Perfect state transfer: Beyond nearest-neighbor couplings (7 pages)

Robert Mereau, David L. Feder

Alastair Kay

In this paper we build on the ideas presented in previous works for perfectly transferring a quantum state between opposite ends of a spin chain using a fixed Hamiltonian. While all previous studies have concentrated on nearest-neighbor couplings, we demonstrate how to incorporate additional terms in the Hamiltonian by solving an inverse eigenvalue problem. We also explore issues relating to the choice of the eigenvalue spectrum of the Hamiltonian, such as the tolerance to errors and the rate of information transfer.

M. Asoudeh, Vahid Karimipour

Matthias Christandl, Luc Vinet, Alexei S. Zhedanov

Certain nonuniformly coupled spin chains can exhibit perfect transfer of quantum states from end to end. Motivated by recent experimental implementations in evanescently coupled waveguide arrays, we extend the simplest such chain to next-to-nearest-neighbor couplings. It is shown analytically that perfect state transfer can be maintained under the extension and that end-to-end entanglement generation (fractional revival) can occur.

Milan Bašić

In this paper we answer the question of when circulant quantum spin networks with nearest-neighbor couplings can give perfect state transfer. The network is described by a circulant graph $G$, which is characterized by its circulant adjacency matrix $A$. Formally, we say that there exists a {\it perfect state transfer} (PST) between vertices $a,b\in V(G)$ if $|F(τ)_{ab}|=1$, for some positive real number $τ$, where $F(t)=\exp(ıAt)$. Saxena, Severini and Shparlinski ({\it International Journal of Quantum Information} 5 (2007), 417--430) proved that $|F(τ)_{aa}|=1$ for some $a\in V(G)$ and $τ\in \R^+$ if and only if all eigenvalues of $G$ are integer (that is, the graph is integral). The integral circulant graph $\ICG_n (D)$ has the vertex set $Z_n = \{0, 1, 2, ..., n - 1\}$ and vertices $a$ and $b$ are adjacent if $\gcd(a-b,n)\in D$, where $D \subseteq \{d : d \mid n,\ 1\leq d

Erin Connelly, Nathaniel Grammel, Michael Kraut +2 more