We establish a direct link between the out-of-time order correlator, a recently suggested measure for probing information scrambling in quantum chaotic systems, and the Loschmidt echo, a wellappreciated diagnostic that captures the dynamical aspect of quantum chaos in the time domain. Two models has been studied to reveal the connection between these two quantities for both early growth (scrambling) regime and the intermediate decay regime. Implications to the Maldacena bound on the decay rate is also briefly discussed.

It is a fundamental problem in physics of what principle limits the correlations as predicted by our current description of nature, based on quantum mechanics. One possible explanation is the "global exclusivity" principle recently discussed in Phys. Rev. Lett. 110, 060402 (2013). In this work we show that this principle actually has a much stronger restriction on the probability distribution. We provide a tight constraint inequality imposed by this principle and prove that this principle singles out quantum correlations in scenarios represented by any graph. Our result implies that the exclusivity principle might be one of the fundamental principles of nature.

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