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Quantum Information Processing

Measurement-induced entropy increment for quantifying genuine coherence

Yue Dai, Jun Hu, Zhou Zhang, Chengjie Zhang, Yuli Dong, Xue‐Feng Wang

Published Aug 1, 2021• 2 citations
Publisher
DOI
10.1007/s11128-021-03199-6

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Relative entropy of coherence can be written as an entropy difference of the original state and the incoherent state closest to it when measured by relative entropy. The natural question is, if we generalize this situation to Tsallis or Rényi entropies, would it define good coherence measures? In other words, we define a difference between Tsallis entropies of the original state and the incoherent state closest to it when measured by Tsallis relative entropy. Taking Rényi entropy instead of the Tsallis entropy, leads to the well-known distance-based Rényi coherence, which means this expression defined a good coherence measure. Interestingly, we show that Tsallis entropy does not generate even a genuine coherence monotone, unless it is under a very restrictive class of operations. Additionally, we provide continuity estimates for both Tsallis and Rényi coherence expressions. Furthermore, we present two coherence measures based on the closest incoherent state when measures by Tsallis or Rényi relative entropy.
Abstract We establish the rigorous operational meaning of dynamical total coherence within the resource non-increasing (RNI) framework for the task of single-parameter quantum channel estimation. By connecting distance-based and maximal-increment-based dynamical coherence measures with the right-logarithmic-derivative (RLD) Fisher information and the Cramér-Rao bound (CRB), we prove that each dynamical coherence measure directly determines the fundamental precision limit of channel parameter estimation. We show that the diamondnorm measure yields a tight error lower bound, the induced trace-norm measure gives a simplified bound for device-limited scenarios, the relative-entropy measure governs the asymptotic error-exponent rate, the l 2 -based measure quantifies the precision gain from optimal input states, and the RLD-Fisher-based measure provides an achievable error upper bound. This work unifies dynamical resource theory with quantum channel estimation and endows dynamical total coherence with clear, task-oriented operational significance.
We propose relative entropy-based quantifiers for genuine multipartite total, quantum, and classical correlations. These correlation measures are applied to investigate the generation of genuine multiparticle correlations in decoherent dynamics induced by the interaction of two qubits with local-independent environments. We consider amplitude- and phase-damping channels and compare their capabilities to spread information through the creation of many-body correlations. We identify changes in behavior for the genuine four- and three-partite total correlations and show that, contrary to amplitude environments, phase-noise channels transform the bipartite correlation initially shared between the qubits into genuine multiparticle system-environment correlations.