Abstract
We continue the study of similarities between quantum information theory and theory of classical Gaussian signals. The possibility of using quantum entropy for classical Gaussian signals was explored a long time ago. Recently we demonstrated that some basic quantum channels can be represented as linear transforms of classical Gaussian signals. Here we consider bipartite quantum systems and show that an important quantum channel given by the partial trace operation has a simple classical representation, namely, a coordinate projection of a classical “prequantum signal.” We also consider the classical signal realization of quantum channels corresponding to state transforms in the process of measurement. The latter induces a difficult interpretational problem — the output signal corresponding to one system depends on a measurement that has been done on the second system. This situation might be interpreted as a sign of quantum nonlocality, action at a distance. Although we do not exclude such a possibility, i.e., that, in complete accordance with Bell, the creation of a realistic prequantum model is impossible without action at a distance, we found another interpretation of this situation that is not related to quantum nonlocality.
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Manuscript submitted by the authors in English on July 26, 2010.
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Khrennikov, A., Ohya, M. & Watanabe, N. Interplay between classical and quantum signals: partial trace and measurement channels. J Russ Laser Res 31, 589–598 (2010). https://doi.org/10.1007/s10946-010-9179-6
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DOI: https://doi.org/10.1007/s10946-010-9179-6