$d+1$ Measurement Bases are Sufficient for Determining $d$-Dimensional Quantum States: Theory and Experiment

• URL: http://arxiv.org/abs/2507.11204v1
• Date: Tue, 15 Jul 2025 11:25:35 GMT
• Title: $d+1$ Measurement Bases are Sufficient for Determining $d$-Dimensional Quantum States: Theory and Experiment
• Authors: Tianqi Xiao, Yaxin Wang, Ying Xia, Zhihao Li, Xiaoqi Zhou,
• Abstract summary: We propose a quantum state tomography scheme that requires only $d+1$ projective measurement bases to fully reconstruct an arbitrary $d$-dimensional quantum state.<n>This approach offers new perspectives for quantum state characterization and measurement design, and holds promise for future applications in quantum information processing.
• Score: 7.402313910092289
• License: http://arxiv.org/licenses/nonexclusive-distrib/1.0/
• Abstract: A long-standing problem in quantum physics is to determine the minimal number of measurement bases required for the complete characterization of unknown quantum states, a question of particular relevance to high-dimensional quantum information processing. Here, we propose a quantum state tomography scheme that requires only $d+1$ projective measurement bases to fully reconstruct an arbitrary $d$-dimensional quantum state. As a proof-of-principle, we experimentally verified this scheme on a silicon photonic chip by reconstructing quantum states for $d=6$, in which a complete set of mutually unbiased bases does not exist. This approach offers new perspectives for quantum state characterization and measurement design, and holds promise for future applications in quantum information processing.

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