A d-dimensional second-order topological insulator (SOTI) can host topologically protected (d-2)-dimensional gapless boundary modes. Here, we show that a 2D non-Hermitian SOTI can host zero-energy ...modes at its corners. In contrast to the Hermitian case, these zero-energy modes can be localized only at one corner. A 3D non-Hermitian SOTI is shown to support second-order boundary modes, which are localized not along hinges but anomalously at a corner. The usual bulk-corner (hinge) correspondence in the second-order 2D (3D) non-Hermitian system breaks down. The winding number (Chern number) based on complex wave vectors is used to characterize the second-order topological phases in 2D (3D). A possible experimental situation with ultracold atoms is also discussed. Our work lays the cornerstone for exploring higher-order topological phenomena in non-Hermitian systems.
Quantum coherence and quantum correlations are of fundamental and practical significance for the development of quantum mechanics. They are also cornerstones of quantum computation and quantum ...communication theory. Searching physically meaningful and mathematically rigorous quantifiers of them are long-standing concerns of the community of quantum information science, and various faithful measures have been introduced so far. We review in this paper the measures of discordlike quantum correlations for bipartite and multipartite systems, the measures of quantum coherence for any single quantum system, and their relationship in different settings. Our aim is to provide a full review about the resource theory of quantum coherence, including its application in many-body systems, and the discordlike quantum correlations which were defined based on the various distance measures of states. We discuss the interrelations between quantum coherence and quantum correlations established in an operational way, and the fundamental characteristics of quantum coherence such as their complementarity under different basis sets, their duality with path information of an interference experiment, their distillation and dilution under different operations, and some new viewpoints of the superiority of the quantum algorithms from the perspective of quantum coherence. Additionally, we review properties of geometric quantum correlations and quantum coherence under noisy quantum channels. Finally, the main progresses for the study of quantum correlations and quantum coherence in the relativistic settings are reviewed. All these results provide an overview for the conceptual implications and basic connections of quantum coherence, quantum correlations, and their potential applications in various related subjects of physics.
The law of statistical physics dictates that generic closed quantum many-body systems initialized in nonequilibrium will thermalize under their own dynamics. However, the emergence of many-body ...localization (MBL) owing to the interplay between interaction and disorder, which is in stark contrast to Anderson localization, which only addresses noninteracting particles in the presence of disorder, greatly challenges this concept, because it prevents the systems from evolving to the ergodic thermalized state. One critical evidence of MBL is the long-time logarithmic growth of entanglement entropy, and a direct observation of it is still elusive due to the experimental challenges in multiqubit single-shot measurement and quantum state tomography. Here we present an experiment fully emulating the MBL dynamics with a 10-qubit superconducting quantum processor, which represents a spin-1/2 XY model featuring programmable disorder and long-range spin-spin interactions. We provide essential signatures of MBL, such as the imbalance due to the initial nonequilibrium, the violation of eigenstate thermalization hypothesis, and, more importantly, the direct evidence of the long-time logarithmic growth of entanglement entropy. Our results lay solid foundations for precisely simulating the intriguing physics of quantum many-body systems on the platform of large-scale multiqubit superconducting quantum processors.
We demonstrate that multipartite entanglement is able to characterize one-dimensional symmetry-protected topological order, which is witnessed by the scaling behavior of the quantum Fisher ...information of the ground state with respect to the spin operators defined in the dual lattice. We investigate an extended Kitaev chain with a Z symmetry identified equivalently by winding numbers and paired Majorana zero modes at each end. The topological phases with high winding numbers are detected by the scaling coefficient of the quantum Fisher information density with respect to generators in different dual lattices. Containing richer properties and more complex structures than bipartite entanglement, the dual multipartite entanglement of the topological state has promising applications in robust quantum computation and quantum metrology, and can be generalized to identify topological order in the Kitaev honeycomb model.
Abstract The density fields constructed by traditional mass assignment methods are susceptible to irritating discreteness, which hinders morphological measurements of cosmic large-scale structure ...(LSS) through Minkowski functionals (MFs). To alleviate this issue, fixed-kernel smoothing methods are commonly used in the literature, at the expense of losing substantial structural information. In this work, we propose to measure MFs with the Delaunay tessellation field estimation (DTFE) technique, with the goal of maximizing the extraction of morphological information from sparse tracers. We perform our analyses starting from matter fields and progressively extending to halo fields. At the matter-field level, we elucidate how discreteness affects morphological measurements of LSS. Then, by comparing with the traditional Gaussian smoothing scheme, we preliminarily showcase the advantages of DTFE for enhancing measurements of MFs from sparse tracers. At the halo-field level, we first numerically investigate various systematic effects on MFs of DTFE fields, which are induced by finite voxel sizes, halo number densities, halo weightings, and redshift space distortions (RSDs), respectively. Then, we explore the statistical power of MFs measured with DTFE for extracting the cosmological information encoded in RSDs. We find that MFs measured with DTFE exhibit improvements by ∼2 orders of magnitude in discriminative power for RSD effects and by a factor of ∼3–5 in constraining power on the structure growth rate over the MFs measured with Gaussian smoothing. These findings demonstrate the remarkable enhancements in statistical power of MFs achieved by DTFE, showing enormous application potentials for our method in extracting various key cosmological information from galaxy surveys.
In this work, we propose a powerful probe of neutrino effects on the large-scale structure (LSS) of the Universe, i.e., Minkowski functionals (MFs). The morphology of LSS can be fully described by ...four MFs. This tool, with strong statistical power, is robust to various systematics and can comprehensively probe all orders of N-point statistics. By using a pair of high-resolution N-body simulations, for the first time, we comprehensively studied the subtle neutrino effects on the morphology of LSS. For an ideal LSS survey of volume ∼ 1.73 Gpc3/h3, neutrino signals are mainly detected from void regions with a significant level up to ∼ 10σ and ∼ 300σ for CDM and total matter density fields, respectively. This demonstrates its enormous potential for much improving the neutrino mass constraint in the data analysis of upcoming ambitious LSS surveys.
Understanding various phenomena in nonequilibrium dynamics of closed quantum many-body systems, such as quantum thermalization, information scrambling, and nonergodic dynamics, is crucial for modern ...physics. Using a ladder-type superconducting quantum processor, we perform analog quantum simulations of both the XX-ladder model and the one-dimensional XX model. By measuring the dynamics of local observables, entanglement entropy, and tripartite mutual information, we signal quantum thermalization and information scrambling in the XX ladder. In contrast, we show that the XX chain, as free fermions on a one-dimensional lattice, fails to thermalize to the Gibbs ensemble, and local information does not scramble in the integrable channel. Our experiments reveal ergodicity and scrambling in the controllable qubit ladder, and open the door to further investigations on the thermodynamics and chaos in quantum many-body systems.
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