Trace distance from the viewpoint of quantum operation techniques
نویسنده
چکیده
In the present paper the trace distance is exposed within the quantum operations formalism. The definition of the trace distance in terms of a maximum over all quantum operations is given. It is shown that for any pair of different states there is uncountably infinite number of maximizing quantum operations. Conversely, for any operation of described type there is uncountably infinite number of those pairs of states that the maximum is reached by the operation. A behavior of the trace distance under considered operations is studied. Relations and distinctions between the trace distance and the sine distance are discussed.
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