Quantum entanglement is one of the most fundamental characteristics of quantum mechanics, yet one of the most intriguing. The interest in quantum entanglement started in the 1930s with the famous EPR paradox and has since found applications in various areas of physics. In this presentation, we will see how this phenomenon allows one to understand the behaviour of quantum systems. In particular, we will investigate two different entanglement measures, namely, the so-called entanglement entropy and the so-called bipartite fidelity. We will study these quantities in two different one-dimensional quantum systems constructed from families of orthogonal polynomials: the so-called XX chain, from the Chebyshev polynomials of the second kind, and the Krawtchouk chain, from the Krawtchouk polynomials.
