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Abstract: We use classical results from the theory of linear preserver problems tocharacterize operators that send the set of pure states with Schmidt rank nogreater than k back into itself, extending known results characterizingoperators that send separable pure states to separable pure states. We alsoprovide a new proof of an analogous statement in the multipartite setting. Weuse these results to develop a bipartite version of a classical result aboutthe structure of maps that preserve rank-1 operators and then characterize theisometries for two families of norms that have recently been studied in quantuminformation theory. We see in particular that for k at least 2 the operatornorms induced by states with Schmidt rank k are invariant only under localunitaries, the swap operator and the transpose map. However, in the k = 1 casethere is an additional isometry: the partial transpose map.



Autor: Nathaniel Johnston

Fuente: https://arxiv.org/







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