arXiv subjects

Hong-Bin Chen

Publications and source records attributed to Hong-Bin Chen.

At least 37 records · Page 2Linked to original sources

arXiv2025

Uniqueness of Parisi measures for enriched convex vector spin glass

In the PDE approach to mean-field spin glasses, it has been observed that the free energy of convex spin glass models could be enriched by adding an extra parameter in its definition, and that the thermodynamic limit of the enriched free energy satisfies a partial differential equation. This parameter can be thought of as a matrix-valued path, and the usual free energy is recovered by setting this parameter to be the constant path taking only the value $0$. Furthermore, the enriched free energy can be expressed using a variational formula, which is a natural extension of the Parisi formula for the usual free energy. For models with scalar spins the Parisi formula can be expressed as an optimization problem over a convex set, and it was shown in [arXiv:1402.5132] that this problem has a unique optimizer thanks to a strict convexity property. For models with vector spins, the Parisi formula cannot easily be written as a convex optimization problem. In this paper, we generalize the uniqueness of Parisi measures proven in [arXiv:1402.5132] to the enriched free energy of models with vector spins when the extra parameter is a strictly increasing path. Our approach relies on a Gateaux differentiability property of the free energy and the envelope theorem.

math.PR↗

arXiv2025

Differentiability and overlap concentration in optimal Bayesian inference

In this short note, we consider models of optimal Bayesian inference of finite-rank tensor products. We add to the model a linear channel parametrized by $h$. We show that at every interior differentiable point $h$ of the free energy (associated with the model), the overlap concentrates at the gradient of the free energy and the minimum mean-square error converges to a related limit. In other words, the model is replica-symmetric at every differentiable point. At any signal-to-noise ratio, such points $h$ form a full-measure set (hence $h=0$ belongs to the closure of these points). For a sufficiently low signal-to-noise ratio, we show that every interior point is a differentiable point.

math.PR↗

arXiv2024

On free energy of non-convex multi-species spin glasses

In [arXiv:2311.08980], it was shown that if the limit of the free energy in a non-convex vector spin glass model exists, it must be a critical value of a certain functional. In this work, we extend this result to multi-species spin glass models with non-convex interactions, where spins from different species may lie in distinct vector spaces. Since the species proportions may be irrational and the existence of the limit of the free energy is not generally known, non-convex multi-species models cannot be approximated by vector spin models in a straightforward manner, necessitating more careful treatment.

cond-mat.dis-nn↗

arXiv2024

Unveiling the nonclassicality within quasi-distribution representations through deep learning

To unequivocally distinguish genuine quantumness from classicality, a widely adopted approach focuses on the negative values of a quasi-distribution representation as compelling evidence of nonclassicality. Prominent examples include the dynamical process nonclassicality characterized by the canonical Hamiltonian ensemble representation (CHER) and the nonclassicality of quantum states characterized by the Wigner function. However, to construct a multivariate joint quasi-distribution function with negative values from experimental data is typically highly cumbersome. Here we propose a computational approach utilizing a deep generative model, processing three marginals, to construct the bivariate joint quasi-distribution functions. We first apply our model to tackle the challenging problem of the CHERs, which lacks universal solutions, rendering the problem ground-truth (GT) deficient. To overcome the GT deficiency of the CHER problem, we design optimal synthetic datasets to train our model. While trained with synthetic data, the physics-informed optimization enables our model to capture the detrimental effect of the thermal fluctuations on nonclassicality, which cannot be obtained from any analytical solutions. This underscores the reliability of our approach. This approach also allows us to predict the Wigner functions subject to thermal noises. Our model predicts the Wigner functions with a prominent accuracy by processing three marginals of probability distributions. Our approach also provides a significant reduction of the experimental efforts of constructing the Wigner functions of quantum states, giving rise to an efficient alternative way to realize the quantum state tomography.

quant-ph↗

arXiv2024

Hamilton-Jacobi equations with monotone nonlinearities on convex cones

We study the Cauchy problem of a Hamilton-Jacobi equation with the spatial variable in a closed convex cone. A monotonicity assumption on the nonlinearity allows us to prescribe no condition on the boundary of the cone. We show the well-posedness of the equation in the viscosity sense and prove several properties of the solution: monotonicity, Lipschitzness, and representations by variational formulas.

math.AP↗

arXiv2024

Photonic non-Markovianity identification by quantum process capabilities of non-CP processes

A Markovian quantum process can be arbitrarily divided into two or more legitimate completely-positive (CP) subprocesses. When at least one non-CP process exists among the divided processes, the dynamics is considered non-Markovian. However, how to utilize minimum experimental efforts, without examining all process input states and using entanglement resources, to identify or measure non-Markovianity is still being determined. Herein, we propose a method to quantify non-CP processes for identifying and measuring non-Markovianity without the burden of state optimization and entanglement. This relies on the non-CP processes as new quantum process capabilities and can be systematically implemented by quantum process tomography. We additionally provide an approach for witnessing non-Markovianity by analyzing at least four system states without process tomography. We faithfully demonstrate that our method can be explicitly implemented using all-optical setups and applied to identify the non-Markovianity of single-photon and two-photon dynamics in birefringent crystals. Our results can also be used to explore non-Markovianity in other dynamical systems where process or state tomography is implementable.

quant-ph↗

arXiv2024

Deep learning the hierarchy of steering measurement settings of qubit-pair states

Quantum steering has attracted increasing research attention because of its fundamental importance, as well as its applications in quantum information science. Here we leverage the power of the deep learning model to infer the steerability of quantum states with specific numbers of measurement settings, which form a hierarchical structure. A computational protocol consisting of iterative tests is constructed to overcome the optimization, meanwhile, generating the necessary training data. According to the responses of the well-trained models to the different physics-driven features encoding the states to be recognized, we can numerically conclude that the most compact characterization of the Alice-to-Bob steerability is Alice's regularly aligned steering ellipsoid; whereas Bob's ellipsoid is irrelevant. We have also provided an explanation to this result with the one-way stochastic local operations and classical communication. Additionally, our approach is versatile in revealing further insights into the hierarchical structure of quantum steering and detecting the hidden steerability.

quant-ph↗

arXiv2023

On the self-overlap in vector spin glasses

We consider vector spin glass models with self-overlap correction. Since the limit of free energy is an infimum, we use arguments analogous to those for generic models to show the following: 1) the averaged self-overlap converges; 2) the self-overlap concentrates; 3) the infimum optimizes over paths whose right endpoints are the limit of self-overlap. Lastly, using these, we directly verify the equivalence between the variational formula obtained in [arXiv:2303.16284] and Panchenko's generalized Parisi formula in [Ann. Probab., 46(2):865-896].

math.PR↗

arXiv2023

Parisi PDE and convexity for vector spins

We consider mean-field vector spin glasses with self-overlap correction. The limit of free energy is known to be the Parisi formula, which is an infimum over matrix-valued paths. We decompose such a path into a Lipschitz matrix-valued path and the quantile function of a one-dimensional probability measure. For such a pair, we associate a Parisi PDE generalized for vector spins. Under mild conditions, we rewrite the Parisi formula in terms of solutions of the PDE. Moreover, for each fixed Lipschitz path, the Parisi functional is strictly convex over probability measures.

math.PR↗

arXiv2023

On Parisi measures of Potts spin glasses with correction

In the Potts spin glass model, inspired by the symmetry argument in [arXiv:2310.06745] for the constrained free energy, we study the free energy with self-overlap correction. Similarly, we simplify the Parisi-type formula, originally an infimum over matrix-valued paths, into an optimization over real-valued paths, which can be interpreted as quantile functions of probability measures on the unit interval. Minimizers are usually called Parisi measures. Using results in [arXiv:2311.10446] generalizing the Auffinger-Chen convexity argument, we deduce the uniqueness of the Parisi measure. The approach in [arXiv:2310.06745] is to perturb the covariance function of the Hamiltonian into one associated with the generic model, prove the results there, and then reduce the perturbation. Here, we choose to perturb the model by adding an external field parametrized by Ruelle probability cascades. This is used in the Hamilton-Jacobi equation approach and we directly apply results in [arXiv:2311.08980].

math.PR↗

arXiv2023

Self-overlap correction simplifies the Parisi formula for vector spins

We propose a simpler approach to identifying the limit of free energy in a vector spin glass model by adding a self-overlap correction to the Hamiltonian. This avoids constraining the self-overlap and allows us to identify the limit with the classical Parisi formula, similar to the proof for scalar models with Ising spins. For the upper bound, the correction cancels self-overlap terms in Guerra's interpolation. For the lower bound, we add an extra perturbation term to make the self-overlap concentrate, a technique already used in [Probab. Math. Phys., 2(2):281-339, Ann. Inst. Henri Poincaré Probab. Stat., 59(3):1143-1182] to ensure the Ghirlanda-Guerra identities. We then remove the correction using a Hamilton-Jacobi equation technique, which yields a formula similar to that in [Ann. Probab., 46(2):865-896]. Additionally, we sketch a direct proof of the main result in [Electron. J. Probab. 25(23):1-17].

math.PR↗

arXiv2023

Adaptively partitioned analog quantum simulation on near-term quantum computers: The nonclassical free-induction decay of NV centers in diamond

The idea of simulating quantum physics with controllable quantum devices had been proposed several decades ago. With the extensive development of quantum technology, large-scale simulation, such as the analog quantum simulation tailoring an artificial Hamiltonian mimicking the system of interest, has been implemented on elaborate quantum experimental platforms. However, due to the limitations caused by the significant noises and the connectivity, analog simulation is generically infeasible on near-term quantum computing platforms. Here we propose an alternative analog simulation approach on near-term quantum devices. Our approach circumvents the limitations by adaptively partitioning the bath into several groups based on the performance of the quantum devices. We apply our approach to simulate the free induction decay of the electron spin in a diamond NV$^-$ center coupled to a huge number of nuclei and investigate the nonclassicality induced by the nuclear spin polarization. The simulation is implemented collaboratively with authentic devices and simulators on IBM quantum computers. We have also applied our approach to address the nonclassical noise caused by the crosstalk between qubits. This work sheds light on a flexible approach to simulate large-scale materials on noisy near-term quantum computers.

quant-ph↗

arXiv2023

Conformal invariance of random currents: a stability result

We show the convergence of the single sourceless critical random current to a limit identifiable with the nested CLE(3). Our approach is based on viewing the random current as a perturbation of the Ising interface, which is known to converge to CLE(3). Instead of focusing solely on the random current, we provide a general framework for the stability of scaling limits under the perturbation by superimposing an independent Bernoulli percolation.

math.PR↗

arXiv2022

A PDE perspective on the Aizenman-Sims-Starr scheme

The limit free energy of an enriched mixed $p$-spin spin glass model has been identified with the solution of a Hamilton-Jacobi equation. In this note, we remark that the Aizenman-Sims-Starr scheme yields a subsolution to the equation.

math.PR↗

arXiv2022

Precession-induced nonclassicality of the free induction decay of NV centers by a dynamical polarized nuclear spin bath

The ongoing exploration of the ambiguous boundary between the quantum and the classical worlds has spurred substantial developments in quantum science and technology. Recently, the nonclassicality of dynamical processes has been proposed from a quantum-information-theoretic perspective, in terms of witnessing nonclassical correlations with Hamiltonian ensemble simulations. To acquire insights into the quantum-dynamical mechanism of the process nonclassicality, here we propose to investigate the nonclassicality of the electron spin free-induction-decay process associated with an NV$^-$ center. By controlling the nuclear spin precession dynamics via an external magnetic field and nuclear spin polarization, it is possible to manipulate the dynamical behavior of the electron spin, showing a transition between classicality and nonclassicality. We propose an explanation of the classicality-nonclassicality transition in terms of the nuclear spin precession axis orientation and dynamics. We have also performed a series of numerical simulations supporting our findings. Consequently, we can attribute the nonclassical trait of the electron spin dynamics to the behavior of nuclear spin precession dynamics.

quant-ph↗

arXiv2022

Maxwell's two-demon engine under pure dephasing noise

The interplay between thermal machines and quantum correlations is of great interest in both quantum thermodynamics and quantum information science. Recently, a quantum Szilárd engine has been proposed, showing that the quantum steerability between a Maxwell's demon and a work medium can be beneficial to a work extraction task. Nevertheless, this type of quantum-fueled machine is usually fragile in the presence of decoherence effects. We provide an example of the pure dephasing process, showing that the engine's quantumness can be degraded. Therefore, in this work, we tackle this question by introducing a second demon who can access a control system and make the work medium pass through two dephasing channels in a manner of quantum superposition. Furthermore, we provide a quantum circuit to simulate our proposed concept and test it on IBMQ and IonQ quantum computers.

quant-ph↗

arXiv2022

Fenchel-Moreau identities on convex cones

A pointed convex cone naturally induces a partial order, and further a notion of nondecreasingness for functions. We consider extended real-valued functions defined on the cone. Monotone conjugates for these functions can be defined in an analogous way to the standard convex conjugate. The only difference is that the supremum is taken over the cone instead of the entire space. We give sufficient conditions for the cone under which the corresponding Fenchel-Moreau biconjugation identity holds for proper, convex, lower semicontinuous, and nondecreasing functions defined on the cone. In addition, we show that these conditions are satisfied by a class of cones known as perfect cones.

math.FA↗

arXiv2022

Rare transitions in noisy heteroclinic networks

We study small white noise perturbations of planar dynamical systems with heteroclinic networks in the limit of vanishing noise. We show that the probabilities of transitions between various cells that the network tessellates the plane into decay as powers of the noise magnitude. We show that the most likely scenario for the realization of these rare transition events involves spending atypically long times in the neighborhoods of certain saddle points of the network. We describe the hierarchy of time scales and clusters of accessibility associated with these rare transition events. We discuss applications of our results to homogenization problems and to the invariant distribution asymptotics. At the core of our results are local limit theorems for exit distributions obtained via methods of Malliavin calculus.

math.PR↗