Entanglement and Symmetry in Multiple-Qubit States: a geometrical approach

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The behavior of quantum states under local unitary transformations (LUTs) and stochastic local quantum operations and classical communication (SLOCC) has proven central to the understanding of entanglement in multipartite quantum systems. In particular, invariants under these operations have provided insight into quantum entanglement in multiple‐qubit states. Relationships between entanglement, mixedness and spin symmetry in multiple‐qubit quantum states can be found by exploiting these properties. For example, concurrence and n‐tangle are naturally expressed in terms of spin‐flip transformations. In the case of specialized entanglement measures and/or special families of states, complementarity relations involving these lengths and state transformations are derivable. Here, the role of geometry in such investigations is explored. Minkowskian geometry is seen to provide elegant representations of entanglement in multiple‐qubit systems, particularly the language of twistors.