Connecting Quantum States: The Role of $q$-Krawtchouk Polynomials and Hypercubes

Recent research has established a connection between the dual $q$-Krawtchouk polynomials, a weighted hypercube, and $q$-Dicke states. This relationship is detailed in the paper titled "A $q$-version of the relation between the hypercube, the Krawtchouk chain and Dicke states," authored by Pierre-Antoine Bernard, Étienne Poliquin, and Luc Vinet. The authors emphasize the representation theoretic foundations based on the quantum algebra $U_q(\mathfrak{su}(2))$.

The study demonstrates how these mathematical constructs can be utilized in quantum physics, particularly in the context of quantum information and computation. The findings may have implications for the development of quantum algorithms and the understanding of quantum states.

The paper spans eight pages and is categorized under Mathematical Physics and Quantum Physics. It was submitted on August 26, 2024, and can be accessed via arXiv with the identifier arXiv:2408.14388.