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Minyi Huang

Publications and source records attributed to Minyi Huang.

At least 19 recordsLinked to original sources
arXiv2026

Risk-sensitive linear-quadratic-Gaussian graphon mean-field games

This paper investigates a class of linear-quadratic-Gaussian risk-sensitive graphon mean-field games, involving an asymptotically infinite population of heterogeneous agents distributed across an asymptotically infinite network, where each agent aims to minimize an exponential cost functional reflecting its risk sensitivity. Following the Nash certainty equivalence methodology, an auxiliary risk-sensitive optimal control problem is constructed and further combined with a consistency condition to determine decentralized strategies of the agents. The well-posedness of the resulting graphon mean-field game equation system, consisting of a family of fully coupled forward-backward differential equations, is established by a fixed point approach under a contraction condition, and by the method of continuity under an operator monotonicity condition, respectively. To prove the epsilon-Nash equilibrium property of the obtained decentralized strategies, one faces significant challenge since the usual L^2 error estimates on mean-field approximations are no longer adequate due to unboundedness of the integrand in the exponentiated cost. The proof will be accomplished by establishing certain exponentiated error estimates instead of L^2 error estimates. Finally, a numerical example is provided to illustrate our results.

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arXiv2025

An uncertainty relation in the case of four observables

Uncertainty is a fundamental and important concept in quantum mechanics. In this work, using the technique in matrix theory, we propose an uncertainty relation of four observables and show that the uncertainty constant is tight. It is argued that this method can deal with the several known uncertainty relations for two, three and four observables in a unified way. The result is also compared with other uncertainty relations of four observables.

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arXiv2025

Triple measurements uncertainty and the distinguishment between the separable and entangled states

Uncertainty and entanglement are both profound and key concepts in quantum theory. For three observables, the tightest uncertainty constants for both product and summation forms are revealed. In this work, we give an alternative proof for three observables, also with a physical interpretation of the uncertainty constants. Our results show that such constants are intimately connected with the distinguishment between separable and entangled states.

quant-ph↗
arXiv2025

The adiabatic theorem for non-Hermitian quantum systems with real eigenvalues and the complex geometric phase

The adiabatic theorem is one of the most interesting and significant theorems in quantum mechanics. However, the adiabatic theorem can fail for general non-Hermitian quantum systems. In this paper, by utilizing the complex geometric phase, the functional calculus for biorthogonal systems and the Gr\"{o}nwall inequality, we prove rigorously that the adiabatic theorem is still valid for diagonalizable non-Hermitian systems with real eigenvalues. The proof also justifies the definition of a complex Berry phase for non-Hermitian systems, in both Abelian and non-Abelian cases.

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arXiv2025

Mean field social optimization: feedback person-by-person optimality and the dynamic programming equation

We consider mean field social optimization in nonlinear diffusion models. By dynamic programming with a representative agent employing cooperative optimizer selection, we derive a new Hamilton--Jacobi--Bellman (HJB) equation to be called the master equation of the value function. Under some regularity conditions, we establish $\epsilon$-person-by-person optimality of the master equation-based control laws, which may be viewed as a necessary condition for nearly attaining the social optimum. A major challenge in the analysis is to obtain tight estimates, within an error of $O(1/N)$, of the social cost having order $O(N)$. This will be accomplished by multi-scale analysis via constructing two auxiliary master equations. We illustrate explicit solutions of the master equations for the linear-quadratic (LQ) case, and give an application to systemic risk.

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arXiv2023

Linear Convergent Distributed Nash Equilibrium Seeking with Compression

Information compression techniques are majorly employed to address the concern of reducing communication cost over peer-to-peer links. In this paper, we investigate distributed Nash equilibrium (NE) seeking problems in a class of non-cooperative games over directed graphs with information compression. To improve communication efficiency, a compressed distributed NE seeking (C-DNES) algorithm is proposed to obtain a NE for games, where the differences between decision vectors and their estimates are compressed. The proposed algorithm is compatible with a general class of compression operators, including both unbiased and biased compressors. Moreover, our approach only requires the adjacency matrix of the directed graph to be row-stochastic, in contrast to past works that relied on balancedness or specific global network parameters. It is shown that C-DNES not only inherits the advantages of conventional distributed NE algorithms, achieving linear convergence rate for games with restricted strongly monotone mappings, but also saves communication costs in terms of transmitted bits. Finally, numerical simulations illustrate the advantages of C-DNES in saving communication cost by an order of magnitude under different compressors.

cs.MA↗
arXiv2023

Entanglement and Teleportation in a 1-D Network with Repeaters

The most simplest form of quantum network is an one dimensional quantum network with a single player in each node. In remote entanglement distribution each of the players carry out measurement at the intermediate nodes to produce an entangled state between initial and final node which are remotely separated. It is imperative to say that the flow of information as well as the percolation of entanglement in a network between the source and target node is an important area of study. This will help us to understand the limits of the resource states as well as the measurements that are carried out in the process of remote entanglement distribution. In this article we investigate how the concurrence of the final entangled state obtained is connected with the concurrences of the initial entangled states present in a 1-D chain. We extend the works done for the pure entangled states for mixed entangled states like Werner states, Bell diagonal states and for general mixed states. We did not limit ourselves to a situation where the measurements are happening perfectly. We also investigate how these relations change when we consider imperfect swapping. We obtain the limits on the number of swappings as well as the success probability measurements to ensure the final state to be entangled state after swapping. In addition to these we also investigate on how much quantum information can be sent from the initial node to the final node (by computing the teleportation fidelity) when the measurement is perfect and imperfect with the same set of examples. Here also we obtain the limits on the number of swapping and the success probability of measurement to ensure that the final state obtained is capable of transferring the information . These results have tremendous future applications in sending quantum information between two quantum processors in remote entangled distribution.

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arXiv2022

Internal nonlocality in generally dilated Hermiticity

According to von Neumann, the global Hamiltonian of whole universe must be Hermitian in order to keep the eigenvalues real and to construct a self-consistent quantum theory. In addition to the open system approach by introducing environmental degrees of freedom to a small system, a global Hermitian Hamiltonian can also be generated through the dilation from a small Hilbert space. For example, a local non-Hermitian $\cal PT$-symmetric system can be simulated with a global Hermitian one by the Naimark dilation. When shared by Alice and Bob, the internal nonlocality in such dilated Hermitian systems is revealed recently, but only with a two-fold structure. In this paper, we extend such a discussion to the generalized case when the two-fold structure breaks. The internal nonlocality is discussed with different correlation pictures and the corresponding correlation bounds. Our results provide a device-independent test on the reliability of the simulation in the global Hermiticity.

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arXiv2022

Solvable dilation model of $\cal PT$-symmetric systems

The dilation method is a practical way to experimentally simulate non-Hermitian, especially $\cal PT$-symmetric quantum systems. However, the time-dependent dilation problem cannot be explicitly solved in general. In this paper, we present a simple yet non-trivial exactly solvable dilation problem with two dimensional time-dependent $\cal PT$-symmetric Hamiltonian. Our system is initially set in the unbroken $\cal PT$-symmetric phase and later goes across the so-called exceptional point and enters the broken $\cal PT$-symmetric phase. For this system, the dilated Hamiltonian and the evolution of $\cal PT$-symmetric system are analytically worked out. Our result clearly showed that the exceptional points do not have much physical relevance in a \textit{time-dependent} system.

quant-ph↗
arXiv2021

Graphon Mean Field Games and the GMFG Equations

The emergence of the graphon theory of large networks and their infinite limits has enabled the formulation of a theory of the centralized control of dynamical systems distributed on asymptotically infinite networks (Gao and Caines, IEEE CDC 2017, 2018). Furthermore, the study of the decentralized control of such systems was initiated in (Caines and Huang, IEEE CDC 2018, 2019), where Graphon Mean Field Games (GMFG) and the GMFG equations were formulated for the analysis of non-cooperative dynamic games on unbounded networks. In that work, existence and uniqueness results were introduced for the GMFG equations, together with an epsilon-Nash theory for GMFG systems which relates infinite population equilibria on infinite networks to finite population equilibria on finite networks. Those results are rigorously established in this paper.

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arXiv2021

LQG Graphon Mean Field Games: Analysis via Graphon Invariant Subspaces

This paper studies approximate solutions to large-scale linear quadratic stochastic games with homogeneous nodal dynamics parameters and heterogeneous network couplings within the graphon mean field game framework in [2]-[4]. A graphon time-varying dynamical system model is first formulated to study the finite and then limit problems of linear quadratic Gaussian graphon mean field games (LQG-GMFG). The Nash equilibrium of the limit problem is then characterized by two coupled graphon time-varying dynamical systems. Sufficient conditions are established for the existence of a unique solution to the limit LQG-GMFG problem. For the computation of LQG-GMFG solutions two methods are established and employed where one is based on fixed point iterations and the other on a decoupling operator Riccati equation; furthermore, two corresponding sets of solutions are established based on spectral decompositions. Finally, a set of numerical simulations on networks associated with different types of graphons are presented.

eess.SY↗
arXiv2021

Linear quadratic mean field games: Decentralized $O(1/N)$-Nash equilibria

This paper studies an asymptotic solvability problem for linear quadratic (LQ) mean field games with controlled diffusions and indefinite weights for the state and control in the costs. We employ a rescaling approach to derive a low dimensional Riccati ordinary differential equation (ODE) system, which characterizes a necessary and sufficient condition for asymptotic solvability. The rescaling technique is further used for performance estimates, establishing an $O(1/N)$-Nash equilibrium for the obtained decentralized strategies.

math.OC↗
arXiv2021

Linear quadratic mean field social optimization: Asymptotic solvability and decentralized control

This paper studies asymptotic solvability of a linear quadratic (LQ) mean field social optimization problem with controlled diffusions and indefinite state and control weights. Starting with an $N$-agent model, we employ a rescaling approach to derive a low-dimensional Riccati ordinary differential equation (ODE) system, which characterizes a necessary and sufficient condition for asymptotic solvability. The decentralized control obtained from the mean field limit ensures a bounded optimality loss in minimizing the social cost having magnitude $O(N)$, which implies an optimality loss of $O(1/N)$ per agent. We further quantify the efficiency gain of the social optimum with respect to the solution of the mean field game.

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arXiv2021

Extracting the internal nonlocality from the dilated Hermiticity

To effectively realize a $\cal PT$-symmetric system, one can dilate a $\cal PT$-symmetric Hamiltonian to some global Hermitian one and simulate its evolution in the dilated Hermitian system. However, with only a global Hermitian Hamiltonian, how do we know whether it is a dilation and is useful for simulation? To answer this question, we consider the problem of how to extract the internal nonlocality in the Hermitian dilation. We unveil that the internal nonlocality brings nontrivial correlations between the subsystems. By evaluating the correlations with local measurements in three different pictures, the resulting different expectations of the Bell operator reveal the distinction of the internal nonlocality. When the simulated $\cal PT$-symmetric Hamiltonian approaches its exceptional point, such a distinction tends to be most significant. Our results clearly make a difference between the Hermitian dilation and other global Hamiltonians without internal nonlocality. They also provide the figure of merit to test the reliability of the simulation, as well as to verify a $\cal PT$-symmetric (sub)system.

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arXiv2021

Linear-Quadratic Mean Field Games with a Major Player: Nash certainty equivalence versus master equations

Mean field games with a major player were introduced in (Huang, 2010) within a linear-quadratic (LQ) modeling framework. Due to the rich structure of major-minor player models, the past ten years have seen significant research efforts for different solution notions and analytical techniques. For LQ models, we address the relation between three solution frameworks: the Nash certainty equivalence (NCE) approach in (Huang, 2010), master equations, and asymptotic solvability, which have been developed starting with different ideas. We establish their equivalence relationships.

math.OC↗
arXiv2021

To quantify the difference of $η$-inner products in $\cal PT$-symmetric theory

In this paper, we consider a typical continuous two dimensional $\cal PT$-symmetric Hamiltonian and propose two different approaches to quantitatively show the difference between the $η$-inner products. Despite the continuity of Hamiltonian, the $η$-inner product is not continuous in some sense. It is shown that the difference between the $η$-inner products of broken and unbroken $\cal PT$-symmetry is lower bounded. Moreover, such a property can lead to an uncertainty relation.

quant-ph↗
arXiv2021

Binary Mean Field Stochastic Games: Stationary Equilibria and Comparative Statics

This paper considers mean field games in a multi-agent Markov decision process (MDP) framework. Each player has a continuum state and binary action, and benefits from the improvement of the condition of the overall population. Based on an infinite horizon discounted individual cost, we show existence of a stationary equilibrium, and prove its uniqueness under a positive externality condition. We further analyze comparative statics of the stationary equilibrium by quantitatively determining the impact of the effort cost.

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