Purest Quantum State Identification

• URL: http://arxiv.org/abs/2502.14334v1
• Date: Thu, 20 Feb 2025 07:42:16 GMT
• Title: Purest Quantum State Identification
• Authors: Yingqi Yu, Honglin Chen, Jun Wu, Wei Xie, Xiangyang Li,
• Abstract summary: We design methods for identifying the purest one within $K$ unknown $n$-qubit quantum states using $N$ samples. This framework provides concrete design principles for overcoming sampling bottlenecks in quantum technologies.
• Score: 13.974066377698044
• License:
• Abstract: Precise identification of quantum states under noise constraints is essential for quantum information processing. In this study, we generalize the classical best arm identification problem to quantum domains, designing methods for identifying the purest one within $K$ unknown $n$-qubit quantum states using $N$ samples. %, with direct applications in quantum computation and quantum communication. We propose two distinct algorithms: (1) an algorithm employing incoherent measurements, achieving error $\exp\left(- \Omega\left(\frac{N H_1}{\log(K) 2^n }\right) \right)$, and (2) an algorithm utilizing coherent measurements, achieving error $\exp\left(- \Omega\left(\frac{N H_2}{\log(K) }\right) \right)$, highlighting the power of quantum memory. Furthermore, we establish a lower bound by proving that all strategies with fixed two-outcome incoherent POVM must suffer error probability exceeding $ \exp\left( - O\left(\frac{NH_1}{2^n}\right)\right)$. This framework provides concrete design principles for overcoming sampling bottlenecks in quantum technologies.

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