Abstract The well known Bell experiment with two actors Alice and Bob is considered. First the simple deduction leading to the CHSH inequality under local realism is reviewed, and some arguments from the literature are recapitulated. Then I take up certain background themes before I enter a discussion of Alice’s analysis of the situation. An important point is that her mind is limited by the fact that her Hilbert space in this context is two-dimensional. General statements about a mind’s limitation during a decision process are derived from recent results on the reconstruction of quantum theory from conceptual variables. These results apply to any decision situation. Let all the data from the Bell experiment be handed over to a new actor Charlie, who performs a data analysis. But his mind is also limited: He has a four-dimensional Hilbert space in the context determined by the experiment. I show that this implies that neither Alice nor Charlie can have the argument leading to the CHSH inequality as a background for making decisions related to the experiment. Charlie may be any data analyst, and he may communicate with any person. It is argued that no rational person can be convinced by the CHSH argument when making empirical decisions on the Bell situation.
Traditional ETF stock selection methods and reinforcement learning models such as the Asynchronous Advantage Actor-Critic (A3C) often suffer from high-dimensional feature spaces and overfitting when applied to complex financial markets. Moreover, static clustering algorithms fail to capture evolving market regimes, as the cluster with higher returns in one period may not remain optimal in the next. To address these limitations, this paper proposes Q-A3C2, a quantum-enhanced A3C framework that integrates time-series dynamic clustering. By embedding Variational Quantum Circuits (VQCs) into the policy network, Q-A3C2 enhances nonlinear feature representation and enables adaptive decision-making at the cluster level. Experimental results on the S and P 500 constituents show that Q-A3C2 achieves a cumulative return of 17.09%, outperforming the benchmark's 7.09%, demonstrating superior adaptability and exploration in dynamic financial environments.
Graphical representations of the
q-creation and the
q-annihilation operators and set partition statistics (Infinite Dimensional Analysis and Quantum Probability Theory)
In this note, we introduce acertain graphical representations of the
q-creation the
q-annihilation, the
q-numb er, and the scalar operators on the
q-Fock space.These are given as the cards on which some flow lines are drawn and increasing and decreasing of the number of lines correspond to creation and annihilation, respectively.By the cards arrangement technique with these cards, of which machinery is the same as of the partition function for the lattice spins model in statistical me- chanics, we write the moments of the
q-Poisson random variable using the number of arc crossings, which is the same set partition statistic as restricted crossings investigated by P. Biane.This result suggests another
q-deformed moments-cumulants relations, which interpolates between the usual and the free cases exactly.This is the joint work with Naoko Saitoh at Ochanomizu University.1The
q -Fock space For aHibert space 7{ and
q∈(−1,1) , the
q-Fock space
Fq(H) can be defined as follows: (see, for instance, [BS1], [BKS]) Let
Ffin(H) be the linear span of vectors of the form
ξ1⊗⋯⊗ξn∈H⊗n , where
n varies in
z≥0 and we put
H⊗0≅CΩ for some distinguished vector
Ω called vacuum.We consider the sesquilinear form
⟨⋅∣⋅⟩q on
FJjn(H) given by the sesquilinear extension of
⟨ξ1⊗⋯⊗ξn∣η1⊗⋯⊗ηm⟩q=δn,m∑π∈Snqi(π)⟨ξ1∣ηπ(1)⟩⋯⟨ξn∣ηπ(n)⟩ ,