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.
The focal point of this thesis is strongly based on quantum entanglement within Quantum Information Science. We provide an indepth analysis of entanglement quantification in both bipartite and multipartite quantum systems, with an emphasis on many-body entanglement. We examine the definitions of entanglement, introduce several entanglement measures, and examine the challenges in expanding these measures to multipartite scenarios. For bipartite systems, we detail entropy-based measures such as von Neumann and Rényi entropies, the entanglement spectrum and important algebraic metrics such as negativity and concurrence. We then elaborate on multipartite entanglement, introducing modern measures and detection techniques including geometric and global entanglement measurements, generalised multipartite concurrence, multipartite negativity, fidelity-based entanglement benchmarks, and entanglement witnesses. Some examples include Greenberger-Horne-Zeilinger (GHZ), and the W states to illustrate the distinction between biseparable and truly multi-partite-entangled states, as well as the SLOCC classification of families of entangled states. We also briefly introduce practical ways of measuring entanglement, such as the SWAP test, quantum state tomography for experimental estimation of entanglement and consequently randomised measurements. We apply these measures to specific quantum states (GHZ, W , graph states, and random states), analysing how entanglement evolves under operations and how different metrics capture distinct features of multi-qubit entanglement. Finally, we conclude with a summary of findings, a discussion of current limitations such as scalability of measures. The thesis is organised into five chapters: Introduction, Entanglement, Multipartite Entanglement Measures, Negativity vs. Three-Tangle, and Conclusion.
Quantum weight enumerators are fundamental tools for analyzing quantum error-correcting codes and multipartite entanglement, offering insights into the existence of quantum error-correcting codes and
k-uniform states. In this work, we establish a connection between quantum weight enumerators and the
n-qubit parallelized SWAP test. We demonstrate that each shadow enumerator corresponds to a probability derived from this test, providing a physical interpretation for the shadow enumerators. Leveraging the non-negativity of these probabilities, we present an elegant proof for the shadow inequalities. Additionally, we show that the Shor-Laflamme weight enumerators and the Rains unitary enumerators can be calculated using the
n-qubit parallelized SWAP test. For applications, we utilize this test to compute the distances of quantum error-correcting codes, determine the
k-uniformity of pure states, and evaluate multipartite entanglement measures. Our results indicate that quantum weight enumerators can be efficiently estimated on quantum computers, opening a path to calculate and verify the distances of quantum error-correcting codes.