Coherence is a fundamental ingredient in quantum physics and a key resource in quantum information processing. The quantification of quantum coherence is of great importance. We present a family of coherence quantifiers based on the Tsallis relative operator entropy. Shannon inequality and its reverse one in Hilbert space operators derived by Furuta [Linear Algebra Appl. 381 (2004) 219] are extended in terms of the parameter of the Tsallis relative operator entropy. These quantifiers are shown to satisfy all the standard criteria for a well-defined measure of coherence and include some existing coherence measures as special cases. Detailed examples are given to show the relations among the measures of quantum coherence.

相干性是量子物理学的基本要素，也是量子信息处理的关键资源。量子相干的量化非常重要。我们提出基于Tsallis相对算子熵的相干量词系列。由Furuta推导的希尔伯特空间算子中的Shannon不等式及其倒数[Linear Algebra Appl。381（2004）219]扩展了Tsallis相对算子熵的参数。这些量词显示满足定义好的一致性度量的所有标准条件，并且包括一些现有的一致性度量作为特殊情况。给出了详细的例子来说明量子相干性度量之间的关系。