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arXiv:2512.20235

A resource-efficient and noise-robust entanglement witness based on the swap test

Sebastiano Guaraldo, Sonia Mazzucchi, Alessio Baldazzi, Stefano Azzini, Lorenzo Pavesi

quant-phSubmitted Dec 23, 2025• Announced Dec 24, 2025• 0 citations
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Abstract

Quantum entanglement is an essential resource for quantum technologies, and the controlled swap test provides a versatile tool for its detection and quantification. Here, we propose a SWAP-based entanglement witness that applies to arbitrary two-qubit states - both pure and mixed - and provides a lower bound on the concurrence. The method is resource-efficient, robust to noise, and platform-independent. As an example, we validate the approach on a room-temperature photonic chip, where the swap test is carried out using only linear and well-established integrated optical components. The robustness of the method against photonic-hardware noise is also analysed. Our results establish a simple and reliable tool for entanglement witnessing.

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34 pages, 6 figures

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Quantum entanglement is an essential resource for quantum technologies, and the controlled swap test provides a versatile tool for its detection and quantification. Here, we propose a SWAP-based entanglement witness that applies to arbitrary two-qubit states - both pure and mixed - and provides a lower bound on the concurrence. The method is resource-efficient, robust to noise, and platform-independent. As an example, we validate the approach on a room-temperature photonic chip, where the swap test is carried out using only linear and well-established integrated optical components. The robustness of the method against photonic-hardware noise is also analysed. Our results establish a simple and reliable tool for entanglement witnessing.
Abstract Quantum entanglement is essential to the development of quantum computation, communications, and technology. The controlled SWAP test, widely used for state comparison, can be adapted to an efficient and useful test for entanglement of a pure state. Here we show that the test can evidence the presence of entanglement (and further, genuine n-qubit entanglement), can distinguish entanglement classes, and that the concurrence of a two-qubit state is related to the test’s output probabilities. We also propose a multipartite measure of entanglement that acts similarly for n-qubit states. The average number of copies of the test state required to detect entanglement decreases for larger systems, to four on average for many (n ≳ 8) qubits for maximally entangled states. For non-maximally entangled states, the number of copies required to detect entanglement increases with decreasing entanglement. Furthermore, the results are robust to second order when typical small errors are introduced to the state under investigation.
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’.
Imperfections in experimental measurement schemes can lead to falsely identifying, or over estimating, entanglement in a quantum system. A recent solution to this is to define schemes that are robust to measurement imperfections-measurement-device-independent entanglement witness (MDI-EW). This approach can be adapted to witness all entangled qubit states for a wide range of physical systems and does not depend on detection efficiencies or classical communication between devices. Here we extend the theory to remove the necessity of prior knowledge about the two-qubit states to be witnessed. Moreover, we tested this model via a novel experimental implementation for MDI-EW that significantly reduces the experimental complexity. By applying it to a bipartite Werner state, we demonstrate the robustness of this approach against noise by witnessing entanglement down to an entangled state fraction close to 0.4.
Abstract Quantum entanglement plays a key role in the field of quantum computing and quantum communication. The controlled SWAP test has been used to detect pure state entanglement ( Foulds S. et al. Quantum Sci. Technol. , 6 (2021) 035002; Beckey J. L. et al. Phys. Rev. Lett. , 127 (2021) 140501). In this paper, we investigate that quantum circuits for controlled SWAP test can be used to detect the entanglement of multipartite mixed state. Based on the measured probability, we propose entanglement criteria for detecting multipartite entanglement and genuine entanglement of pure states. In addition, we give representation of the entanglement measures based on the measured probability of the controlled SWAP tests. Numerical examples are used to illustrate the efficiency of the entanglement criteria.
This paper presents an efficient method for detecting entanglement in high-dimensional two-qudit states by mapping the Hilbert space onto the space of two qubits. This transformation enables the use of well-established two-qubit entanglement witnesses. The proposed approach is not restricted to any specific class of states, successfully identifies a vast majority of pure entangled states, and requires a number of measurements that does not increase with the dimensionality of the qudits. The method demonstrates solid sensitivity when applied to two notable classes of states—incomplete-permutation-symmetric states and random pure states mixed with white noise—and is shown to be feasible with current experimental techniques.