On clustering states

Derek W. Robinson

Takanori Sugimoto, Katsuhiro Morita, Takami Tohyama

The authors provide a concept of the Haldane states designed in spin cluster chains, where S=1/2 spins in a cluster strongly interact with each other as compared with inter cluster interactions. As an extension of the Affleck-Kenned-Lieb-Tasaki state, the Haldane states are demonstrated in the spin cluster chains whose cluster consists of not only even but also odd number of spins. Particularly, the Haldane state in the case of an odd number of spins in a cluster is induced by the magnetic field and emerges as a magnetization plateau.

Yaakov S. Weinstein, Gerald N. Gilbert

We consider the effects of decoherence on the entanglement of photonic cluster states. Large photonic cluster states can be constructed via so-called fusion operations from smaller photonic cluster states. Due to this construction process, it is necessary to store these primitive cluster states in some way so as to have them available for attempted fusion operations. While in storage the photonic cluster states may undergo dephasing. The effects of dephasing on primitive cluster states is explored here with the aim of determining how to locally rotate the qubits of the cluster state in the hopes of losing the least amount of entanglement due to the dephasing process.

Hans J. Briegel

Huzihiro Araki, Akitaka Kishimoto

Yoshiko Kanada-En’yo

I investigate entanglement entropy of one-dimensional (1D) cluster states to discuss the delocalization of clusters in linear-chain $3\ensuremath{\alpha}$- and $4\ensuremath{\alpha}$-cluster states. In analysis of entanglement entropy of 1D Tohsaki-Horiuchi-Schuck-R\"opke (THSR) and Brink-Bloch cluster wave functions, I show clear differences in the entanglement entropy between localized cluster wave functions and delocalized cluster wave functions. To clarify spatial regions where the entanglement entropy is generated by the delocalization of clusters, I analyze the spatial distribution of entanglement entropy. In the linear-chain $3\ensuremath{\alpha}$-cluster state, the delocalization occurs dominantly in a low-density tail region while it is relatively suppressed in an inner region because of the Pauli blocking effect between clusters. In the linear-chain $4\ensuremath{\alpha}$ state having a larger system size than the linear-chain $3\ensuremath{\alpha}$ state, the delocalization occurs in the whole system. The entanglement entropy is found to be a measure of the delocalization of clusters in the 1D cluster systems.