Entropic cohering power in quantum operations

Kaifeng Bu, Asutosh Kumar, Lin Zhang +1 more

Zhengjun Xi, Ming‐Liang Hu, Yongming Li +1 more

By using relative entropy of coherence, we characterize the coherence gain induced by some quantum evolutions, including the cohering power of unitary operations and the decohering power of quantum operations. We find that the cohering power of the controlled unitary operation can be reduced to the cohering power of the corresponding unitary operation. We observe that the global coherence generated via incoherent operation applied to the system and an incoherent ancilla do not exceed the amount of coherence contained in the initial system. Our result provides a much tighter lower bound of coherence for the initial quantum state, and give an interesting chain of inequalities for coherence, quantum correlation and entanglement. We also strengthen the relations between quantum correlations and coherence.

Jozef Gruska, Hiroshi Imai, Keiji Matsumoto

Tariq Aziz, Meng-Long Song, Ye Liu +1 more

We present a geometric approach to characterize quantum coherence through entropic diagrams that map the eigenvalue spectra of density matrices into a two-dimensional space defined by von Neumann and Tsallis-2 entropies. We derive the relative entropy of coherence using the Schur-Horn majorization theorem and introduce a new coherence monotone—the relative cross-entropy of coherence—which is valid only for mixed states and whose behavior under various classes of quantum operations is examined in detail. Interestingly, our approach reveals distinct entropy-coherence distillation curves and introduces the notion of degenerate coherence distillation, where coherence is concentrated into higher-dimensional, partially uniform spectral configurations. Although the degenerate coherence distillation does not always surpass standard qubit coherence distillation in asymptotic rate, it may offer an operationally meaningful alternative for protocols that require high-dimensional or symmetrically structured coherence resources. In addition, we derive a refined entropic uncertainty relation that incorporates the maximum eigenvalue of post-measurement states, which leads to state-dependent bounds that improve upon the conventional Maassen-Uffink bound. These findings suggest that entropic diagrams may serve not only as a useful visual and analytical tool but also as a guide for developing resource-efficient strategies in quantum information processing.

Sarah Chehade, Anna Vershynina

Chiranjib Mukhopadhyay, Arun Kumar Pati, Sk Sazim

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.