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The problem of combating de-coherence by weak measurements has already been studied for the amplitude damping channel and for specific input states. We generalize this to a large four-parameter family of qubit channels and for the average fidelity over all pure states. As a by-product we classify all the qubit channels which have one invariant pure state and show that the parameter manifold of these channels is isomorphic to S 2 × S 1 × S 1 and contains many interesting sub-classes of channels. By tuning the parameter of the weak measurement, we show that it is possible to increase the average input-output fidelity without blocking too many particles to pass through the channel. Quantitative... 

We introduce the concepts of cohering and decohering power of quantum channels. Using the axiomatic definition of the coherence measure, we show that the optimization required for calculations of these measures can be restricted to pure input states and hence greatly simplified. We then use two examples of this measure, one based on the skew information and the other based on the l1 norm; we find the cohering and decohering measures of a number of one-, two-, and n-qubit channels. Contrary to the view at first glance, it is seen that quantum channels can have cohering power. It is also shown that a specific property of a qubit unitary map is that it has equal cohering and decohering power in... 

In general quantum operations, or quantum channels cannot be inverted by physical operations, i.e., by completely positive trace-preserving maps. An arbitrary state passing through a quantum channel loses its fidelity with the input. Given a quantum channel E, we discuss the concept of its quasi-inverse as a completely positive trace-preserving map Eqi which when composed with E increases its average input-output fidelity in an optimal way. The channel Eqi comes as close as possible to the inverse of a quantum channel. We give a complete classification of such maps for qubit channels and provide quite a few illustrative examples. © 2020 American Physical Society