Soklakov Andrei N, Schack Rüdiger
Department of Mathematics, Royal Holloway, University of London, Egham, Surrey TW20 0EX, United Kingdom.
Phys Rev E Stat Nonlin Soft Matter Phys. 2002 Sep;66(3 Pt 2A):036212. doi: 10.1103/PhysRevE.66.036212. Epub 2002 Sep 23.
We show that the coarse-grained quantum baker's map exhibits a linear entropy increase at an asymptotic rate given by the Kolmogorov-Sinai entropy of the classical chaotic baker's map. The starting point of our analysis is a symbolic representation of the map on a string of N qubits, i.e., an N-bit register of a quantum computer. To coarse grain the quantum evolution, we make use of the decoherent histories formalism. As a by-product, we show that the condition of medium decoherence holds asymptotically for the coarse-grained quantum baker's map.
我们表明，粗粒化量子面包师映射在渐近速率下呈现线性熵增加，该速率由经典混沌面包师映射的柯尔莫哥洛夫 - 西奈熵给出。我们分析的起点是在一串N个量子比特上对该映射进行符号表示，即量子计算机的一个N位寄存器。为了对量子演化进行粗粒化，我们利用退相干历史形式。作为一个副产品，我们表明对于粗粒化量子面包师映射，中等退相干条件渐近成立。
