Quantum Predictive Filtering

Abstract: How can relevant information be extracted from a quantum process? In many situations, only some part of the total information content produced by an information source is useful. Can one then find an efficient encoding, in the sense of retaining the largest fraction of relevant information? This paper offers one possible solution by giving a generalization of a classical method designed to retain as much relevant information as possible in a lossy data compression. A key feature of the method is to introduce a second information source to define relevance. We quantify the advantage a quantum encoding has over the best classical encoding in general, and we demonstrate using examples that a substantial quantum advantage is possible. A main result, however, is that if the relevant information is purely classical, then a classical encoding is optimal.