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Error-correction codes are central for fault-tolerant information processing. Here we develop a rigorous framework to describe various coding models based on quantum resource theory of superchannels. We find, by treating codings as superchannels, a hierarchy of coding models can be established, including the entanglement assisted or unassisted settings, and their local versions. We show that these coding models can be used to classify error-correction codes and accommodate different computation and communication settings depending on the data type, side channels, and pre-/postprocessing. We believe the coding hierarchy could also inspire new coding models and error-correction methods.

We study partial coherence and its connections with entanglement. First, we provide a sufficient and necessary condition for bipartite pure state transformation under partial incoherent operations: A bipartite pure state can be transformed to another one if and only if a majorization relationship holds between their partial coherence vectors. As a consequence, we introduce the concept of maximal partial coherent states in the sense that they can be used to construct any bipartite state of the same system via partial incoherent operations. Second, we provide a strategy to construct measures of partial coherence by the use of symmetric concave functions. Third, we establish some relationships between partial coherence and entanglement. We show that the minimal partial coherence under local unitary operations is a measure of entanglement for bipartite pure states, which can be extended to all mixed states by convex-roof. We also show that partial coherence measures are induced through maximal entanglement under partial incoherent operations for bipartite pure states. There is a one-to-one correspondence between entanglement and partial coherence measures., Comment: 12 pages, 2 figures, 1 table

The optimal state-independent lower bounds for the sum of variances or deviations of observables are of significance for the growing number of experiments that reach the uncertainty limited regime. We present a framework for computing the tight uncertainty relations of variance or deviation via determining the uncertainty regions, which are formed by the tuples of two or more of quantum observables in random quantum states induced from the uniform Haar measure on the purified states. From the analytical formulae of these uncertainty regions, we present state-independent uncertainty inequalities satisfied by the sum of variances or deviations of two, three and arbitrary many observables, from which experimentally friend entanglement detection criteria are derived for bipartite and tripartite systems., Comment: 42 pages; a few typoes in the published version are corrected in this version

We propose a unified framework for random locations exhibiting some probabilistic symmetries such as stationarity, self-similarity, etc. A theorem of Noether's type is proved, which gives rise to a conservation law describing the change of the density function of a random location as the interval of interest changes. We also discuss the boundary and near boundary behavior of the distributions of the random locations., Comment: 26 pages

Memory (non-Markovian) effect is found to be able to accelerate quantum evolution [S. Deffner and E. Lutz, Phys. Rev. Lett. 111, 010402 (2013)]. In this work, for an atom in a structured reservoir, we show that the mechanism for the speedup is not only related to non-Markovianity but also to the population of excited states under a given driving time. In other words, it is the competition between non-Markovianity and population of excited states that ultimately determines the acceleration of quantum evolution in memory environment. A potential experimental realization for verifying the above phenomena is discussed by using a nitrogen-vacancy (N-V) center embedded in a planar photonic crystal cavity (PCC) under the current experimental conditions., Comment: 6 pages, 4 figures, published version

Memory effect of non-Markovian dynamics in open quantum systems is often believed to be beneficial for quantum information processing. In this work, we employ an experimentally controllable two-photon open system, with one photon experiencing a dephasing environment and the other being free from noise, to show that non-Markovian effect may also have a negative impact on quantum tasks such as remote state preparation: For a certain period of controlled time interval, stronger non-Markovian effect yields lower fidelity of remote state preparation, as opposed to the common wisdom that more information leads to better performance. As a comparison, a positive non-Markovian effect on the RSP fidelity with another typical non-Markovian noise is analyzed. Consequently, the observed dual character of non-Markovian effect will be of great importance in the field of open systems engineering., Comment: 7 pages, 5 figures

Quantum Fisher information, as an intrinsic quantity for quantum states, is a central concept in quantum detection and estimation. When quantum measurements are performed on quantum states, classical probability distributions arise, which in turn lead to classical Fisher information. In this article, we exploit the classical Fisher information induced by quantum measurements, and reveal a rich hierarchical structure of such measurement-induced Fisher information. We establish a general framework for the distribution and transfer of the Fisher information. In particular, we illustrate three extremal distribution types of the Fisher information: the locally owned type, the locally inaccessible type, and the fully shared type. Furthermore, we indicate the significant role played by the distribution and flow of the Fisher information in some physical problems, e.g., the non-Markovianity of open quantum processes, the environment-assisted metrology, the cloning and broadcasting, etc., Comment: 6 pages

It is well known that classical information can be cloned, but non-orthogonal quantum states cannot be cloned, and non-commuting quantum states cannot be broadcast. We conceive a scenario in which the object we want to broadcast is the statistical distinguishability, as quantified by quantum Fisher information, about a signal parameter encoded in quantum states. We show that quantum Fisher information cannot be cloned, whilst it might be broadcast even when the input states are non-commuting. This situation interpolates between cloning of classical information and no-broadcasting of quantum information, and indicates a hybrid way of information broadcasting which is of particular significance from both practical and theoretical perspectives., Comment: 5 pages. Improved version. Any comments is welcome