Dr. Liang Xu Profile

Dr. Liang Xu

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Proceedings Article | 6 November 2023 Paper

Direct tomography of high-dimensional entangled states

Hongkuan Xia, Liang Xu, Lijian Zhang

Proceedings Volume 12921, 1292145 (2023) https://doi.org/10.1117/12.2691751

KEYWORDS: Quantum systems, Quantum amplitude, Entangled states, Quantum probability, Quantum state tomography, Photons, Quantum protocols, Quantum entanglement, Polarization, Quantum optics experiments

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Weak measurement enables the direct measurement of the wavefunction by associating the weak values with the probability amplitudes, which is known as Direct Tomography (DT). Compared to standard quantum state tomography, DT requires far fewer measurement bases and avoids reconstruction algorithm, showing distinct advantages in the characterization of high-dimensional quantum states. Here, we propose a general parallel extension of the DT protocol for entangled systems involving multiple particles with the probability amplitudes corresponding to the joint weak values. By coupling each particle of the quantum system with the independent meter state, we obtain joint weak values of nonlocal observables through collective measurements on the post-selected meter states. Our rigorous derivation allows for large coupling strengths, which significantly reduces statistical errors. We experimentally demonstrate the feasibility of our protocol by performing DT of path-entangled photonic states in three dimensions, achieving fidelities between the results of DT and those of standard quantum state tomography of over 95%. Our results provide a powerful tool for tomography of entangled states and investigation of their nonlocal properties.

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