In the quantum compression scheme proposed by Schumacher, Alice compresses a message that Bob decompresses. In that approach, there is some probability of failure and, even when successful, some distortion of the state. For sufficiently large blocklengths, both of these imperfections can be made arbitrarily small while achieving a compression rate that asymptotically approaches the source coding bound. However, direct implementation of Schumacher compression suffers from poor circuit complexity. In this paper, we consider a slightly different approach based on classical syndrome source coding. The idea is to use a linear error-correcting code and treat the message to be compressed as an error pattern. If the message is a correctable error (i.e., a coset leader) then Alice can use the error-correcting code to convert her message to a corresponding quantum syndrome. An implementation of this based on polar codes is described and simulated. As in classical source coding based on polar codes, Alice maps the information into the ``frozen" qubits that constitute the syndrome. To decompress, Bob utilizes a quantum version of successive cancellation coding.

翻译：在舒马赫提出的量子压缩方案中，爱丽丝压缩信息，鲍勃解压缩。该方法存在一定的失败概率，即使成功，也会导致量子态的失真。当块长度足够大时，这两种缺陷都可以任意减小，同时压缩率渐近地达到信源编码界。然而，舒马赫压缩的直接实现存在电路复杂度过高的问题。本文考虑一种基于经典伴随式信源编码的略微不同的方法。其核心思想是利用线性纠错码，将待压缩的消息视为一种错误模式。如果该消息是可纠正错误（即陪集首），则爱丽丝可利用该纠错码将其消息转换为相应的量子伴随式。本文描述并模拟了基于极化码的实现方案。与基于极化码的经典信源编码类似，爱丽丝将信息映射到构成伴随式的"冻结"量子比特上。鲍勃则利用连续消除编码的量子版本进行解压缩。