Two-state transfer: a generalization of pair and plus state transfer

• DOI: 10.48550/arxiv.2404.16654
• Publication Date: 2024-04-25
• Authors: Sooyeong Kim; Hermie Monterde; Bahman Ahmadi; Ada Chan; Stephen Kirkland; Sarah Plosker
• Keywords: Quantum Physics; 05C50, 81P45, 05C76, 15A18, 81Q10; FOS: Mathematics; Mathematics - Combinatorics; FOS: Physical sciences; Combinatorics (math.CO); 0101 mathematics; Quantum Physics (quant-ph); 01 natural sciences

In the study of quantum state transfer, one is interested in being able to transmit a with high fidelity within spin network. most literature, interest taken be associated standard basis vector; however, more general states have recently been considered. Here, we consider linear combination two vertex states, which encompasses definitions pair and plus connected weighted graphs. A two-state graph $X$ form $\mathbf{e}_u+s\mathbf{e}_v$, where $u$ $v$ are vertices $s$ non-zero real number. If $s=-1$ or $s=1$, then such called state, respectively. this paper, investigate transfer between two-states, Hamiltonian adjacency, Laplacian signless matrix graph. By analyzing spectral properties Hamiltonian, characterize strongly cospectral two-states built from vertices. This allows us perfect (PST) complete graphs, cycles hypercubes. We also produce infinite families graphs that admit strong cospectrality PST neither nor states. Using singular values vectors, show line implies formed by corresponding edges $X$. Furthermore, provide conditions converse previous statement holds. As an application, trees, unicyclic Cartesian products.