Entanglement generated by Ising model has been studied for several authors in order to understand the relation between it and magnetic properties of materials, principally using one or two dimensional models for two or more particles. In this work, Ising model evolution is solved in three dimensions for two parts including an inhomogeneous magnetic field, giving an detailed study of the entanglement properties derived from interaction. Some relations between entanglement and energy or spin are developed specifically to stablish candidates for entanglement witness. Finally, some basic quantum control operations are prescripted for this model as to preserve the properties of the system as for transfer information between the two parts. These last schemes of control are useful when initial state is completely known, to gain domain on the system. It prevents to introduce more sophisticated control schemes which normally are necessary when initial state is at least partially unknown.
Entanglement generated by the Heisenberg model has been studied by several authors in order to understand its relation to the magnetic properties of materials, using mainly particular cases in one or two dimensions for two or more particles. In this work, the evolution of the Heisenberg model is solved for two particles including an inhomogeneous magnetic field in three dimensions, giving a detailed study of the entanglement properties derived from this interaction. Some relations between entanglement and energy or spin are verified, based on known relations for these observables. Finally, some possible quantum control operations are suggested to drive bipartite qubits with an external magnetic field, controlling their evolution into a periodical behavior. These operations become useful to preserve the system properties as well as to transfer information between two parts which can be exploited in engineering applications (e.g. quantum computation or quantum information).
Control of quantum entanglement has been considered as elemental physical resource for quantum applications in Quantum Information and Quantum Computation. Control of entangled states on a couple of atoms, ions or quantum dots are milestones in almost all quantum applications towards a scalable spin-based quantum computers or quantum devices. For magnetic systems, Ising model is an interaction which generates and modifies entanglement properties of quantum systems based on matter. In addition, when this interaction includes driven magnetic fields, it can be controlled to sustain, characterize or modify entanglement and other quantum properties. In this work, recent results about evolution in a general anisotropic three dimensional Ising model including an inhomogeneous magnetic field is considered to obtain some general quantum control effects for their sustainability, programmed evolution or transformation: Evolution loops and Exchange operations. This control is achievable through a set of physical parameters, whose prescriptions are reported. The use of a non local basis in the model to express time evolution lets take advantage to describe and control the system, in particular with those issues associated with entanglement and operations mentioned before. Finally, some analysis about equivalent gates based on our development is made including an example with teleportation, using one of the gates constructed.
Entanglement is considered a basic physical resource for modern quantum applications as Quantum Information and Quantum Computation. Interactions based on specific physical systems able to generate and sustain entanglement are subject to deep research to get understanding and control on it. Atoms, ions or quantum dots are considered key pieces in quantum applications because they are elements in the development toward a scalable spin-based quantum computer through universal and basic quantum operations. Ising model is a type of interaction generating entanglement in quantum systems based on matter. In this work, a general bipartite anisotropic Ising model including an inhomogeneous magnetic field is analyzed in a non-local basis. This model summarizes several particular models presented in literature. When evolution is expressed in the Bell basis, it shows a regular block structure suggesting a [Formula: see text] decomposition. Then, their algebraic properties are analyzed in terms of a set of physical parameters which define their group structure. In particular, finite products of pulses in this interaction are analyzed in terms of [Formula: see text] covering. Thus, evolution denotes remarkable properties, in particular those related potentially with entanglement and control, which give a fruitful arena for further quantum developments and generalization.
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.
Ising interactions between qubits can produce distortion on entangled pairs generated for engineering purposes (e.g., for quantum computation or quantum cryptography). The presence of parasite magnetic fields destroys or alters the expected behavior for which it was intended. In addition, these pairs are generated with some dispersion in their original configuration, so their discrimination is necessary for applications. Nevertheless, discrimination should be made after Ising distortion. Quantum control helps in both problems; making some projective measurements upon the pair to decide the original state to replace it, or just trying to reconstruct it using some procedures which do not alter their quantum nature. Results about the performance of these procedures are reported. First, we will work with pure systems studying restrictions and advantages. Then, we will extend these operations for mixed states generated with uncertainty in the time of distortion, correcting them by assuming the control prescriptions for the most probable one.
The evolution of entanglement in a one-dimensional Ising chain is numerically studied under various initial conditions. We analyze two problems concerning the dynamics of entanglement: (i) generation of the entanglement from the pseudopure separable state and (ii) transportation of the entanglement from one end of the chain to the other. The model investigated is a one-dimensional Ising spin-1/2 chain with nearest-neighbor interactions placed in an external magnetic field and irradiated by a weak resonant transverse field. The possibility of selective initialization of partially entangled states is considered. It was shown that, in spite of the use of a model with direct interactions between the nearest neighbors, entanglement between remote spins is generated.