COMPUTING THE DEGREE-4 INVARIANT POLYNOMIAL BASIS FOR 7 QUBITS
https://doi.org/10.55452/1998-6688-2024-21-3-128-136
Abstract
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.
Supporting agencies: This research was supported by the Science Committee of the Ministry of Science and Higher Education of the Republic of Kazakhstan (Grant No. AP14869221).
About the Author
A. Amanov
Kazakh-British Technical University
Kazakhstan
Kazakhstan
PhD student
050000, Almaty
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Review
For citations:
Amanov A. COMPUTING THE DEGREE-4 INVARIANT POLYNOMIAL BASIS FOR 7 QUBITS. Herald of the Kazakh-British technical university. 2024;21(3):128-136. https://doi.org/10.55452/1998-6688-2024-21-3-128-136
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