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Unraveling the secrets of how much nonstabilizerness a quantum dynamic can generate is crucial for harnessing the power of magic states, the essential resources for achieving quantum advantage and realizing fault-tolerant quantum computation. In this work, we introduce the amortized $\alpha$-stabilizer R\'enyi entropy, a magic monotone for unitary operations that quantifies the nonstabilizerness generation capability of quantum dynamics. Amortization is key in quantifying the magic of quantum dynamics, as we reveal that nonstabilizerness generation can be enhanced by prior nonstabilizerness in input states when considering the $\alpha$-stabilizer R\'enyi entropy, while this is not the case for robustness of magic or stabilizer extent. We demonstrate the versatility of the amortized $\alpha$-stabilizer R\'enyi entropy in investigating the nonstabilizerness resources of quantum dynamics of computational and fundamental interest. In particular, we establish improved lower bounds on the $T$-count of quantum Fourier transforms and the quantum evolutions of one-dimensional Heisenberg Hamiltonians, showcasing the power of this tool in studying quantum advantages and the corresponding cost in fault-tolerant quantum computation., Comment: 5 + 7 pages, 2 figures

Wave-particle duality, the cornerstone of quantum mechanics, illustrates essential trade-offs between two complementary aspects of quantum systems. Captured by Bohr's complementarity principle, the wave-particle duality relation indicates that perfect path discrimination in a multipath interferometer obliterates interference patterns and vice versa. In this work, from the perspective of coherence resource manipulation, we uncover a novel duality relation between quantum coherence and distinguishability in ensembles of mutually orthogonal pure states. We demonstrate the sum of `co-bits', coherence preserved after discrimination, and classical bits, distinguishability extracted through perfect discrimination is bounded. One cannot simultaneously extract all classical information and preserve coherence. Such duality relation exposes an inherent trade-off between quantum coherence and classical distinguishability resources. Our findings offer a fresh perspective and advance our understanding of the intrinsic complementary relationship between quantum and classical resources., Comment: 7 pages plus appendix

The unique features of entanglement and non-locality in quantum systems, where there are pairs of bipartite states perfectly distinguishable by general entangled measurements yet indistinguishable by local operations and classical communication, hold significant importance in quantum entanglement theory, distributed quantum information processing, and quantum data hiding. This paper delves into the entanglement cost for discriminating two bipartite quantum states, employing positive operator-valued measures (POVMs) with positive partial transpose (PPT) to achieve optimal success probability through general entangled measurements. First, we introduce an efficiently computable quantity called the spectral PPT-distance of a POVM to quantify the localness of a general measurement. We show that it can be a lower bound for the entanglement cost of optimal discrimination by PPT POVMs. Second, we establish an upper bound on the entanglement cost of optimal discrimination by PPT POVMs for any pair of states. Leveraging this result, we show that a pure state can be optimally discriminated against any other state with the assistance of a single Bell state. This study advances our understanding of the pivotal role played by entanglement in quantum state discrimination, serving as a crucial element in unlocking quantum data hiding against locally constrained measurements., Comment: 17 pages

In quantum computing, the nonstabilizerness of quantum operations is crucial for understanding and quantifying quantum speedups. In this study, we explore the phenomena of nonstabilizerness of the quantum SWITCH, a novel structure that allows quantum states to pass through operations in a superposition of different orders, outperforming traditional circuits in numerous tasks. To assess its nonstabilizerness, we propose the magic resource capacity of a quantum process to quantitatively examine the nonstabilizerness of general quantum transformations. We find that the completely stabilizer-preserving operations, which cannot generate magic states under standard conditions, can be transformed to do so when processed by the quantum SWITCH. Furthermore, when considering the impact of noise, although the nonstabilizerness of each path may be annihilated, their superposition could still preserve the overall nonstabilizerness. These findings reveal the unique properties of the quantum SWITCH and open avenues in research on nonstabilizer resources of general quantum architecture., Comment: 6+7 pages, 7 figures

In the realm of fault-tolerant quantum computing, stabilizer operations play a pivotal role, characterized by their remarkable efficiency in classical simulation. This efficiency sets them apart from non-stabilizer operations within the quantum computational theory. In this Letter, we investigate the limitations of classically-simulable measurements in distinguishing quantum states. We demonstrate that any pure magic state and its orthogonal complement of odd prime dimensions cannot be unambiguously distinguished by stabilizer operations, regardless of how many copies of the states are supplied. We also reveal intrinsic similarities and distinctions between the quantum resource theories of magic states and entanglement in quantum state discrimination. The results emphasize the inherent limitations of classically-simulable measurements and contribute to a deeper understanding of the quantum-classical boundary., Comment: 5+8 pages, 1 figure

Given the existing COVID-19 pandemic worldwide, it is critical to systematically study the interactions between hosts and coronaviruses including SARS-Cov, MERS-Cov, and SARS-CoV-2 (cause of COVID-19). We first created four host-pathogen interaction (HPI)-Outcome postulates, and generated a HPI-Outcome model as the basis for understanding host-coronavirus interactions (HCI) and their relations with the disease outcomes. We hypothesized that ontology can be used as an integrative platform to classify and analyze HCI and disease outcomes. Accordingly, we annotated and categorized different coronaviruses, hosts, and phenotypes using ontologies and identified their relations. Various COVID-19 phenotypes are hypothesized to be caused by the backend HCI mechanisms. To further identify the causal HCI-outcome relations, we collected 35 experimentally-verified HCI protein-protein interactions (PPIs), and applied literature mining to identify additional host PPIs in response to coronavirus infections. The results were formulated in a logical ontology representation for integrative HCI-outcome understanding. Using known PPIs as baits, we also developed and applied a domain-inferred prediction method to predict new PPIs and identified their pathological targets on multiple organs. Overall, our proposed ontology-based integrative framework combined with computational predictions can be used to support fundamental understanding of the intricate interactions between human patients and coronaviruses (including SARS-CoV-2) and their association with various disease outcomes., Comment: 32 pages, 1 table, 6 figures

To improve the global optimization ability of traditional GEP algorithm, a Multicellular gene expression programming algorithm based on fuzzy control (Multicellular GEP Algorithm Based On Fuzzy Control, MGEP-FC) is proposed. The MGEP-FC algorithm describes the size of cross rate, mutation rate and real number mutation rate by constructing fuzzy membership function. According to the concentration and dispersion of individual fitness values in population, the crossover rate, mutation rate and real number set mutation rate of genetic operation are dynamically adjusted. In order to make the diversity of the population continue in the iterative process, a new genetic operation scheme is designed, which combines the new individuals with the parent population to build a temporary population, and the diversity of the temporary and subpopulation are optimized. The results of 12 Benchmark optimization experiments show that the MGEP-FC algorithm has been greatly improved in stability, global convergence and optimization speed., Comment: in Chinese