We classify four qubit states under SLOCC operations, that is, we classify the orbits of the group SL(2, C) 4 on the Hilbert space H4 = (C2) ⊗4. We approach the classification by realising this representation as a symmetric space of maximal rank. We first describe general methods for classifying the orbits of such a space. We then apply these methods to obtain the orbits in our special case, resulting in a complete and irredundant classification of SL(2, C) 4-orbits on H4. It follows that an element of (C2) ⊗4 is conjugate to an element of precisely 87 classes of elements. Each of these classes either consists of one element or of a parameterised family of elements, and the elements in the same class all have equal stabiliser in SL(2, C) 4. We also present a complete and irredundant classification of elements and stabilisers up to the action of Sym4 SL(2, C) 4 where Sym4 permutes the four tensor factors of (C2) ⊗4.

Classification of four qubit states and their stabilisers under SLOCC operations / Dietrich, Heiko; de Graaf, Willem A.; Marrani, Alessio; Origlia, Marcos. - In: JOURNAL OF PHYSICS. A, MATHEMATICAL AND THEORETICAL. - ISSN 1751-8113. - 55:9(2022), pp. 09530201-09530227. [10.1088/1751-8121/ac4b13]

Classification of four qubit states and their stabilisers under SLOCC operations

Dietrich, Heiko;de Graaf, Willem A.;Marrani, Alessio;
2022-01-01

Abstract

We classify four qubit states under SLOCC operations, that is, we classify the orbits of the group SL(2, C) 4 on the Hilbert space H4 = (C2) ⊗4. We approach the classification by realising this representation as a symmetric space of maximal rank. We first describe general methods for classifying the orbits of such a space. We then apply these methods to obtain the orbits in our special case, resulting in a complete and irredundant classification of SL(2, C) 4-orbits on H4. It follows that an element of (C2) ⊗4 is conjugate to an element of precisely 87 classes of elements. Each of these classes either consists of one element or of a parameterised family of elements, and the elements in the same class all have equal stabiliser in SL(2, C) 4. We also present a complete and irredundant classification of elements and stabilisers up to the action of Sym4 SL(2, C) 4 where Sym4 permutes the four tensor factors of (C2) ⊗4.
2022
9
Dietrich, Heiko; de Graaf, Willem A.; Marrani, Alessio; Origlia, Marcos
Classification of four qubit states and their stabilisers under SLOCC operations / Dietrich, Heiko; de Graaf, Willem A.; Marrani, Alessio; Origlia, Marcos. - In: JOURNAL OF PHYSICS. A, MATHEMATICAL AND THEORETICAL. - ISSN 1751-8113. - 55:9(2022), pp. 09530201-09530227. [10.1088/1751-8121/ac4b13]
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Utilizza questo identificativo per citare o creare un link a questo documento: https://hdl.handle.net/11572/341559
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