Generalising Wigner's theorem

Abstract

We analyse linear maps of operator algebras ${\mathcal{B}}_H(\mathcal{H})$ mapping the set of rank-$k$ projectors onto the set of rank-$l$ projectors surjectively. We give a complete characterisation of such maps for prime $n=\dim \mathcal{H}$. The solution is known for $k=l=1$ as the Wigner's theorem.

6 pages

References in corpus (4)

• Optimal entanglement criterion for mixed quantum states
• Clean Positive Operator Valued Measures
• Separability criteria and bounds for entanglement measures
• Two elementary proofs of the Wigner theorem on symmetry in quantum mechanics

Cited by in corpus (3)

• Positive Maps From Irreducibly Covariant Operators
• Symmetry witnesses
• Wigner's type theorem in terms of linear operators which send projections of a fixed rank to projections of other fixed rank