is susceptible to decoherence. To address this, research in quantum optics has explored filtering techniques such as photon ancillas and Rydberg atom blockade to restore entangled states. We introduce an approach to entanglement retrieval that exploits the features of non-Hermitian systems. By designing an anti-parity-time two-state guiding configuration, we demonstrate efficient extraction of entanglement from any input state. This filter is implemented on a lossless waveguide network and achieves near-unity fidelity under single- and two-photon excitation and is scalable to higher photon levels, remaining robust against decoherence during propagation. Our results offer an approach to using non-Hermitian symmetries to address central challenges in quantum technologies.
ABSTRACT Non‐Hermitian systems have attracted increasing attention in recent years, particularly those exhibiting Parity‐Time (PT) symmetry. Quantum metrology establishes the ultimate attainable bounds for parameter estimation in both Hermitian and non‐Hermitian systems. However, comparatively little is known about non‐Hermitian systems with anti‐Parity‐Time (APT) symmetry. In this work, we investigate the theoretical bounds on quantum parameter estimation precision for an APT‐symmetric system governed by the Bogoliubov–de Gennes (BdG) Hamiltonian. We explicitly derive the expression for the quantum Fisher information (QFI) and compare the attainable precision limits for both multiplicative and non‐multiplicative parameters in the BdG Hamiltonian. Our analysis of the effective QFI reveals that quantum parameter estimation precision can be significantly enhanced as the system approaches the exceptional point with unbroken APT symmetry, where Heisenberg scaling becomes achievable. We also examine how the effective QFI depends on the choice of initial states. Furthermore, we demonstrate that entanglement in multi‐particle initial state can provide an additional enhancement to the QFI. The ratio of limit of parameter estimation precision of the entangled state to the greatest one we have found over all the tensor product states is 1.22, which is greater than 1. Our analysis of two‐particle states confirms that entanglement in the initial state can further increase the QFI, highlighting it as a valuable quantum resource. These findings lay a theoretical foundation for future experimental explorations of parameter estimation in APT‐symmetric non‐Hermitian systems.