Positive Maps and Entanglement in Real Hilbert Spaces

Locally Tomographic Shadows (Extended Abstract)

“…The example of primary interest here takes C = CPM R , the category of finite-dimensional real Hilbert spaces with morphisms H → K given by completely positive linear mappings L (H) → L (K). In contrast to the complex case, there exist linear mappings L s (H) → L s (K) that preserve positivity but not adjoints [9]. We reserve the term positive for those linear mappings that preserve both.…”

Non-locality of conjugation symmetry: characterization and examples in quantum network sensing

“…This perspective entails considering a specific real subspace within multipartite complex Hilbert spaces. The impact of restricting multipartite systems to real scenarios has been observed in state discrimination [11][12][13][14][15][16], monogamy of entanglement [17,18], non-locality [19,20], and most recently, in field-dependent entanglement [21]. However, it is important to note that, in general, a real subspace of a composite complex space cannot be represented as a mere composition of real subspaces.…”