One of the fundamental tasks in quantum information theory is quantum data compression, which can be realized via quantum autoencoders that first compress quantum states to low-dimensional ones and then recover to the original ones with a reference state. When taking a pure reference state, there exists an upper bound for the encoding fidelity, which limits the compression of states with high entropy. To overcome the entropy inconsistency, we allow the reference state to be a mixed state and propose a cost function that combines the encoding fidelity and the quantum mutual information. We consider the reference states to be a mixture of maximally mixed states and pure states and propose three strategies for setting the ratio of mixedness. Numerical simulations of different states and experimental implementations on IBM quantum computers illustrate the effectiveness of our approach.

量子信息论的基本任务之一是量子数据压缩，这可以通过量子自动编码器来实现，量子自动编码器首先将量子态压缩到低维态，然后用参考态恢复到原始态。当采用纯参考状态时，编码保真度存在上限，这限制了高熵状态的压缩。为了克服熵不一致，我们允许参考状态为混合状态，并提出一种结合编码保真度和量子互信息的成本函数。我们认为参考状态是最大混合状态和纯状态的混合，并提出了三种设置混合比率的策略。不同状态的数值模拟和 IBM 量子计算机上的实验实现说明了我们方法的有效性。