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.
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.
Quantum correlations and entanglement are fundamental resources for quantum information and quantum communication processes. Developments in these fields normally assume stable resources, not susceptible of distortion. That is not always the case, Heisenberg interactions between qubits can produce distortion on entangled pairs generated for engineering purposes (e. g. quantum computation or quantum cryptography). The presence of parasite magnetic fields modifies the expected properties and behavior for which the pair was intended. Quantum measurement and control help to discriminate the original state in order to correct it or reconstruct it using some procedures which do not alter their quantum nature. Different kinds of quantum entangled pairs driven by a Heisenberg Hamiltonian with an additional inhomogeneous magnetic field become distorted. They can be reconstructed by adding an external magnetic field with fidelity close to one. In addition, each state can be efficiently discriminated. Combining both processes, first reconstruction without discrimination and after discrimination with adequate non-local measurements, it is possible to (a) improve the discrimination, and (b) reprepare faithfully the original state. The complete process gives fidelities better than 0.9. Some results about a class of equivalence for the required measurements are found, allowing to select the experimentally most adequate.
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.
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 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).
Entanglement is the resource that most sharply distinguishes quantum information processing from its classical counterpart, and this thesis examines it from two complementary directions: how it can be detected and quantified, and how it, together with the broader machinery of quantum correlations, interference, and measurement, can be put to use. We first study two simple, measurable conditions that detect bipartite entanglement, and show that the extent to which either is violated yields a lower bound on the negativity of a state. The bound is established for two qubits, extended to systems of arbitrary finite dimension, and sharpened when partial knowledge of the Schmidt vectors is available. We then turn to discrete-outcome quantum sensor networks, in which one seeks only to determine which detectors, or which group or spatial pattern of detectors, has responded to a signal. Working in the weak-interaction regime, where the output states are nonorthogonal, we use minimum-error and unambiguous state discrimination to show that entangled initial states and collective measurements confer an advantage when detectors are grouped, and we develop a shift-operator formalism that gives closed-form success probabilities for the detection of shifted patterns in one- and two-dimensional arrays. Next we consider the problem of learning two unknown pure qubit states, together with their probabilities of occurrence, from a scrambled stream; we show that receiving the systems in identically prepared pairs supplies exactly the extra quantum information needed, since the resulting two-qubit state in the symmetric subspace has a unique decomposition into pure product states, which we recover by tomography. Finally, we show how interference and measurement can convert information encoded in the phases of quantum amplitudes into information encoded in their magnitudes, amplifying the amplitudes that carry useful information and suppressing those that do not, and we apply this technique to states produced by the quantum approximate optimization algorithm for the MaxCut and minimum-vertex-cover problems. Throughout, a single theme recurs: the correlations and superpositions permitted by quantum mechanics are at once something to be measured and something to be exploited.
Discrete-time quantum walks are among the branches of quantum information and computation. They are platforms for developing quantum algorithms for quantum computers. In addition, due to their universal primitive nature, discrete-time quantum walks have been used to simulate other quantum systems and phenomena that are observed in physics and chemistry. To fully utilize the potentials that the discrete-time quantum walks hold in their applications, control over the discrete-time quantum walks and their properties becomes essential. In this dissertation, we propose two models for attaining a high level of control over the discrete-time quantum walks. In the first one, we incorporate a dynamical nature for the unitary operator performing the quantum walks. This enables us to readily control the properties of the walker and produce diverse behaviors for it. We show that with our proposal, the important properties of the discrete-time quantum walks such as variance would indeed improve. To explore the potential of this proposal, we apply it in the simulations of topological phases in condensed matter physics. With our proposal, we can control the simulations and determine the type of topological phenomena that should be simulated. In addition, we confirm simulations of topological phases and boundary states that can be observed in one-, two- and three-dimensional systems. Finally, we report the emergence of exotic phase structures in form of cell-like structures that contain all types of topological phases and boundary states of certain classes. In our second proposal, we take advantage of resources available in quantum mechanics, namely quantum entanglement and entangled qubits. In this proposal, we use entangled qubits in the structure of a quantum walk and show that by tuning the initial entanglement between these qubits and how these qubits are modified through the walk, one is able to produce diverse behaviors for the quantum walk and control its behavior.