Projected Dynamic Programming for Sequential Quantum State Discrimination

Quantum Physics [Submitted on 16 Apr 2026] Projected Dynamic Programming for Sequential Quantum State Discrimination Jaehun Jeong, Donghwa Ji, Hyunjun Jang, Kabgyun Jeong Sequential Quantum State Discrimination (SQSD) can be naturally framed as a sequential decision-making problem: at each time step, an agent must decide whether to perform an additional measurement to gather more information or to conclude with an optimal decision based on the current belief. In this paper, we formally cast SQSD into a static-hidden-state Partially Observable Markov Decision Process (POMDP) framework. We demonstrate that this formulation precisely subsumes the conventional minimum-error discrimination (MED) scheme as a special one-step case. Furthermore, we apply a regular grid-based discretization to the continuous belief simplex and approximate the possibly continuous measurement space using a finite library. Then we provide rigorous mathematical bounds on the resulting errors and analyze the computational complexity for both offline planning and online execution. Our analysis confirms that the inherent trade-off between accuracy and complexity, as well as the curse of dimensionality regarding the number of hypotheses, are also prominently observed in the quantum regime. Finally, we provide a working example of binary state discrimination to derive explicit forms of various functions and present numerical simulations for trine state discrimination to visualize the sequential structure of our POMDP-based SQSD. Comments: 54 pages, 18 figures Subjects: Quantum Physics (quant-ph) Cite as: arXiv:2604.15393 [quant-ph]   (or arXiv:2604.15393v1 [quant-ph] for this version)   https://doi.org/10.48550/arXiv.2604.15393 Focus to learn more Submission history From: Jaehun Jeong [view email] [v1] Thu, 16 Apr 2026 08:21:40 UTC (29,728 KB) Access Paper: HTML (experimental) view license Current browse context: quant-ph < prev   |   next > new | recent | 2026-04 References & Citations INSPIRE HEP NASA ADS Google Scholar Semantic Scholar Export BibTeX Citation Bookmark Bibliographic Tools Bibliographic and Citation Tools Bibliographic Explorer Toggle Bibliographic Explorer (What is the Explorer?) Connected Papers Toggle Connected Papers (What is Connected Papers?) Litmaps Toggle Litmaps (What is Litmaps?) scite.ai Toggle scite Smart Citations (What are Smart Citations?) Code, Data, Media Demos Related Papers About arXivLabs Which authors of this paper are endorsers? | Disable MathJax (What is MathJax?)