Premium
On the Local Unitary Equivalence of States of Multi‐partite Systems
Author(s) -
Ziman M.,
Štelmachović P.,
Bužek V.
Publication year - 2001
Publication title -
fortschritte der physik
Language(s) - English
Resource type - Journals
SCImago Journal Rank - 1.469
H-Index - 71
eISSN - 1521-3978
pISSN - 0015-8208
DOI - 10.1002/1521-3978(200110)49:10/11<1123::aid-prop1123>3.0.co;2-q
Subject(s) - unitary state , unitary transformation , mathematics , hilbert space , equivalence (formal languages) , pure mathematics , quantum state , quantum , discrete mathematics , algebra over a field , quantum mechanics , physics , law , political science
Two pure states of a multi‐partite system are alway are related by a unitary transformation acting on the Hilbert space of the hole system. This transformation involves multi‐partite transformations. On the other hand some quantum information protocols such as the quantum teleportation and quantum dense coding are based on equivalence of some classes of states of bi‐partite systems under the action of local (one‐particle) unitary operations.In this paper we adress the question: “Under what conditions are the two states states, ϱ and σ of a multi‐partite system locally unitary equivalent?” We present a set of conditions which have to be satisfied in order that the two states are locally unitary equivalent.In addition, we study whether it is possible to prepare a state of a multi‐qudit system. Which is devided into two parts A and B , by unitary operations acting only on the systems A and B , separately.