Quantifying quantum coherence based on the Tsallis relative operator entropy

Abstract: 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.