We study a spin chain with an anisotropic XXZ coupling in a magnetic field. Such a chain models several proposed types of quantum computers. The chain contains a defect with a different on-site energy. The interaction between excitations leads to the onset of two-excitation states localized next to the defect. In a resonant situation scattering of excitations on each other might cause decay of an excitation localized on the defect. We find that destructive many-particle quantum interference eliminates this decay. Numerical results confirm the analytical predictions.
We analyze localization of interacting excitations in a system of qubits or spins. The system is modeled by a spin chain with an anisotropic (XXZ) exchange coupling in a magnetic field. Localization occurs on a defect with an excess on-site spin-flip energy. Such a defect corresponds to a qubit with the level spacing different from other qubits. Because of the interaction, a single defect may lead to multiple localized states. We find energy spectra and localization lengths of the two-excitation states. An excitation remains localized on the defect even where energy conservation allows scattering into extended states. This is due to destructive quantum interference in the two-excitation scattering channels, and it facilitates the operation of a quantum computer. Analytical results are obtained for strong anisotropy and are confirmed by numerical studies.
We investigate the ability of dimerized spin chains with defects to generate EPR pairs to very high fidelity through their natural dynamics. We propose two protocols based on different initializations of the system, which yield the same maximally entangled Bell state after a characteristic time. This entangling time can be varied through engineering the weak/strong couplings' ratio of the chain, with larger values giving rise to an exponentially faster quantum entangling operation. We demonstrate that there is a set of characteristic values of the coupling, for which the entanglement generated remains extremely high. We investigate the robustness of both protocols to diagonal and off-diagonal disorder. Our results demonstrate extremely strong robustness to both perturbation types, up to strength of 50\% of the weak coupling. Robustness to disorder can be further enhanced by increasing the coupling ratio. The combination of these properties makes the use of our proposed device suitable for the rapid and robust generation of Bell states in quantum information processing applications.
Simple physical interactions between spin-
1∕2 particles may result in quantum states that exhibit exotic correlations that are difficult to find if one simply explores state spaces of multipartite systems. In particular, we present a detailed investigation of the well-known Ising model of a chain (ring) of spin-
1∕2 particles (qubits) in a transverse magnetic field. We present explicit expressions for eigenstates of the model Hamiltonian for arbitrary number of spin-
1∕2 particles in the chain in the standard (computer) basis, and we investigate quantum entanglement between individual qubits. We analyze bipartite as well as multipartite entanglement in the ground state of the model. In particular, we show that bipartite entanglement between pairs of qubits of the Ising chain (measured in terms of a concurrence) as a function of the parameter $\ensuremath{\lambda}$ has a maximum around the point $\ensuremath{\lambda}=1$, and it monotonically decreases for large values of $\ensuremath{\lambda}$. We prove that in the limit $\ensuremath{\lambda}\ensuremath{\rightarrow}\ensuremath{\infty}$ this state is locally unitary equivalent to an
N-partite Greenberger-Horn-Zeilinger state. We also analyze a very specific eigenstate of the Ising Hamiltonian with a zero eigenenergy (we denote this eigenstate as the
X-state). This
X-state exhibits the ``extreme'' entanglement in a sense that an arbitrary subset
A of $k\ensuremath{\leqslant}n$ qubits in the Ising chain composed of
N=2n+1 qubits is maximally entangled with the remaining qubits (set
B) in the chain. In addition, we prove that by performing a local operation just on the subset
B, one can transform the
X-state into a direct product of
k singlets shared by the parties
A and
B. This property of the
X-state can be utilized for new secure multipartite communication protocols.
Abstract In this contribution we consider an advantageous building block with potential for various quantum applications: a device based on coupled spins capable of generating and sharing out an entangled pair of qubits. Our model device is a dimerized spin chain with three weakly coupled embedded sites (defects). Three different entangling protocols were proposed for this chain in [1] and [2], one producing a Cluster state building block and two generating a Bell state, depending on the initial state injection. Here we compare the robustness of such protocols as quantum entangling gates against different types of fabrication (static energy fluctuations) and operation (timing injection delays) errors.