arXiv subjects

Teena Thomas

Publications and source records attributed to Teena Thomas.

7 recordsLinked to original sources

arXiv2026

Birth and Death of Entanglement in Hamiltonian-Driven Quantum Games under Decoherence

Quantum game theory investigates the influence of quantum resources on strategic decision-making. In this work, two-player quantum games based on the Transverse Field Ising Model(TFIM) are investigated under amplitude-damping decoherence. The TFIM Hamiltonian naturally produces a family of entangling gates, enabling a physically motivated implementation of quantum games. The effects of noise on Nash equilibria, players' payoffs, concurrence and coherence of the quantum states for different initial states and strategy pairs are analyzed. The results show that decoherence progressively suppresses quantum strategic advantages, with maximum damping driving all outcomes to identical classical payoffs. The concurrence and coherence analysis of the states generated in the quantum game reveal initial state and strategy dependent quantum correlation dynamics, including entanglement sudden birth and death.

quant-ph↗

arXiv2026

Emergence of Strategic Equilibria from Transverse Field Ising Hamiltonian Dynamics

Game theory studies strategic decision-making among rational agents, and many classical games can be mapped onto interaction models such as the Ising model. Quantum game theory extends this framework by allowing players to exploit quantum superposition and entanglement. In this work, we study quantum games using an operator-based formulation derived from the transverse-field quantum Ising model. We show that the Hamiltonian-driven dynamics naturally generate entangling operator which resolve the dilemma in the game settings. This leads to a clear quantum advantage over classical outcomes. Unlike standard quantization schemes based on fixed entangling gates, the present approach enables tunable entanglement, controlled directly by physical Hamiltonian parameters, providing a hardware-relevant perspective on quantum game design.

quant-ph↗

arXiv2023

On property-$(P_1)$ and semi-continuity properties of restricted Chebyshev-center maps in $\ell_{\infty}$-direct sums

For a compact Hausdorff space $S$, we prove that the closed unit ball of a closed linear subalgebra of the space of real-valued continuous functions on $S$, denoted by $C(S)$, satisfies property-$(P_1)$ (the set-valued generalization of strong proximinality) for the non-empty closed bounded subsets of the bidual of $C(S)$. Various stability results related to property-$(P_1)$ and semi-continuity properties of restricted Chebyshev-center maps are also established. As a consequence, we derive that if $Y$ is a proximinal finite co-dimensional subspace of $c_0$ then the closed unit ball of $Y$ satisfies property-$(P_1)$ for the non-empty closed bounded subsets of $\ell_{\infty}$ and the restricted Chebyshev-center map of the closed unit ball of $Y$ is Hausdorff metric continuous on the class of non-empty closed bounded subsets of $\ell_{\infty}$. We also investigate a variant of the transitivity property, similar to the one discussed in [C. R. Jayanarayanan and T. Paul, Strong proximinality and intersection properties of balls in Banach spaces, J. Math. Anal. Appl., 426(2):1217--1231, 2015], for property-$(P_1)$.

math.FA↗

arXiv2023

On Kakutani's characterization of the closed linear sublattices of $C(X)$ -- Revisited

In his paper [Concrete representation of abstract $(M)$-spaces. (A characterization of the space of continuous functions.), Ann. of Math., $42 (2)$ ($1941$), $994$--$1024$.], S. Kakutani gave an interesting representation of the closed linear sublattices of the space of real-valued continuous functions on a compact Hausdorff space, which is determined by a set of algebraic relations. In this short note, we present a simple proof of this representation without using any profound lattice theory or functional analysis results, making this proof accessible even to undergraduate students.

math.FA↗

arXiv2022

On Property-$(P_{1})$ in Banach spaces

We discuss a set-valued generalization of strong proximinality in Banach spaces, introduced by J. Mach [Continuity properties of Chebyshev centers, J. Approx. Theory, 29(3):223--230, 1980] as property-$(P_1)$. We establish that if the closed unit ball of a closed subspace of a Banach space $X$ possesses property-$(P_1)$ for each of the classes of closed bounded, compact and finite subsets of $X$, then so does the subspace. It is also proved that the closed unit ball of an $M$-ideal in an $L_{1}$-predual space satisfies property-$(P_{1})$ for the compact subsets of the space. For a Choquet simplex $K$, we provide a sufficient condition for the closed unit ball of a finite co-dimensional closed subspace of $A(K)$ to satisfy property-$(P_{1})$ for the compact subsets of $A(K)$. This condition also helps to establish the equivalence of strong proximinality of the closed unit ball of a finite co-dimensional subspace of $A(K)$ and property-$(P_{1})$ of the closed unit ball of the subspace for the compact subsets of $A(K)$. Further, for a compact Hausdorff space $S$, a characterization is provided for a strongly proximinal finite co-dimensional closed subspace of $C(S)$ in terms of property-$(P_{1})$ of the subspace and that of its closed unit ball for the compact subsets of $C(S)$. We generalize this characterization for a strongly proximinal finite co-dimensional closed subspace of an $L_{1}$-predual space. As a consequence, we prove that such a subspace is a finite intersection of hyperplanes such that the closed unit ball of each of these hyperplanes satisfy property-$(P_1)$ for the compact subsets of the $L_1$-predual space and vice versa. We conclude this article by providing an example of a closed subspace of a non-reflexive Banach space which satisfies $1 \frac{1}{2}$-ball property and does not admit restricted Chebyshev centre for a closed bounded subset of the Banach space.

math.FA↗

arXiv2022

Some stability properties of restricted Chebyshev centers in Banach spaces

In this paper, we discuss the stability of (restricted) Chebyshev centers in few function spaces. For an extremally disconnected compact Hausdorff space $K$ and a finite dimensional Banach space $X$, we prove the existence of Chebyshev centers of closed bounded subsets of the space of $X$-valued continuous functions on $K$, $C(K,X)$ and that of compact subsets of $M$-ideals in $C(K,X)$. It is also proved that the existence of restricted Chebyshev centers is stable in the space of vector-valued bounded functions on an arbitrary set. Furthermore, the stability of continuity properties of the Chebyshev-center map of a Banach space $X$ in dependence on the continuity properties of the Chebyshev-center map of $C(K,X)$ is studied.

math.FA↗

arXiv2022

Restricted Chebyshev centers in $L_1$-predual spaces

In this paper, we provide a necessary and sufficient condition for the existence of a restricted Chebyshev center of a compact subset of an $L_{1}$-predual space in a closed convex subset of the $L_{1}$-predual space. We also provide a geometrical characterization of an $L_{1}$-predual space in terms of the restricted Chebyshev radius in the following manner. A real Banach space $X$ is an $L_{1}$-predual space if and only if for each non-empty finite subset $F$ of $X$ and closed convex subset $V$ of $X$, $rad_{V}(F) = rad_{X}(F) + d(V, cent_{X}(F))$, where we denote $rad_{X}(F)$, $rad_{V}(F)$, $cent_{X}(F)$ and $d(V, cent_{X}(F))$ to be the Chebyshev radius of $F$ in $X$, the restricted Chebyshev radius of $F$ in $V$, the set of Chebyshev centers of $F$ in $X$ and the distance between the sets $V$ and $cent_{X}(F)$ respectively. Furthermore, we explicitly describe the Chebyshev centers of closed bounded subsets of an $M$-summand in the space of real-valued continuous functions on a compact Hausdorff space.

math.FA↗