COMPUTING THE DEGREE-4 INVARIANT POLYNOMIAL BASIS FOR 7 QUBITS

4 ДӘРЕЖЕЛІ 7 КУБИТТІҢ ИНВАРИАНТТЫҚ КӨПМҮШЕЛЕР БАЗИСІН ЕСЕПТЕУ
ВЫЧИСЛЕНИЕ БАЗИСА ИНВАРИАНТНЫХ МНОГОЧЛЕНОВ СТЕПЕНИ 4 ДЛЯ 7 КУБИТОВ
Amanov A.
2024 Kazakh-British Technical University

Herald of the Kazakh British Technical UNiversity
2024 #21 Issue 3 128 - 136 pp.

Understanding the complexity of entangled states within the context of SLOCC (stochastic local operations and classical communications) involving several number qubits is essential for advancing our knowledge of quantum systems. This complexity is often analyzed by classifying the states via local symmetry groups. Practically, tthe resulting classes can be distinguished using invariant polynomials, but the size of these polynomials grows rapidly. Hence, it is crucial to obtain the smallest possible invariants. In this short note, we compute the basis of invariant polynomials of 7 qubits of degree 4, which are the smallest degree invariants. We obtain these polynomials using the representation theory and algebraic combinatorics.

invariant polynomials; quantum entanglement , SLOCC

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Kazakh-British Technical University, Almaty, 050000, Kazakhstan

Kazakh-British Technical University

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