This thesis focuses on the experimental creation and detection of a variety of quantum correlations using nuclear magnetic resonance hardware. Quantum entanglement, being most common and counter-intuitive, is one of the main type considered in this thesis. Quantum correlations play a major role in achieving, the much talked, computational speedup. Creation and detection of such correlations experimentally is a major thrust area in experimental quantum information processing field. Main goals of the studies undertaken in this thesis were to come up with strategies to detect the entanglement in a 'state-independent' way and with low experimental resources. The core of all the detection protocols is based on our own developed method which enables us to measure any observable with high accuracy. The experimental protocol has been successfully implemented to detect the entanglement of random two-qubit pure states. Further, the schemes for the experimental detection as well as classification of generic and general three-qubit pure states have also been devised and implemented successfully. Quantum correlation possessed by mixed and$/$or separable states e.g. non-classical, bound-entanglement and of non-local nature were also investigated. In all the investigations, the results were verified by one or more alternative ways e.g. full quantum state tomography.
This thesis focuses on the experimental creation and detection of a variety of quantum correlations using nuclear magnetic resonance hardware. Quantum entanglement, being most common and counter-intuitive, is one of the main type considered in this thesis. Quantum correlations play a major role in achieving, the much talked, computational speedup. Creation and detection of such correlations experimentally is a major thrust area in experimental quantum information processing field. Main goals of the studies undertaken in this thesis were to come up with strategies to detect the entanglement in a 'state-independent' way and with low experimental resources. The core of all the detection protocols is based on our own developed method which enables us to measure any observable with high accuracy. The experimental protocol has been successfully implemented to detect the entanglement of random two-qubit pure states. Further, the schemes for the experimental detection as well as classification of generic and general three-qubit pure states have also been devised and implemented successfully. Quantum correlation possessed by mixed and/or separable states e.g. non-classical, bound-entanglement and of non-local nature were also investigated. In all the investigations, the results were verified by one or more alternative ways e.g. full quantum state tomography.
One of the main foci of modern applied quantum information theory\nis the production of large-scale quantum entanglement involving many\nparticles, to achieve the next-generation quantum technologies. Although a full-scale quantum computer is still far away in time, in the next\nfew years we can expect to have quantum devices composed of up to a\nhundred controllable qubits. The primary challenge in moving towards\nsuch devices lies in the development of reliable and resource-efficient\ndetection techniques to prove genuine quantum advantage. The main\nobjective of this thesis is to investigate novel methods to detect the presence of quantum correlations in such systems, in particular, quantum\nentanglement and quantum nonlocality.\nThe first part of this thesis is dedicated to entanglement detection\nin large-scale quantum systems. Our main goal is to develop a novel\nprobabilistic method in which entanglement is seen as an ability of a\nquantum system to accomplish certain information-processing tasks.\nWe show that for certain classes of large (e.g. few tens of qubits) quantum states, even a single copy of a quantum state suffices to detect\nentanglement with a high confidence. Compared to the standard detection methods, this makes our method exceptionally resource-efficient.\nThe developed probabilistic scheme applies to multiple classes of states, vital for quantum computation, such as cluster states or ground\nstates of local Hamiltonians.\nIn the second part of this thesis, we develop a generic framework\nfor translating any entanglement witness into a resource-efficient probabilistic scheme. We show that the confidence level of entanglement\ndetection grows exponentially fast with the number of detection events,\nwhich makes this ansatz very efficient and reliable. Furthermore, we\npresent the first experimental performance of our method by verifying\nthe presence of entanglement in a photonic six-qubit cluster state.\nThe third part of this thesis describes the extension of our entanglement verification method to quantum nonlocality. Concrete examples\nare presented where we convert Bell’s inequalities into the probabilistic\nprocedure and incorporate our method into self-testing schemes. We\nshow that the performance of our method significantly exceeds the ability of the existing methods for detection of quantum nonlocality and\nself-testing.\nThe last part of this thesis is a study of the weak-convergence properties of random variables generated by quantum measurements. Beginning with a sequence of random variables generated by repeated\nunsharp quantum measurements, we study the limit distribution of\nmeasured relative frequency. We provide the de Finetti-type of representation theorem for all separable states, showing that the measured\ndistribution can be well approximated by a mixture of normal distributions. Additionally, we investigate the convergence rates and show\nthat the relative frequency converges to some constant at the rate of\norder 1=pN for all separable inputs. Finally, we provide an example of\na strictly unsharp quantum measurement where we obtain better scaling by using entangled inputs. We find such behaviour of entangled\nstates relevant for quantum information processing.
We undertake experimental detection of the entanglement present in arbitrary three-qubit pure quantum states on an NMR quantum information processor. Measurements of only four observables suffice to experimentally differentiate between the six classes of states which are inequivalent under stochastic local operation and classical communication. The experimental realization is achieved by mapping the desired observables onto Pauli z operators of a single qubit, which is directly amenable to measurement. The detection scheme is applied to known entangled states as well as to states randomly generated using a generic scheme that can construct all possible three-qubit states. The results are substantiated via direct full quantum state tomography as well as via negativity calculations and the comparison suggests that the protocol is indeed successful in detecting tripartite entanglement without requiring any a priori information about the states.
Nuclear magnetic resonance (NMR) was successfully employed to test several protocols and ideas in quantum information science. In most of these implementations, the existence of entanglement was ruled out. This fact introduced concerns and questions about the quantum nature of such bench tests. In this paper, we address some issues related to the non-classical aspects of NMR systems. We discuss some experiments where the quantum aspects of this system are supported by quantum correlations of separable states. Such quantumness, beyond the entanglement-separability paradigm, is revealed via a departure between the quantum and the classical versions of information theory. In this scenario, the concept of quantum discord seems to play an important role. We also present an experimental implementation of an analogue of the single-photon Mach-Zehnder interferometer employing two nuclear spins to encode the interferometric paths. This experiment illustrates how non-classical correlations of separable states may be used to simulate quantum dynamics. The results obtained are completely equivalent to the optical scenario, where entanglement (between two field modes) may be present.
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.
Entanglement is one of the most fascinating features of quantum theory, as it fundamentally distinguishes quantum systems from classical systems. It not only might play a role in natural processes, but provides an especially powerful resource for a plethora of quantum information protocols, including quantum state teleportation, superdense coding as well as quantum computation schemes. However, for larger systems involving more than two parties, it is a challenging task to verify and characterize entanglement. In this thesis, efficient means for detecting genuine multipartite entanglement in multiqubit quantum systems will be derived, demonstrated, and discussed. Beyond that, methods for quantum state and process tomography will be introduced, which allow to analyze and investigate prepared multipartite states or even the performance of whole setups. Some typical obstacles for reliable state tomography will be pointed out, together with new means to understand experimentally obtained data. Finally, the measurement problem, which describes the unavoidable backaction of a measurement process to the quantum state under investigation, will be illustrated. Together with the discussion of different methods of quantum measurements, the optimal measurement instruments for binary qubit measurements will be derived. These optimal measurement instruments allow to perform a quantum measurement, providing a tunable amount of information about the quantum state, while avoiding any unnecessary disturbance to the state. This set of optimal instruments will be compared to other measurement schemes, such as measurements based on the optimal quantum cloning protocol.
Random local measurements have recently been proposed to construct entanglement witnesses and thereby detect the presence of bipartite entanglement. We experimentally demonstrate the efficacy of one such scheme on a two-qubit NMR quantum-information processor. We show that a set of three random local measurements suffices to detect the entanglement of a general two-qubit state. We experimentally generate states with different amounts of entanglement and show that the scheme is able to clearly witness entanglement. We perform complete quantum state tomography for each state and compute state fidelity to validate our results. Further, we extend previous results and perform a simulation using random local measurements to optimally detect bipartite entanglement in a hybrid system of $2\ensuremath{\bigotimes}3$ dimensionality.