Quantifying coherence with quantum addition
This work provides a new theoretical tool for quantifying quantum coherence in mixed states, relevant to quantum information theory.
The authors prove a reverse entropy power equality for quantum addition channels, which allows them to analytically confirm a previously conjectured inequality. They introduce a new coherence measure based on the relative entropic difference between quantum addition and classical mixture, which is bounded by the relative entropy of coherence and used to derive a state-dependent uncertainty relation.
Quantum addition channels have been recently introduced in the context of deriving entropic power inequalities for finite dimensional quantum systems. We prove a reverse entropy power equality which can be used to analytically prove an inequality conjectured recently for arbitrary dimension and arbitrary addition weight. We show that the relative entropic difference between the output of such a quantum additon channel and the corresponding classical mixture quantitatively captures the amount of coherence present in a quantum system. This new coherence measure admits an upper bound in terms of the relative entropy of coherence and is utilized to formulate a state-dependent uncertainty relation for two observables. Our results may provide deep insights to the origin of quantum coherence for mixed states that truly come from the discrepancy between quantum addition and the classical mixture.