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arXiv · 2108.12299

Geometric Bloch Vector Solution to Minimum Error Discriminations of Mixed Qubit States

Mahdi Rouhbakhsh N.·Seyed Arash Ghoreishi
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Abstract

We investigate minimum-error (ME) discrimination for mixed qubit states using a geometric approach. By analyzing positive operator-valued measure (POVM) solutions and introducing Lagrange operator $\Gamma$, we develop a four-step structured instruction to find $\Gamma$ for $N$ mixed qubit states. Our method covers optimal solutions for two, three, and four mixed qubit states, including a novel result for four qubit states. We introduce geometric-based POVM classes and non-decomposable subsets for constructing optimal solutions, enabling us to find all possible answers for the general problem of minimum-error discrimination for $N$ mixed qubit states with arbitrary a priori probabilities.

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Mahdi Rouhbakhsh N., Seyed Arash Ghoreishi. 2021-08-27. Geometric Bloch Vector Solution to Minimum Error Discriminations of Mixed Qubit States. https://doi.org/10.1007/s11128-023-04080-4

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