Coherence resource power of isocoherent states

LOSADA, MARCELO; BOSYK, GUSTAVO M.; FREYTES, HECTOR; SERGIOLI, GIUSEPPE

Scientific Reports

Nature Publishing Group

Año: 2022 vol. 12 p. 1 - 10

We address the problem of comparing quantum states with the same amount of coherence in termsof their coherence resource power given by the preorder of incoherent operations. For any coherencemeasure, two states with null or maximum value of coherence are equivalent with respect to thatpreorder. This is no longer true for intermediate values of coherence when pure states of quantumsystems with dimension greater than two are considered. In particular, we show that, for any value ofcoherence (except the extreme values, zero and the maximum), there are infnite incomparable purestates with that value of coherence. These results are not peculiarities of a given coherence measure,but common properties of every well-behaved coherence measure. Furthermore, we show that forqubit mixed states there exist coherence measures, such as the relative entropy of coherence, thatadmit incomparable isocoherent states.