相关论文: Dressed coherent states in finite quantum systems:…

A new representation of Game Theory is developed in this paper. State of players is represented by a density matrix, and payoff function is a set of hermitian operators, which when applied onto the density matrix give the payoff of players.…

A total set of states for which we have no resolution of the identity (a `pre-basis'), is considered in a finite dimensional Hilbert space. A dressing formalism renormalizes them into density matrices which resolve the identity, and makes…

An interaction system has a finite set of agents that interact pairwise, depending on the current state of the system. Symmetric decomposition of the matrix of interaction coefficients yields the representation of states by self-adjoint…

Coherent states are introduced and their properties are discussed for all simple quantum compact groups. The multiplicative form of the canonical element for the quantum double is used to introduce the holomorphic coordinates on a general…

Effect of replacing the classical game object with a quantum object is analyzed. We find this replacement requires a throughout reformation of the framework of Game Theory. If we use density matrix to represent strategy state of players,…

In the classical context, the cooperative game theory concept of the Shapley value has been adapted for post hoc explanations of machine learning models. However, this approach does not easily translate to eXplainable Quantum ML (XQML).…

We illustrate the mass and charge renormalization procedures in quantum field theory using, as an example, a simple model of interacting electrons and photons. It is shown how addition of infinite renormalization counterterms to the…

A geometric characterization of transition amplitudes between coherent states, or equivalently, of the hermitian scalar product of holomorphic cross sections in the associated D - M tilda - module, in terms of the embedding of the cohe-…

We investigate the construction of coherent states for quantum theories of connections based on graphs embedded in a spatial manifold, as in loop quantum gravity. We discuss the many subtleties of the construction, mainly related to the…

Quantum dynamics of coherent states is studied within quantum field theory using two complementary methods: by organizing the evolution as a Taylor series in elapsed time and by perturbative expansion in coupling within the…

We analyze the relationships between game theory and quantum mechanics and the extensions to statistical physics and information theory. We use certain quantization relationships to assign quantum states to the strategies of a player. These…

According to Shapley's game-theoretical result, there exists a unique game value of finite cooperative games that satisfies axioms on additivity, efficiency, null-player property and symmetry. The original setting requires symmetry with…

We propose the study of quantum games from the point of view of quantum information theory and statistical mechanics. Every game can be described by a density operator, the von Neumann entropy and the quantum replicator dynamics. There…

We previously proposed a mechanism to effectively obtain, after a long time development, a Hamiltonian being Hermitian with regard to a modified inner product $I_Q$ that makes a given non-normal Hamiltonian normal by using an appropriately…

Geometric phases arise naturally in a variety of quantum systems with observable consequences. They also arise in quantum computations when dressed states are used in gating operations. Here we show how they arise in these gating operations…

The simulation of quantum transport in a realistic, many-particle system is a nontrivial problem with no quantitatively satisfactory solution. While real-time propagation has the potential to overcome the shortcomings of conventional…

Models of disorder with a direction (constant imaginary vector-potential) are considered. These non-Hermitian models can appear as a result of computation for models of statistical physics using transfer matrix technique or describe…

In this dissertation, we analyze the computational properties of game-theoretic centrality measures. The key idea behind game-theoretic approach to network analysis is to treat nodes as players in a cooperative game, where the value of each…

We present a novel representation of coupled matter-photon systems that allows the application of many-body methods developed for purely fermionic systems. We do so by rewriting the original coupled light-matter problem in a…

Oftentimes, the Shapley value becomes infeasible for games with many players. However, establishing symmetry allows for polynomial-time computation. To examine this reduction, we identify the spectrum of homogeneous group games by using an…