Entropic no-disturbance as a physical principle

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.arXiv:1803.07925v1 [quant-ph]

Quantum space-time marginal problem: global causal structure from local causal information

“…This has crucial applications in our understanding of Bell nonlocality and quantum contextuality [22][23][24][25][26], for which the local (non-contextual) hidden variable (LHV/NCHV) model is proved to be equivalent to a joint probability model. The existence of LHV/NCHV models can be turned into a classical marginal problem [25,27,[38][39][40].…”

Antilinear superoperator, quantum geometric invariance, and antilinear symmetry for higher-dimensional quantum systems

“…The phenomenon is now known as monogamy of quantum correlations. It's shown that there exist monogamy relations for Bell nonlocality [24][25][26][27][28], quantum steering [29], and entanglement [17,30,31]. In this section, we study the monogamy equalities of entanglement restricted by quantum geometric invariance.…”