INVARIANT POLYNOMIALS WITH APPLICATIONS TO QUANTUM COMPUTING
КВАНТТЫҚ ЕСЕПТЕУЛЕРГЕ ҚОЛДАНЫЛАТЫН ИНВАРИАНТТЫ КӨПМҮШЕЛЕР
ИНВАРИАНТНЫЕ МНОГОЧЛЕНЫ С ПРИМЕНЕНИЕМ К КВАНТОВЫМ ВЫЧИСЛЕНИЯМ
Amanov A.
2024Kazakh-British Technical University
Herald of the Kazakh British Technical UNiversity
2024#21Issue 295 - 105 pp.
In quantum information theory, understanding the complexity of entangled states within the context of SLOCC (stochastic local operations and classical communications) involving d qubits (or qudits) is essential for advancing our knowledge of quantum systems. This complexity is often analyzed by classifying the states via local symmetry groups. The resulting classes can be distinguished using invariant polynomials, which serve as a measure of entanglement. This paper introduces a novel method for obtaining invariant polynomials of the smallest degrees, which significantly enhances the efficiency of characterizing SLOCC classes of entangled quantum states. Our method not only simplifies the process of identifying these classes but also provides a robust tool for analyzing the entanglement properties of complex quantum systems. As a practical application, we demonstrate the derivation of minimal degree invariants in specific cases, illustrating the effectiveness of our approach in real-world scenarios. This advancement has the potential to streamline various processes in quantum information theory, making it easier to understand, classify, and utilize entangled states effectively.
invariant polynomials , quantum entanglement , SLOCC
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Kazakh-British Technical University, Almaty, 050000, Kazakhstan
Kazakh-British Technical University
10 лет помогаем публиковать статьи Международный издатель
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