No / We consider two distant mesoscopic SQUID rings, approximated with two-level systems, interacting with two-mode microwaves. The Hamiltonian of the system is used to calculate its time evolution. The cases with microwaves which at t = 0 are in separable states (classically correlated) or entangled states (quantum mechanically correlated) are studied. It is shown that the Josephson currents in the two SQUID rings are also correlated.

When faced with Duhemian problems of underdetermination, scientific method suggests neither a circumvention of such difficulties via the uncritical acceptance of background assumptions, nor the employment of epistemically unsatisfying subjectivist models of rational retainment. Instead, scientists are challenged to attack problems of underdetermination 'head-on', through a careful analysis of the severity of the testing procedures responsible for the production and modeling of their anomalous data. Researchers faced with the task of explaining empirical anomalies, employ a number of diverse and clever experimental techniques designed to cut through the Duhemian mists, and account for potential sources of error that might weaken an otherwise warranted inference. In lieu of such progressive experimental procedures, scientists try to identify the actual inferential work that an existing experiment is capable of providing so as to avoid ascribing to its output more discriminative power than it is rightfully due. We argue that the various strategies adopted by researchers involved in the testing of Bell's inequality, are well represented by Mayo's error-statistical notion of scientific evidence. In particular, an acceptance of her stringent demand for the output of severe tests to stand at the basis of rational inference, helps to explain the methodological reactions expressed by scientists in response to the loopholes that plagued the early Bell experiments performed by Alain Aspect et al.. At the same time, we argue as a counterpoint, that these very reactions present a challenge for 'top-down' approaches to Duhem's problem. / Master of Arts

Long-term storage of quantum information has diverse applications in quantum information science. This work presents an experimental realization of quantum memories with lifetimes greater then 0.1 s. The memories are based on cold rubidium atoms confined in one-dimensional optical lattices. First realization of lattice-based quantum memory and entanglement between a light field and a spin wave is presented in Chapter II. Chapter III describes two different methods (two-photon and magnetic) of compensation for inhomogeneous differential light shifts between the memory levels due to optical trapping potentials, and demonstration of entanglement between a telecom-band light field and a light-shift compensated memory qubit. Highly excited Rydberg atoms present a unique platform for study of strongly correlated systems and quantum information, because of their enormous dipole moments and consequent strong, long-range interactions. In the experiment described in Chapter IV single collective Rydberg excitations are created in a cold atomic gas. After a variable storage period the excitations are converted into light. As the principal quantum number n of the Rydberg level is increased beyond ~ 70, no more than a single excitation is retrieved from the entire mesoscopic ensemble of atoms. In Chapter V, by spatially selective conversion of the spin wave into a light field, we demonstrate that Rydberg-level interactions create long-range correlations of collective atomic excitations. These results hold promise for studies of dynamics and disorder in many-body systems with tunable interactions and for scalable quantum information networks. Chapter VI presents initial observations of coherent many-body Rabi oscillations between the ground level and a Rydberg level using several hundred cold rubidium atoms. The strongly pronounced oscillations indicate a nearly complete excitation blockade of the entire mesoscopic ensemble by a single excited atom.

In this thesis, the entangled mixed states of two qubits are considered. In the case where the matrix rank of the corresponding density matrix is 2, such a state can be purified to a pure state of 3 qubits. By utilizing this representation, the classification of such states of two qubits by stochastic local operations assisted by classical communication (SLOCC) is obtained. Also for such states, the optimal ensemble that appears in the computation of the concurrence and entanglement of formation is obtained.

This thesis describes the design, development, and implementation of a pulsed source of polarization-entangled photons using spontaneous parametric down-conversion in a Sagnac interferometer. A tangle of 0.9286 ± 0.0015, fidelity to the state (|10〉 + |01〉)/√2 of 0.9798 ± 0.0004 and a brightness of 597 pairs/s/mW were demonstrated. Spontaneous parametric down-conversion is a nonlinear optical process in which one photon is split into two lower-frequency photons while conserving momentum and energy, in this experiment nearly degenerate photons are produced. These photons are then interfered at the output beamsplitter of the interferometer, exchanging path entanglement for polarization entanglement and generating the desired polarization-entangled photon pairs.

This thesis describes the design, development, and implementation of a pulsed source of polarization-entangled photons using spontaneous parametric down-conversion in a Sagnac interferometer. A tangle of 0.9286 ± 0.0015, fidelity to the state (|10〉 + |01〉)/√2 of 0.9798 ± 0.0004 and a brightness of 597 pairs/s/mW were demonstrated. Spontaneous parametric down-conversion is a nonlinear optical process in which one photon is split into two lower-frequency photons while conserving momentum and energy, in this experiment nearly degenerate photons are produced. These photons are then interfered at the output beamsplitter of the interferometer, exchanging path entanglement for polarization entanglement and generating the desired polarization-entangled photon pairs.

Being a puzzling feature of quantum mechanics, entanglement caused many debates since the infancy days of quantum theory. But it is the last two decades that it has started to be seen as a resource for physical tasks which are not possible or extremely infeasible to be done classically. Popular examples are quantum cryptography - secure communication based on laws of physics - and quantum computation - an exponential speedup for factoring large integers. On the other hand, with current technological restrictions it seems to be difficult to preserve specific entangled states and to distribute them among distant parties. Therefore a precise measurement of quantum entanglement is necessary. In this thesis, common bipartite and multipartite entanglement measures in the literature are reviewed. Mathematical definitions, proofs of satisfaction of basic axioms and significant properties for each are given as far as possible. For Tangle and Geometric Measure of Entanglement, which is a multipartite measure, results of numerical calculations for some specific states are shown.

Entanglement is a special correlation of the quantum states of two or more particles. It is also a useful resource enabling us to complete tasks that cannot be done by classical means. As a result, the transformation of entangled states of distant particles by local means arose as an important problem in quantum information theory. In this thesis, we first review some of the studies done on the entanglement transformations. We also develop the necessary and sufficient conditions for the deterministic transformation of W-type states.

At the interface of quantum information and condensed matter physics, the study of entanglement in quantum many-body systems requires a new toolset which combines concepts from each. This thesis introduces a set of computational methods to study phases and phase transitions in lattice models of quantum systems, using the Renyi entropies as a means of quantifying entanglement. The scaling of entanglement entropy can give valuable insight into the phase of a condensed matter system. It can be used to detect exotic types of phases, to pinpoint transitions between phases, and can give us universal information about a system. The first approach in this thesis is a technique to measure entanglement in finite size lattice systems using zero-temperature quantum Monte Carlo simulations. The algorithm is developed, implemented, and used to explore anomalous entanglement scaling terms in the spin-1/2 Heisenberg antiferromagnet. In the second part of this thesis, a new and complementary numerical technique is introduced to study entanglement not just in finite size systems, but as we approach the thermodynamic limit. This “numerical linked-cluster expansion” is used to study two different systems at their quantum critical points — continuous phase transitions occurring at zero temperature, at which these systems exhibit universal properties. Remarkably, these universal properties can be reflected in the scaling of entanglement. Entanglement offers a new perspective on condensed matter systems, one which takes us closer to genuinely understanding what goes on in these materials at the quantum mechanical level. This thesis demonstrates the first steps in developing an extensive list of computational tools that can be used to study entanglement over a wide range of interacting quantum many-body systems. With the ever increasing computational power available, it may be only a matter of time before these tools are used to create a comprehensive framework for the characterization of condensed matter phases and phase transitions.

In this thesis we study the time evolution of Rényi and entanglement entropies of thermal states in Conformal Field Theory (CFT). These quantities are usually hard to compute but Ryu-Takayanagi (RT) and Hubeny-Rangamani-Takayanagi (HRT) proposals allow us to find the same quantities using calculations in general relativity. We will introduce main concepts of holography, quantum information and conformal field theory that will be used to derive the results of this thesis. In the first part of the thesis, we explicitly compute entanglement entropy of the rotating BTZ black hole by directly applying HRT proposal and finding lengths of spacelike geodesics. Rényi entropy of thermal state perturbed by a local quantum quench is computed by mapping correlators on two glued cylinders to the plane for field theory containing a single free boson and for 2d CFTs in the large c limit. We consider Thermofield Double State (TFD) which is an entangled state in direct product of two 2D CFTs. It is conjectured to be holographically equivalent to the eternal BTZ black hole. TFD state is perturbed by a local quench in one CFT and mutual information between two intervals in two CFTs is computed. We find when mutual information vanishes and interpret this as scrambling time, i.e. time scale required for the system to thermalize. This field theory result is modelled with a massive free falling particle in the BTZ black hole. We have computed the back-reaction of the particle on the metric of BTZ and used RT proposal to find holographic entanglement entropy. Finally, we generalize this calculation to the case of rotating BTZ with inner and outer horizons. It is dual to the CFT with different temperatures for left and right moving modes. We calculate mutual information and scrambling time and find exact agreement between results in the gravity and those in the CFT.