# Bell States via Two-Particle Contact Interaction: Shannon Entropy as an Indicator of Entanglement Dynamics

## TL;DR

This paper demonstrates that Shannon entropy can serve as a reliable indicator of entanglement dynamics in two-particle quantum systems, providing a new approach for analyzing entanglement in various physical models.

## Contribution

It introduces Shannon entropy as an alternative measure of entanglement, showing its equivalence to concurrence in systems with Bell-like eigenstates involving tunneling and contact interactions.

## Key findings

- Shannon entropy mirrors concurrence over time in entangled states.
- Bell-like eigenstates emerge from the interplay of tunneling and contact interaction.
- The approach applies to systems with spatial and spin degrees of freedom.

## Abstract

We study the coherent dynamics of two interacting particles in a quantum double-well and show that the Shannon entropy can be a definitive signature of entanglement as an alternative to concur- rence, a connection not reported previously. This physical model, involving tunneling and contact interaction, is akin to the Hubbard model which explains the physics of interacting particles in peri- odic potentials. We show that an interplay between tunneling and contact interaction produces Bell like eigenstates ensuring thereby that the concurrence and the Shannon entropy, two quantities with vastly different physical interpretations, develop the same time dependence. Our result, applied to three experimentally realized physical models works for both spatial and spin degrees of freedom and is significant as it provides a novel measure of entanglement applicable to many systems currently being explored for scalable quantum computation.