量子資料傳輸之動態壓縮

Abstract

量子計算較傳統計算上佔優勢的地方，在於其平行計算的能力。更甚者，由於量子位元數目的增加與其系統擴大的程度是成指數相關，因而當此一事實與其平行計算的能力相結合，便隱含了其計算速度較之於傳統計算呈指數加倍的可能性。確實，對於某些特殊難解的問題，相較於傳統的演算法，量子演算法已經展現了其強大的計算優勢，也因此，針對量子資料在資訊理論上的一些問題，就成為了無可避免的探討課題。 資料的壓縮法，它是資料儲存與資訊傳遞時最重要的中心問題之一。在本論文中，在已知欲傳送之量子狀態集合(可將其視為一量子符號之集合）,但不知其傳送機率分佈的前提下，針對一序列從此集合中獨立且相同選取之純態量子位元，我們將結合量子版的靜態霍夫曼資料壓縮法與傳統的動態霍夫曼樹，來建構出量子版的動態霍夫曼資料壓縮法。 其中量子版的靜態霍夫曼資料壓縮法是由 Samuel, Christopher 和 Daniel 在2000年所提出。

The most important advantage of the quantum computing system is its power of parallelism. Moreover, the quantum system increases exponentially with the size of the particles contained by the system. Therefore it enables exponentially parallelism, which also implies the exponentially speed-up than possible classically. Indeed, quantum information has been shown that can provide significant advantages for certain problems, so a discussion of the quantum information theory seems unavoidable. The problem of compression is the central part of the storage and transmission of quantum data. In this thesis, we provide an adaptive quantum compression scheme, which combines the quantum Huffman coding scheme mentioned by Samuel, Christopher and Daniel in 2000, with the classical adaptive Huffman trees to compress a sequence of i.i.d. pure-state quantum signals, without the knowledge of the probability distribution for the given quantum symbol set.