  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.
