Entropy, Superposition and Dynamical Maps

Antonio Zecca A

Garani Ananthakrishna, E. C. G. Sudarshan, Vittorio Gorini

Heide Narnhofer

We estimate the dynamical entropy for the quantized CAT map. It turns out that the result depends on the rotation parameter and positivity of the dynamical entropy demands asymptotic abelianness. Further the estimates offer a counterexample to the additivity of the dynamical entropy for tensor products.

Etang Chen

George Androulakis, Duncan Wright

Linearity of a dynamical entropy means that the dynamical entropy of the n-fold composition of a dynamical map with itself is equal to n times the dynamical entropy of the map for every positive integer n. We show that the quantum dynamical entropy introduced by Słomczyński and Życzkowski is nonlinear in the time interval between successive measurements of a quantum dynamical system. This is in contrast to Kolmogorov-Sinai dynamical entropy for classical dynamical systems, which is linear in time. We also compute the exact values of quantum dynamical entropy for the Hadamard walk with varying Lüders-von Neumann instruments and partitions.

Jincheng Zhang

Quantum information entropy is a critical component of quantum computing, and current optimization methods often struggle to efficiently utilize this information. This paper introduces the Dynamic Entropy Mapping Algorithm (DEMA), a novel algorithm designed to dynamically adjust quantum bit allocation to maximize quantum information yield. The core mechanism leverages quantum information entropy as a dynamic optimization target, employing iterative adjustments to optimize the quantum state. We demonstrate the effectiveness of DEMA through simulations and theoretical analysis, showcasing a significant improvement in quantum information utilization.