Entropic No-Disturbance as a Physical Principle

TL;DR

This paper develops an entropic framework for quantum nonlocality and contextuality, revealing monogamy relations and implications for quantum networks, by extending no-disturbance principles with information-theoretic measures.

Contribution

It introduces an entropic form of the no-disturbance principle, characterizes entropic contextuality and nonlocality, and establishes monogamy relations relevant for quantum communication.

Findings

Entropic nonlocal correlations are monogamous.

Entropic contextuality tests are monogamous.

Entropic monogamy relations are extended to multiparty scenarios.

Abstract

The celebrated Bell-Kochen-Specker no-go theorem asserts that quantum mechanics does not present the property of realism, the essence of the theorem is the lack of a joint probability distributions for some experiment settings. In this work, we exploit the information theoretic form of the theorem using information measure instead of probabilistic measure and indicate that quantum mechanics does not present such entropic realism neither. The entropic form of Gleason's no-disturbance principle is developed and it turns out to be characterized by the intersection of several entropic cones. Entropic contextuality and entropic nonlocality are investigated in depth in this framework. We show how one can construct monogamy relations using entropic cone and basic Shannon-type inequalities. The general criterion for several entropic tests to be monogamous is also developed, using the criterion, we demonstrate that entropic nonlocal correlations are monogamous, entropic contextuality tests are monogamous and entropic nonlocality and entropic contextuality are also monogamous. Finally, we analyze the entropic monogamy relations for multiparty and many-test case, which plays a crucial role in quantum network communication.