On the Brukner-Zeilinger approach to quantum information

What is it about?

In the paper, the following important question is addressed. What is the correct measure of information in quantum measurements? Despite of many efforts, there is no general consensus with respect to a proper answer. Brukner and Zeilinger proposed and motivated one of most fruitful approaches to this question. Their approach was later criticized for several reasons. The present paper suggests an intuitive and genuine expansion of the Brukner-Zeilinger approach. It is actually leads to an operationally invariant measure of information and does not suffer from the problem mentioned earlier. Rather surprising connection between the information approach and symmetric informationally complete measurements in quantum mechanics has been observed. It is shown that the Brukner-Zeilinger approach can be reasonably treated in the case of limited detector efficiency. We also discuss potential applications of the proposed ideas in studies of systems for quantum information processing.

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Why is it important?

The original approach of Brukner and Zeilinger was based on the use of a complete set of mutually unbiased bases (MUBs). Except for prime power dimensions, the existence of a complete set of MUBs is an open question. In the paper, three additional schemes for obtaining operationally invariant measure are proposed. It is very important since these schemes can certainly been implemented, at least in prnciple. Another essential step is a proper formulation of the approach of Brukner and Zeilinger in the case of detection inefficiencies. The proposed schemes could be used for estimating some properties of quantum channels given as a "black box".

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