عنوان مجله
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Poincare Journal of Analysis and Applications
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کلیدواژهها
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positive operator-valued measure, quantum detection problem,
injectivity, Schatten p-class, frame, g-frame.
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چکیده
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The main issues in quantum detection theory are the injectivity and
state estimation problems, which recently linked and partially studied via frame
theory on Hilbert spaces. Inspired by some recent researches and works on the
quantum detection problem by (discrete) frames, continuous frames and fusion
frames, in this note we examine the quantum detection problem for generalized
frames (g-frames). In the theory of g-frames, instead of using the frame element
itself, we use a family of bounded operators.We characterize injectivity problem
by g-frames and with the help of these characterizations, we give some equivalent
conditions for the injectivity problems. We answer the injectivity problems both for
trace and Hilbert-Schmidt classes of operators.
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