56 citations · 164 across the 18 of their papers we have counts for
18 papers
On the expected number of critical points of locally isotropic Gaussian random fields
Hao Xu, Haoran Yang, Qiang Zeng
We consider locally isotropic Gaussian random fields on the -dimensional Euclidean space for fixed . Using the so called Gaussian Orthogonally Invariant matrices first studie…
Controlled entanglement source for quantum cryptography
Qiang Zeng, Haoyang Wang, Huihong Yuan +5
Quantum entanglement has become an essential resource in quantum information processing. Existing works employ entangled quantum states to perform various tasks, while little atten…
Hessian spectrum at the global minimum and topology trivialization of locally isotropic Gaussian random fields
Hao Xu, Qiang Zeng
We study the energy landscape near the ground state of a model of a single particle in a random potential with trivial topology. More precisely, we find the large dimensional limit…
Complexity of Gaussian random fields with isotropic increments: critical points with given indices
Antonio Auffinger, Qiang Zeng
We study the landscape complexity of the Hamiltonian where is a smooth Gaussian process with isotropic increments on . This mode…
One-way Einstein-Podolsky-Rosen steering beyond qubits
Qiang Zeng
Quantum steering has been exploited as an important resource in modern quantum information processing. Owing to its directional nature, some quantum states that are asymmetric unde…
Reliable experimental certification of one-way Einstein-Podolsky-Rosen steering
Qiang Zeng, Jiangwei Shang, H. Chau Nguyen +1
Quantum steering is a recently-defined form of quantum correlation which lies at the heart of quantum mechanics. In difference from other types of quantum correlations, quantum ste…
Complexity of Gaussian random fields with isotropic increments
Antonio Auffinger, Qiang Zeng
We study the energy landscape of a model of a single particle on a random potential, that is, we investigate the topology of level sets of smooth random fields on o…
Existence of two-step replica symmetry breaking for the spherical mixed p-spin glass at zero temperature
Antonio Auffinger, Qiang Zeng
We provide the first examples of two-step replica symmetry breaking (2-RSB) models for the spherical mixed p-spin glass at zero temperature. Precisely, we show that for a certain c…
The SK model is infinite step replica symmetry breaking at zero temperature
Antonio Auffinger, Wei-Kuo Chen, Qiang Zeng
We prove that the Parisi measure of the mixed p-spin model at zero temperature has infinitely many points in its support. This establishes Parisi's prediction that the functional o…
Harmonic analysis approach to Gromov--Hausdorff convergence for noncommutative tori
Marius Junge, Sepideh Rezvani, Qiang Zeng
We show that the rotation algebras are limit of matrix algebras in a very strong sense of convergence for algebras with additional Lipschitz structure. Our results generalize to hi…
Free monotone transport for infinite variables
Brent Nelson, Qiang Zeng
We extend the free monotone transport theorem of Guionnet and Shlyakhtenko to the case of infinite variables. As a first application, we provide a criterion for when mixed -Gaus…
An application of free transport to mixed -Gaussian algebras
Brent Nelson, Qiang Zeng
We consider the mixed -Gaussian algebras introduced by Speicher which are generated by the variables , where and…
Ultraproduct methods for mixed -Gaussian algebras
Marius Junge, Qiang Zeng
We provide a unified ultraproduct approach for constructing Wick words in mixed -Gaussian algebras, which are generated by , , where $a_ia^*_j - q_{…
Subgaussian 1-cocycles on discrete groups
Marius Junge, Qiang Zeng
We prove the Poincaré inequalities with constant for -cocycles on countable discrete groups under Bakry--Emery's -criterion. These inequalities determine…
Poincaré type inequalities for group measure spaces and related transportation cost inequalities
Qiang Zeng
Let be a countable discrete group with an orthogonal representation on a real Hilbert space . We prove Poincaré inequalities for the group measure space $L_\infty(…
Kolmogorov's law of the iterated logarithm for noncommutative martingales
Qiang Zeng
We prove Kolmogorov's law of the iterated logarithm for noncommutative martingales. The commutative case was due to Stout. The key ingredient is an exponential inequality proved re…
Noncommutative martingale deviation and Poincaré type inequalities with applications
Marius Junge, Qiang Zeng
We prove a deviation inequality for noncommutative martingales by extending Oliveira's argument for random matrices. By integration we obtain a Burkholder type inequality with sati…
Noncommutative Bennett and Rosenthal inequalities
Marius Junge, Qiang Zeng
In this paper we extend the Bernstein, Prohorov and Bennett inequalities to the noncommutative setting. In addition we provide an improved version of the noncommutative Rosenthal i…