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.
We study multipartite entanglement measures for a one-dimensional Ising chain that is capable of showing both integrable and nonintegrable behavior. This model includes the kicked transverse Ising model, which we solve exactly using the Jordan-Wigner transform, as well as nonintegrable and mixing regimes. The cluster states arise as a special case and we show that while one measure of entanglement is large, another measure can be exponentially small, while symmetrizing these states with respect to up and down spins produces those with large entanglement content uniformly. We also calculate exactly some entanglement measures for the nontrivial but integrable case of the kicked transverse Ising model. In the nonintegrable case we begin on extensive numerical studies that show that large multipartite entanglement is accompanied by diminishing two-body correlations, and that time averaged multipartite entanglement measures can be enhanced in nonintegrable systems.
Generating entanglement between more parties is one of the central tasks and challenges in the backdrop of building quantum technologies. Here we propose a measurement-based protocol for producing multipartite entangled states which can be later fed into some network for realizing suitable quantum protocols. We consider weak entangling measurement on two parties as the basic unit of operation to create entanglement between more parties starting from an entangled state with a lesser number of parties and auxiliary systems in the form of a single-qubit or entangled state itself. We call the introduced expansion procedure, ``multipartite entanglement inflation.'' In the context of inflating bipartite entanglement to more number of parties, surprisingly, maximally entangled states as inputs turn out to be worse than that of the nonmaximally entangled states, Haar uniformly generated pure states having a moderate amount of entanglement and the Werner state with a certain threshold noise. We also report that the average multipartite entanglement created from the initial Greenberger-Horne-Zeilinger- and the
W-class states are almost the same. Interestingly, we also observe that for Haar uniformly generated pure states, unentangled auxiliary systems are sometimes more advantageous than the protocol with multiple copies of the initial entangled states.
Highly entangled states called cluster states are a universal resource for measurement-based quantum computing (QC). Here we propose an efficient method for producing large cluster states using superconducting quantum circuits. We show that a large cluster state can be efficiently generated in just one step by turning on the interqubit coupling for a short time. Because the interqubit coupling is only switched on during the time interval for generating the cluster state, our approach is also convenient for preparing the initial state for each qubit and for implementing one-way QC via single-qubit measurements. Moreover, the cluster state is robust against parameter variations.
We present a robust method, based only on measurements, to produce superconducting cluster states. The measurement of the current of a few parallel Josephson-junction qubits realizes a novel type of quantum-state selector. Using this selector, one can produce various quantum entangled states and also realize a controlled-NOT gate without requiring an exact control of the interqubit interactions. In particular, cluster states for quantum computation could be produced with only single-qubit measurements.
We consider multiqubit systems and relate quantitatively the problems of generating cluster states with high values of concurrence of assistance, and of generating states with maximal bipartite entanglement. We prove an upper bound for the concurrence of assistance. We consider dynamics of spin-
1∕2 systems that model qubits, with different couplings and possible presence of magnetic field, to investigate the appearance of the discussed entanglement properties. We find that states with maximal bipartite entanglement can be generated by an isotropic
XY Hamiltonian, and their generation can be controlled by the initial state of one of the spins. The same Hamiltonian is capable of creating states with high concurrence of assistance from a suitably chosen initial state. We show that the production of graph states using the Ising Hamiltonian is controllable via a single-qubit rotation of one spin-
1∕2 subsystem in the initial multiqubit state. We show that the property of Ising dynamics to convert a product-state basis into a special maximally entangled basis is temporally enhanced by the application of a suitable magnetic field. Similar basis transformations are found to be feasible in the case of isotropic
XY couplings with a magnetic field.