Perfect transfer of arbitrary states in quantum spin networks

We propose a class of qubit networks that admit perfect state transfer of any two-dimensional quantum state in a fixed period of time. We further show that such networks can distribute arbitrary entangled states between two distant parties, and can, by using such systems in parallel, transmit the higher-dimensional systems states across the network. Unlike many other schemes for quantum computation and communication, these networks do not require qubit couplings to be switched on and off. When restricted to $N$-qubit spin networks of identical qubit couplings, we show that $2{\log }_{3}N$ is the maximal perfect communication distance for hypercube geometries. Moreover, if one allows fixed but different couplings between the qubits then perfect state transfer can be achieved over arbitrarily long distances in a linear chain. This paper expands and extends the work done by Christandl et al., Phys. Rev. Lett. 92, 187902 (2004).

Figure 1

An example of a five-column graph that allows perfect state transfer between either end.

Figure 2

Couplings $J_n$ that admit perfect state transfer from $A$ to $B$ in a five-qubit chain. Eigenvalues $m$ of the equivalent spin-2 particle are also shown. This is the projection of Fig. 1 onto a chain.

Figure 3

Scheme for transferring an arbitrary two-qubit density matrix $\rho$, using two engineered spin chains ($C_1$ and $C_2$). This example has a chain length of $N_C=6$.