This thesis studies the manipulation of entanglement in three-qubit quantum systems. I consider the operational setting in which the qubits are distributed to three spatially separated parties. The parties act locally on their quantum systems and share classical communication with one another, a scenario commonly called local operations and classical communication (LOCC). In the LOCC setting, there are two different classes of entanglement in multipartite systems, called the GHZ and W classes, which are inequivalent in the sense that states from one class cannot be transformed into the other without the consumption of additional entanglement. In this thesis, I first show that the LOCC conversion of certain GHZ and W-class states becomes possible by using only one additional ebit (“entangled bit”) of shared entanglement. In many cases, this can be proven as the minimal amount of needed entanglement. I then consider the problem of one-way communication transformations from general three-qubit states into two-qubit maximally entangled states, known as EPR states. An optimal protocol in terms of success probability is provided for W-class states. The success probability of this protocol coincides with the optimal success probability if two of the parties are allowed to act jointly within the same laboratory. In other words, forcing the locality constraint on all three parties does not weaken their capabilities for obtaining bipartite entanglement when starting from a W-class state. I also present that this property holds for certain types of GHZ-class states as well.

<p> The quantum non-demolition (QND) measurement process begins by entangling the system to be measured, a qubit for example, with an ancillary degree of freedom, usually a system with an infinite-dimensional Hilbert space. The ancilla is amplified to convert the quantum signal into a measurable classical signal. The continuous classical signal is recorded by a measurement apparatus; a discrete measurement outcome is recovered by thresholding the integrated signal record. Measurements play a central role in technologies based on quantum theory, like quantum computation and communication. They form the basis for a wide range of operations, ranging from state initialization to quantum error correction. Quantum measurements used for quantum computation must satisfy three essential requirements of being high fidelity, quantum non-demolition and efficient. Satisfying these criteria necessitates control over all the parts of the quantum measurement process, especially generating the ancilla, entangling it with the qubit and amplifying it to complete the measurement. </p><p> For superconducting quantum circuits, a promising platform for realizing quantum computation, a natural choice for the ancillae are modes of microwave-frequency electromagnetic radiation. In the paradigm of circuit quantum electrodynamics (cQED) with three-dimensional circuits, the most commonly used ancillae are coherent states, since they are easy to generate, process and amplify. Using these flying coherent states, we present results for achieving QND measurements of transmon qubits with fidelities of <i>F</i>> 0.99 and efficiencies of &eta; = 0.56 &plusmn; 0.01. By also treating the measurement as a more general quantum operation, we use the ancillae as carriers of quantum information to generate remote entanglement between two transmon qubits in separate cavities. By using microwave single photons as the flying qubits, it is possible to generate remote entanglement that is robust to loss since the generation of entanglement is uniquely linked to a particular measurement outcome. We demonstrate, in a single experiment, the ability to efficiently generate and detect single microwave photons and use them to generate robust remote entanglement between two transmon qubits. This operation forms a crucial primitive in modular architectures for quantum computation. The results of this thesis extend the experimental toolbox at the disposal to superconducting circuits. Building on these results, we outline proposals for remote entanglement distillation as well as strategies to further improve the performance of the various tools.</p><p>

<p> This hermeneutic research attempts to address the mind and body problem using complementarity from quantum physics and dual aspect monism from philosophy. Quantum mechanics and dual-aspect monism offer ways to explain complex phenomena that include aspects that are seemingly contradictory. In quantum physics, wave&ndash;particle complementarity describes how an atom is both a particle and a wave. In dual-aspect monism, the underlying domain of the universe is neither physical nor mental, but these are both aspects of the ontology. Applying these ideas from quantum mechanics and dual-aspect monism to the existing paradigms within psychology provides different perspectives on the mind-body problem. To begin the process of applying these theories, the physis is imagined to be a particle and the psyche is imagined to be a wave. Complementarity is then used to explore the psyche and the physis. Psyche and physis are also surveyed using dual aspect monism. As the psyche and physis are explored as two different aspects of one ontology, this research attempts to examine how this would manifest within our existence, and what the theories would mean for the splits within the field of psychology. This research found that the frame used to approach psychology (psyche or physis) impacts the results, and trying to approach psychology without using one aspect or the other is difficult to symbolize, and or practice. For depth psychology, this research has shown that retreating entirely to the imaginal or the unconscious may be an unbalanced approach. Keywords: psychology, quantum physics, complementarity, dual-aspect monism</p><p>

Despite the great effort and achievements made towards understanding proton spin structure in the past few decades, a complete picture is still elusive. Parton distribution functions (PDFs), which in quantum chromodynamics (QCD) encode the momentum and helicity distributions of quarks and gluons inside a proton, provide the means by which to quantify the proton structure information. Being inherently nonperturbative, PDFs have to be extracted from unpolarized and polarized lepton-hadron and hadron-hadron scattering data. In particular, experiments that measure unpolarized and polarized jet observables can provide insight into the momentum and helicity distributions of gluons, which have generally been more difficult to determine reliably than those of quarks.In the past, extraction of the spin-averaged and spin-dependent (or helicity) PDFs has been performed in separate analyses. In this thesis, we perform the first simultaneous extraction of both types of quantities from deep-inelastic scattering (DIS), Drell-Yan and single jet observables, within the Monte Carlo global QCD analysis framework developed by the Jefferson Lab Angular Momentum (JAM) Collaboration. The results from this work indicate that the gluon helicity distributions depend rather strongly on the theory assumptions on which the global analysis is based, which calls for the need of measurements with higher precision. As an application of the new simultaneous JAM analysis, we perform an impact study for future Electron-Ion Collider (EIC) data with parity-conserving and parity-violating polarization asymmetries on quark and gluon helicity distributions in the proton. The extrapolation of structure functions from the current data is studied for the first time in the context of the impact study. Theory assumptions, such as SU(2) and SU(3) flavor symmetries, are also studied to give a more thorough understanding of the impact of EIC pseudodata on proton spin structure.

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Quantum computers can efficiently simulate natural processes and solve certain types of mathematical problems. Two of the key issues preventing the development of platforms to realize a scalable quantum machine are the decoherence of the qubits due to the interaction with the environment and the existence of a large overhead to correct errors. Although there already exist noisy intermediate-scale quantum machines, we still need to improve much to be able to solve problems faster than the already existing classical computers. In this dissertation, we explore two approaches to tackle both issues. We propose a scheme where, using quasi-Majorana zero modes located at the edges of nanowires, we construct a logical Majorana zero mode on a network of nanowires. We show that just by modulating the voltage on the nanowires, it is possible to manipulate the position of the logical Majorana zero mode. This could be a significant step towards performing a braiding operation in two dimensions, which is a necessary part of making a fault-tolerant topological quantum computer. In addition to this, we study how disorder in an interacting quantum many-body system can help protect coherence on a given basis. We also employ an experimentally-accessible measurement-based protocol to study local coherence in such systems.

The discovery of the three-dimensional topological insulator (TI) has enormously impacted our understanding of quantum materials. These novel materials are characterized by the topology rather than some order parameters. The TIs are the materials that exhibit insulating properties in the bulk while possessing the metallic state on the surface. These surface states are protected by time-reversal symmetry; as a result, the electrons featuring surface states are spin-polarized. After the discovery of TIs, other topological semimetallic (TSM) states were discovered, which enhanced the understanding and widened the reach of topological materials. Discoveries of various topological phases such as Dirac, Weyl, nodal line semimetals, etc., provided not only novel quasi-particles in condensed matter physics but also promised the discoveries of new technology based on these topological quantum materials. The next focus of the recent research has been on understanding the interplay among topology, superconductivity, magnetism, geometry, correlation, etc. In this thesis, using angle-resolved photoemission spectroscopy (ARPES), time-resolved ARPES (tr-ARPES), magnetic and transport measurements, in conjunction with first-principles calculations, we studied diverse anisotropies in different topological quantum materials, where anisotropic properties are originated due to the numerous factors including geometry, crystalline symmetry, magnetic orientation, and topology. First, we studied the electronic structures of transition metal dipnictides, which crystallize in the low symmetry space group; found that these crystals show different surface behaviors with different cleaving planes. These materials show high magnetoresistance despite having topologically trivial band structures. Our studies reveal that high magnetoresistance in these materials does not necessarily come from the TSM state. Next, we investigated the anisotropic Dirac cone structure in a tetradymite material, which features the Dirac node arc state in addition to the anisotropic Dirac cone at a high symmetry point away from the zone center. Our topological analysis shows that the material possesses multi-fermionic states, which is rare in topological quantum materials. In our next project, we chose a kagome lattice-based material that could provide an ideal platform to study the interplay among geometry, magnetism, correlation, and topology. We investigated magnetic, transport, and electronic structure, in which we revealed that the material possesses anisotropic Hall resistivities and demonstrates multi-orbital fermiology. Finally, using tr-ARPES we revealed the cooling mechanism of the transient topological bulk state in a nodal line semimetal, and our theoretical analysis corroborates our experimental results that the optical and acoustic phonon relaxation follow the linear decay process.

Presented is a study of quantum entanglement from the perspective of the theory of quantum information dynamics. We consider pairwise entanglement and present an analytical development using joint ladder operators, the sum of two single-particle fermionic ladder operators. This approach allows us to write down analytical representations of quantum algorithms and to explore quantum entanglement as it is manifested in a system of qubits.;We present a topological representation of quantum logic that views entangled qubit spacetime histories (or qubit world lines) as a generalized braid, referred to as a super-braid. The crossing of world lines may be either classical or quantum mechanical in nature, and in the latter case most conveniently expressed with our analytical expressions for entangling quantum gates. at a quantum mechanical crossing, independent world lines can become entangled. We present quantum skein relations that allow complicated superbraids to be recursively reduced to alternate classical histories. If the superbraid is closed, then one can decompose the resulting superlink into an entangled superposition of classical links. Also, one can compute a superlink invariant, for example the Jones polynomial for the square root of a knot.;We present measurement-based quantum computing based on our joint number operators. We take expectation values of the joint number operators to determine kinetic-level variables describing the quantum information dynamics in the qubit system at the mesoscopic scale. We explore the issue of reversibility in quantum maps at this scale using a quantum Boltzmann equation. We then present an example of quantum information processing using a qubit system comprised of nuclear spins. We also discuss quantum propositions cast in terms of joint number operators.;We review the well known dynamical equations governing superfluidity, with a focus on self-consistent dynamics supporting quantum vortices in a Bose-Einstein condensate (BEC). Furthermore, we review the mutual vortex-vortex interaction and the consequent Kelvin wave instability. We derive an effective equation of motion for a Fermi condensate that is the basis of our qubit representation of superfluidity.;We then present our quantum lattice gas representation of a superfluid. We explore aspects of our model with two qubits per point, referred to as a Q2 model, particularly its usefulness for carrying out practical quantum fluid simulations. We find that it is perhaps the simplest yet most comprehensive model of superfluid dynamics. as a prime application of Q2, we explore the power-law regions in the energy spectrum of a condensate in the low-temperature limit. We achieved the largest quantum simulations to date of a BEC and, for the first time, Kolmogorov scaling in superfluids, a flow regime heretofore only obtainably by classical turbulence models.;Finally, we address the subject of turbulence regarding information conservation on the small scales (both mesoscopic and microscopic) underlying the flow dynamics on the large hydrodynamic (macroscopic) scale. We present a hydrodynamic-level momentum equation, in the form of a Navier-Stokes equation, as the basis for the energy spectrum of quantum turbulence at large scales. Quantum turbulence, in particular the representation of fluid eddies in terms of a coherent structure of polarized quantum vortices, offers a unique window into the heretofore intractable subject of energy cascades.

Qweak is an experiment currently running at the Thomas Jefferson National Accelerator Facility that uses parity-violating elastic electron-proton scattering to measure the weak charge of the proton QPweak . Longitudinally polarized electrons are scattered off a liquid hydrogen target and pass through a toroidal-field magnetic spectrometer. This experiment is a sensitive test for physics beyond the Standard Model, as QPweak is well predicted in the Standard Model. This dissertation describes the first direct measurement of QPweak . The precision that will be generated by the final 4% measurement will allow the probing of certain classes of new physics up to 2.5 TeV. In this dissertation, the design and status of the complete experiment are discussed, including the details of the asymmetry measurements and preliminary results from several studies of experimental systematics. This dissertation also includes a full description of the design, construction, commissioning, and use of the vertical drift chambers (VDC) used in the Qweak experiment to measure the scattered electron's profile and the momentum transfer (Q 2) of the ep scattering. The Q 2 was measured to be 0.0274 +/- 0.0013 GeV2/c 2 and QPweak was measured to be 0.102 +/- 0.036, which is consistent with the Standard Model.