عنوان مجله
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INTERNATIONAL JOURNAL OF GEOMETRIC METHODS IN MODERN PHYSICS
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چکیده
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A quantum injective frame is a frame whose measurements for density operators can be
used as a distinguishing feature in a quantum system, and the frame quantum detection
problem demands a characterization of all such frames. Very recently, the quantum
detection problem for continuous as well as discrete frames in both finite and infinite
dimensional Hilbert spaces received significant attention. The quantum detection problem
pertaining to the characterization of informationally complete positive operatorvalued
measures (POVM) can be split into two cases: The quantum injectivity or state
separability problem and the rang analysis or quantum state estimation problem. Building
upon this notion, this note is aimed at the quantum detection problem for fusion
frames. The injectivity of a family of vectors and a family of closed subspaces is characterized
in terms of some operator equations in Hilbert–Schmidt and trace classes.
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