A sufficient Entanglement Criterion Based On Quantum Fisher Information and Variance

We derive criterion in the form of inequality based on quantum Fisher information and quantum variance to detect multipartite entanglement. It can be regarded as complementary of the well-established PPT criterion in the sense that it can also detect bound entangled states. The inequality is motivated by Y.Akbari-Kourbolagh $et\ al.$[Phys. Rev A. 99, 012304 (2019)] which introduced a multipartite entanglement criterion based on quantum Fisher information. Our criterion is experimentally measurable for detecting any $N$-qudit pure state mixed with white noisy. We take several examples to illustrate that our criterion has good performance for detecting certain entangled states.Comment: 11 pages, 1 figur

Computation of the p6p^6 order low-energy constants with tensor sources

We present the results of calculations of the $p^4$ and $p^6$ order low-energy constants for the chiral Lagrangian with tensor sources for both two and three flavors of pseudoscalar mesons. This is a generalization of our previous work on similar calculations without tensor sources in terms of the quark self-energy $\Sigma(p^2)$, based on the first principle derivation of the low-energy effective Lagrangian and computation of the low-energy constants with some rough approximations. With the help of partial integration and some epsilon relations, we find that some $p^6$ order operators with tensor sources appearing in the literature are related to each other. That leaves 98 independent terms for $n$-flavor, 92 terms for three-flavor, and 65 terms for two-flavor cases. We also find that the odd-intrinsic-parity chiral Lagrangian with tensor sources cannot independently exist in any order of low-energy expansion.Comment: 29 page

Entropic uncertainty relations with quantum memory in a multipartite scenario

Entropic uncertainty relations demonstrate the intrinsic uncertainty of nature from an information-theory perspective. Recently, a quantum-memory-assisted entropic uncertainty relation for multiple measurements was proposed by Wu $et\ al.$ [Phys Rev A. 106. 062219 (2022)]. Interestingly, the quantum-memory-assisted entropic uncertainty relation for multiple measurement settings can be further generalized. In this work, we propose two complementary multipartite quantum-memory-assisted entropic uncertainty relations and our lower bounds depend on values of complementarity of the observables, (conditional) von-Neumann entropies, Holevo quantities, and mutual information. As an illustration, we provide several typical cases to exhibit that our bounds are tighter and outperform the previous bounds.Comment: 7 pages, 3 figure

New Class of Two-Loop Neutrino Mass Models with Distinguishable Phenomenology

We discuss a new class of neutrino mass models generated in two loops, and explore specifically three new physics scenarios: (A) doubly charged scalar, (B) dark matter, and (C) leptoquark and diquark, which are verifiable at the 14 TeV LHC Run-II. We point out how the different Higgs insertions will distinguish our two-loop topology with others if the new particles in the loop are in the simplest representations of the SM gauge group

Dynamical Computation on Coefficients of Electroweak Chiral Lagrangian from One-doublet and Topcolor-assisted Technicolor Models

Based on previous studies deriving the chiral Lagrangian for pseudo scalar mesons from the first principle of QCD, we derive the electroweak chiral Lagrangian and build up a formulation for computing its coefficients from one-doublet technicolor model and a schematic topcolor-assisted technicolor model. We find that the coefficients of the electroweak chiral Lagrangian for the topcolor-assisted technicolor model are divided into three parts: direct TC2 interaction part, TC1 and TC2 induced effective Z' particle contribution part, and ordinary quarks contribution part. The first two parts are computed in this paper and we show that the direct TC2 interaction part is the same as that in the one-doublet technicolor model, while effective Z' contributions are at least proportional to the p^2 order parameter \beta_1 in the electroweak chiral Lagrangian and typical features of topcolor-assisted technicolor model are that it only allows positive T and U parameters and the T parameter varies in the range 0\sim 1/(25\alpha), the upper bound of T parameter will decrease as long as Z' mass become large. The S parameter can be either positive or negative depending on whether the Z' mass is large or small. The Z' mass is also bounded above and the upper bound depend on value of T parameter. We obtain the values for all the coefficients of the electroweak chiral Lagrangian up to order of p^4.Comment: 52 pages, 15 figure

Electroweak Chiral Lagrangian for a Hypercharge-universal Topcolor Model

Electroweak chiral Lagrangian for a hypercharge-universal topcolor model is investigated. We find that the assignments of universal hypercharge improve the results obtained previously from K.Lane's prototype natural TC2 model by allowing a larger Z' mass resulting in a very small T parameter and the S parameter is still around the order of +1Comment: 12 pages, 7 figure

Computation of the p6 order chiral Lagrangian coefficients from the underlying theory of QCD

We present results of computing the p6 order low energy constants in the normal part of chiral Lagrangian both for two and three flavor pseudo-scalar mesons. This is a generalization of our previous work on calculating the p4 order coefficients of the chiral Lagrangian in terms of the quark self energy Sigma(p2) approximately from QCD. We show that most of our results are consistent with those we can find in the literature.Comment: 51 pages,2 figure

Slicing-free Inverse Regression in High-dimensional Sufficient Dimension Reduction

Sliced inverse regression (SIR, Li 1991) is a pioneering work and the most recognized method in sufficient dimension reduction. While promising progress has been made in theory and methods of high-dimensional SIR, two remaining challenges are still nagging high-dimensional multivariate applications. First, choosing the number of slices in SIR is a difficult problem, and it depends on the sample size, the distribution of variables, and other practical considerations. Second, the extension of SIR from univariate response to multivariate is not trivial. Targeting at the same dimension reduction subspace as SIR, we propose a new slicing-free method that provides a unified solution to sufficient dimension reduction with high-dimensional covariates and univariate or multivariate response. We achieve this by adopting the recently developed martingale difference divergence matrix (MDDM, Lee & Shao 2018) and penalized eigen-decomposition algorithms. To establish the consistency of our method with a high-dimensional predictor and a multivariate response, we develop a new concentration inequality for sample MDDM around its population counterpart using theories for U-statistics, which may be of independent interest. Simulations and real data analysis demonstrate the favorable finite sample performance of the proposed method

Parameterized Multi-observable Sum Uncertainty Relations

The uncertainty principle is one of the fundamental features of quantum mechanics and plays an essential role in quantum information theory. We study uncertainty relations based on variance for arbitrary finite $N$ quantum observables. We establish a series of parameterized uncertainty relations in terms of the parameterized norm inequalities, which improve the exiting variance-based uncertainty relations. The lower bounds of our uncertainty inequalities are non-zero unless the measured state is the common eigenvector of all the observables. Detailed examples are provided to illustrate the tightness of our uncertainty relations.Comment: 12 pages, 3 figure