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.
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.
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.
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).
Summary form only given. Entangled states of multi-particle systems are arguably the quintessential feature of quantum mechanics. In addition to their central role in discussions of non-local quantum correlations, they form the basis of quantum information, and enable such phenomena as quantum cryptography, quantum dense coding, teleportation, and quantum computation. Via the process of spontaneous parametric downconversion in a pair of nonlinear crystals, it is now possible to produce, with high efficiency, pairs of photons entangled in their polarisation degree of freedom. We can also control both the extent of entanglement and the purity of the state. Density matrices for states generated by this method, and measured using tomographic techniques, are shown.
Building a working quantum computer that is able to perform useful calculations remains a challenge. With this thesis, we are trying to contribute a small piece to this puzzle by addressing three of the many fundamental questions one encounters along the way of reaching that goal. These questions are: (i) What is an easy way to create highly entangled states as a resource for quantum computation? (ii) What can we do to efficiently quantify states of noisy entanglement in systems coupled to the outside world? (iii) How can we protect and store fragile quantum states for arbitrary long times? \n \nThe first two questions are the subject of part one of this thesis, `Entanglement Measures & Highly Entangled States'. We devise a particular proposal for generating entanglement within a solid-state setup, starting first with the tripartite case and continuing with a generalization to four and more qubits. The main idea there is to realize systems with highly entangled ground states in order for entanglement to be created by merely cooling to low enough temperatures. We have addressed the issue of quantifying entanglement in these systems by numerically calculating mixed-state entanglement measures and maximizing the latter as a function of the external magnetic field strength. The research along these lines has led to the development of the numerical library 'libCreme'. \n \nThe second part of the thesis, 'Self-Correcting Quantum Memories', addresses the question how to reliably store quantum states long enough to perform useful calculations. Every computer, be it classical or quantum, needs the information it processes to be protected from corruption caused by faulty gates and perturbations from interactions with its environment. However, quantum states are much more susceptible to these adverse effects than classical states, making the manipulation and storage of quantum information a challenging task. Promising candidates for such 'quantum memories' are systems exhibiting topological order, because they are robust against local perturbations, and information encoded in their ground state can only be manipulated in a non-local fashion. We extend the so-called toric code by repulsive long-range interactions between anyons and show that this makes the code stable against thermal fluctuations. Furthermore, we investigate incoherent effects of quenched disorder in the toric code and similar systems.
The highly parallel nature of the fundamental principles of quantum mechanics means that certain key resource-intensive tasks --- including searching, code decryption and medical, chemical and material simulations --- can be computed polynomially or even exponentially faster with a quantum computer. In spite of its remarkably fast development, the field of quantum computing is still young, and a large-scale prototype using any one of the candidate quantum bits (or 'qubits') under investigation has yet to be developed. Spin-based qubits in condensed matter systems are excellent candidates. Spins controlled using magnetic resonance have provided the first, most advanced, and highest fidelity experimental demonstrations of quantum algorithms to date. Despite having highly promising control characteristics, most physical ensembles investigated using magnetic resonance are unable to produce entanglement, a critical missing ingredient for a pure-state quantum computer. Quantum objects are said to be entangled if they cannot be described individually: they remain fundamentally linked regardless of their physical separation. Such highly non-classical states can be exploited for a host of quantum technologies including teleportation, metrology, and quantum computation. Here I describe how to experimentally create, control and characterise entangled quantum ensembles using magnetic resonance. I first explore the relationship between entanglement and quantum metrology and demonstrate a sensitivity enhancement over classical resources using molecular sensors controlled with liquid-state nuclear magnetic resonance. I then examine the computational potential of irreversible relaxation processes in combination with traditional reversible magnetic resonance control techniques. I show how irreversible processes can polarise both nuclear and electronic spins, which improves the quality of qubit initialisation. I discuss the process of quantum state tomography, where an arbitrary quantum state can be accurately measured and characterised, including components which go undetected using traditional magnetic resonance techniques. Lastly, I combine the above findings to initialise, create and characterise entanglement between an ensemble of electron and nuclear spin defects in silicon. I further this by generating pseudo-entanglement between an ensemble of nuclear spins mediated by a transient electron spin in a molecular system. These findings help pave the way towards a particular architecture for a scalable, spin-based quantum computer.
The discrimination of quantum measurements is an important subject of quantum information processes. In this paper we present a novel protocol for local quantum measurement discrimination with multi-qubit entanglement systems. It is shown that, in the case of Bob did not know Alice's result of measurement, if both two observers (Alice and Bob) agreed in advance that Alice should measure her qubits before an appointed time t, the local discrimination of two different kinds of measurement can be completed via numerous eight-qubit GHZ entangled states and selective projective measurement.