Generalizing multipartite concentratable entanglement for practical applications: mixed, qudit and optical states

Foulds, Steph; Prove, Oliver; Kendon, Viv

Abstract

The controlled SWAP test for detecting and quantifying entanglement applied to pure qubit states is robust to small errors in the states and efficient for large multi-qubit states (Foulds et al. 2021 Quantum Sci. Technol. 6, 035002 (doi:10.1088/2058-9565/abe458)). We extend this, and the related measure concentratable entanglement (CE), to enable important practical applications in quantum information processing. We investigate the lower bound of concentratable entanglement given in (Beckey et al. 2023 Phys. Rev. A 107, 062425 (doi:10.1103/physreva.107.062425)) and conjecture an upper bound of the mixed-state concentratable entanglement that is robust to c-SWAP test errors. Since experimental states are always slightly mixed, our work makes the c-SWAP test and CE measure suitable for application in experiments to characterize entanglement. We further present the CE of some key higher-dimensional states such as qudit states and entangled optical states to validate the CE as a higher-dimensional measure of entanglement. This article is part of the theme issue ‘The quantum theory of light’.

Citation

Foulds, S., Prove, O., & Kendon, V. (2024). Generalizing multipartite concentratable entanglement for practical applications: mixed, qudit and optical states. Philosophical Transactions of the Royal Society A: Mathematical, Physical and Engineering Sciences, 382(2287), Article 20240411. https://doi.org/10.1098/rsta.2024.0411

• Journal Article Type: Article
• Acceptance Date: Nov 18, 2024
• Online Publication Date: Dec 24, 2024
• Publication Date: Dec 30, 2024
• Deposit Date: Jan 7, 2025
• Publicly Available Date: Jan 7, 2025
• Journal: Philosophical Transactions of the Royal Society A: Mathematical, Physical and Engineering Sciences
• Print ISSN: 1364-503X
• Electronic ISSN: 1471-2962
• Publisher: The Royal Society
• Peer Reviewed: Peer Reviewed
• Volume: 382
• Issue: 2287
• Article Number: 20240411
• DOI: https://doi.org/10.1098/rsta.2024.0411
• Keywords: SWAP test, quantum entanglement, concentratable entanglement
• Public URL: https://durham-repository.worktribe.com/output/3230012