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Klasik olmayan ilintileri çok çeşitli kuantum mekaniksel sistemdelerde gözlemek mümkündür. Bu ilintilerin karakterizasyonu ve ölçümü, kuantum enformasyon teorisi içerisinde önemli ve halen aktif araştırmanın devam ettiği bir alandır. Çeşitli yoğun madde fiziği sistemlerinde klasik olmayan ilintileri inceleyerek, bu sistemlerle ilgili önemli bilgiler edinilebildiği bilinmektedir. Özellikle faz diyagramında kuantum kritik noktalar bulunduran modellerde ilintilerin kritik nokta etrafındaki beklenmedik davranışı oldukça ilgi çekmiştir. Biz bu çalışmamızda, iki değişik kuantum spin modelini klasik olmayan ilintiler gozüyle inceledik. Ayrıca, iki alt sistemden oluşan kuantum hallerinin önemli bir alt kümesinde, çeşitli ilinti ölçütlerinin nasıl davrandığını tartıştık.İlk olarak, spin-j ve spin-1/2 altsistemlerden oluşan, dönmeler altında değişmez hallerde kuantum uyuşmazlık ölçütünü analitik olarak hesapladık. Sonuçlarımızı benzer simetrilere sahip sistemlerin kuantum uyuşmazlığı ve dolaşıklığı ile karşılaştırdık. İncelediğimiz sistemdeki uyumşmazlık miktarının karşılaştırdığımız hallerdekinden daha fazla olduğunu gözlemledik. İkinci olarak, bir boyutlu XY spin modelinde sonlu sıcaklıkta, çeşitli kuantum ve toplam ilintilerin davranışını araştırdık. Bu ilintilerin kuantum kritik noktayı doğru tespit etmesinin, Hamiltonyen değişkenlerine önemli ölçüde bağlı olduğunu gösterdik. Son olarak, iki ve üç parçacık için spin-1 Bose-Hubbard modelinde sonlu sıcaklıkta dolaşıklık ve daha genel kuantum ilinti ölçütlerinin davranışını inceledik. Sistemdeki taban hal değişikliklerinin iki ölçüt tarafından da işaret edildiğini gösterdik. Non-classical correlations arise in various quantum mechanical systems. Characterizationand quantification of these correlations is an important and active branch of researchin the field of quantum information theory. Investigation of non-classical correlationsin condensed matter systems gives important insights about the characteristics ofthese systems. In particular, systems possessing a quantum critical point in their phasediagrams have attracted much attention due to the peculiar behavior of correlations nearthese points. In this thesis, we have investigated two distinct quantum spin models fromthe perspective of correlations and, we have discussed the correlation content of an importantsubclass of bipartite states.We start by an analytical calculation of the quantum discord for a system composed ofspin-j and spin-1/2 subsystems possessing rotational symmetry. We have compared ourresults with the quantum discord of states having similar symmetries and seen that in rotationallyinvariant states the amount of quantum discord is much higher. Moreover, usingthe well known entanglement properties of these states, we have compared their quantumdiscord with entanglement and seen that quantum discord is higher than the entanglement.Next, we have investigated the thermal quantum correlations and entanglement in spin-1Bose-Hubbard model with two and three particles. We have demonstrated that the energylevel crossings in the ground state of the system are signalled by both the behavior ofthermal quantum correlations and entanglement. Finally, we have investigated variousthermal quantum and total correlations in the anisotropic XY spin-chain with transversemagnetic field. We have shown that the ability of the considered measures to estimatethe critical points of this system at finite temperature strongly depends on the anisotropyparameter of the Hamiltonian. Furthermore, we have studied the effect of temperature onlong-range correlations of the XY chain. 63

We present a nonlinear generalization of quantum mechanics where one can copy arbitrary pure states with fidelities higher than those of the quantum cloners. Weinberg's nonlinear quantum mechanics has been criticized for its possible implications for superluminal communication. We demonstrate that universal symmetric cloners can make better copies than standard quantum ones and yet they do not violate the no-signalling principle. If linearity constraint is added, we show that for a given fidelity there is a unique cloner which can be written down explicitly.

We show that certain coherences, termed as heat-exchange coherences, which contribute to the thermalization process of a quantum probe in a repeated interactions scheme, can modify the spectral response of the probe system. We suggest the use of the power spectrum as a way to experimentally assess the apparent temperature of non-thermal atomic clusters carrying such coherences and also prove that it is useful to measure the corresponding thermalization time of the probe, assuming some information is provided on the nature of the bath. We explore this idea in two examples in which the probe is assumed to be a single-qubit and a single-cavity field mode. Moreover, for the single-qubit case, we show how it is possible to perform a quantum simulation of resonance fluorescence using such repeated interactions scheme with clusters carrying different class of coherences., Scientific and Technological Research Council of Turkey (TÜBİTAK); EU-COST Action

We examine the emergence of objectivity via quantum Darwinism through the use of a collision model, i.e., where the dynamics is modeled through sequences of unitary interactions between the system and the individual constituents of the environment, termed "ancillas." By exploiting versatility of this framework, we show that one can transition from a "Darwinistic" to an "encoding" environment by simply tuning their interaction. Furthermore, we establish that in order for a setting to exhibit quantum Darwinism we require a mutual decoherence to occur between the system and environmental ancillas, thus showing that system decoherence alone is not sufficient. Finally, we demonstrate that the observation of quantum Darwinism is sensitive to a nonuniform system-environment interaction., Science Foundation Ireland Starting Investigator Research Grant "SpeedDemon"; Royal Society Newton Mobility Grant; European Union (European Union); Horizon 2020; European Union Collaborative Project QuProCS; Scientific and Technological Research Council of Turkey (TÜBİTAK); DfE-SFI Investigator Program; H2020 Collaborative Project TEQ; COST Action "QTSpace"; FFABR

We examine a simple scheme to generate genuine multipartite entangled states across disjoint qubit registers. We employ a shuttle qubit that is sequentially coupled, in an energy preserving manner, to the constituents within each register through rounds of interactions. We establish that stable $W$-type entanglement can be generated among all qubits within the registers. Furthermore, we find that the entanglement is sensitive to how the shuttle is treated, showing that a significantly larger degree is achieved by performing projective measurements on it. Finally, we assess the resilience of this entanglement generation protocol to several types of noise and imperfections, showing that it is remarkably robust., Comment: 11 pages, 7 figures. Close to published version

Protecting quantum states from the decohering effects of the environment is of great importance for the development of quantum computation devices and quantum simulators. Here, we introduce a continuous dynamical decoupling protocol that enables us to protect the entangling gate operation between two qubits from the environmental noise. We present a simple model that involves two qubits which interact with each other with a strength that depends on their mutual distance and generates the entanglement among them, as well as in contact with an environment. The nature of the environment, that is, whether it acts as an individual or common bath to the qubits, is also controlled by the effective distance of qubits. Our results indicate that the introduced continuous dynamical decoupling scheme works well in protecting the entangling operation. Furthermore, under certain circumstances, the dynamics of the qubits naturally led them into a decoherence-free subspace which can be used complimentary to the continuous dynamical decoupling., Comment: 9 pages, 3 figures, close to published version

We consider a finite-time quantum Otto cycle with single and two-spin-$1/2$ systems as its working medium. In order to mimic adiabatic dynamics at a finite-time, we employ a shortcut-to-adiabaticity technique and evaluate the performance of the engine including the cost of the shortcut. We compare our results with the true adiabatic and non-adiabatic performances of the same cycle. Our findings clearly indicate that the use of shortcut-to-adiabaticity scheme significantly enhances the performance of the quantum Otto engine as compared to its adiabatic and non-adiabatic counterparts for different figures of merit., Comment: 11 pages, 3 figures. Close to published version

We investigate the evolution of a target qubit caused by its multiple random collisions with $N$-qubit clusters. Depending on the cluster state, the evolution of the target qubit may correspond to its effective interaction with a thermal bath, a coherent (laser) drive, or a squeezed bath. In cases where the target qubit relaxes to a thermal state its dynamics can exhibit a quantum advantage, whereby the target-qubit temperature can be scaled up proportionally to $N^2$ and the thermalization time can be shortened by a similar factor, provided the appropriate coherence in the cluster is prepared by non-thermal means. We dub these effects quantum super-thermalization due to its analogies to super-radiance. Experimental realizations of these effects are suggested., Comment: 9 pages, 8 figures

We consider the dynamics of a collisional model in which both the system and environment are embodied by spin-$1/2$ particles. In order to include non-Markovian features in our model we introduce interactions among the environmental qubits and investigate the effect that different models of such interaction have on the degree of non-Markovianity of the system's dynamics. By extending that interaction beyond the nearest-neighbour, we enhance the degree of non-Markovianity in the system's dynamics. A further significant increase can be observed if a collective interaction with the forthcoming environmental qubits is considered. However, the observed degree of non-Markovianity in this case is non-monotonic with the increasing number of qubits included in the interaction. Moreover, one can establish a connection between the degree of non-Markovianity in the evolution of the system and the fading behaviour of quantum coherence in its state as the number of collisions grow. We complement our study with an investigation on system-environment correlations and present an example of their importance on a physical upper bound on the trace distance derivative., 9 pages, 7 figures. Close to published version

We consider finite-sized atomic systems with varying number of particles which have dipolar interactions among them and are also under the collective driving and dissipative effect of a thermal photon environment. Focusing on the simple case of two atoms, we investigate the impact of different parameters of the model on the coherence contained in the system. We observe that, even though the system is initialized in a completely incoherent state, it evolves to a state with a finite amount of coherence and preserves that coherence in the long-time limit in the presence of thermal photons. We propose a scheme to utilize the created coherence in order to change the thermal state of a single two-level atom by having it repeatedly interact with a coherent atomic beam. Finally, we discuss the scaling of coherence as a function of the number of particles in our system up to N = 7., Lockheed-Martin Corp.; Koç Üniversitesi

We explore quantum and classical correlations along with coherence in the ground states of spin-1 Heisenberg chains, namely the one-dimensional XXZ model and the one-dimensional bilinear biquadratic model, with the techniques of density matrix renormalization group theory. Exploiting the tools of quantum information theory, that is, by studying quantum discord, quantum mutual information, and three recently introduced coherence measures in the reduced density matrix of two nearest neighbor spins in the bulk, we investigate the quantum phase transitions and special symmetry points in these models. We point out the relative strengths and weaknesses of correlation and coherence measures as figures of merit to witness the quantum phase transitions and symmetry points in the considered spin-1 Heisenberg chains. In particular, we demonstrate that, as none of the studied measures can detect the infinite-order Kosterlitz-Thouless transition in the XXZ model, they appear to be able to signal the existence of the same type of transition in the biliear biquadratic model. However, we argue that what is actually detected by the measures here is the SU(3) symmetry point of the model rather than the infinite-order quantum phase transition. Moreover, we show in the XXZ model that examining even single site coherence can be sufficient to spotlight the second-order phase transition and the SU(2) symmetry point., Foundation for Development of UNESP (FUNDUNESP); Sao Paulo Research Foundation (FAPESP); National Counsel of Technological and Scientific Development (CNPq); National Institute for Science and Technology of Quantum Information (INCT-IQ); Minas Gerais Research Foundation (FAPEMIG); CNPq; INCT-IQ