Quantum entanglement is widely renounced as one of the most fundamental concepts of quantum mechanics. Such phenomenon exhibit non-local interaction properties which cannot be explained classically. In this thesis, we address a number of problems associated with creating, transferring and engineering of entanglement between two separate parties. The work is motivated by a desire to better understand the dynamics of entanglement between systems. In particular, the research is mainly focused on the study of the dynamics of the well known maximally entangled Bell state under different influences such as decoherence and inter-qubit coupling. We show the connection between coherence and entanglement using the system sub jected to decoherence. We also confirm the transfer of entanglement between completely isolated partite using the double Jaynes-Cummings model. Based on this result, we propose a new conservation criterion proven to be general for single excitation systems. Such conservation criterion are then compared and extended to a general N qubit systems. In addition, an attempt is made to evaluate entanglement conservation rules for the EPR- like multipartite entanglement. We also describe a new technique for solving entanglement in the top-down way ignoring physical setup.
Quantum entanglement is widely renounced as one of the most fundamental concepts of quantum mechanics. Such phenomenon exhibit non-local interaction properties which cannot be explained classically. In this thesis, we address a number of problems associated with creating, transferring and engineering of entanglement between two separate parties. The work is motivated by a desire to better understand the dynamics of entanglement between systems. In particular, the research is mainly focused on the study of the dynamics of the well known maximally entangled Bell state under different influences such as decoherence and inter-qubit coupling. We show the connection between coherence and entanglement using the system sub jected to decoherence. We also confirm the transfer of entanglement between completely isolated partite using the double Jaynes-Cummings model. Based on this result, we propose a new conservation criterion proven to be general for single excitation systems. Such conservation criterion are then compared and extended to a general N qubit systems. In addition, an attempt is made to evaluate entanglement conservation rules for the EPR- like multipartite entanglement. We also describe a new technique for solving entanglement in the top-down way ignoring physical setup.
The object of this PhD Thesis is light and matter quantum interaction including studies on cavity and circuit quantum electrodynamics (CQED and cQED), quantum information theory and entanglement dynamics in open systems. In recent years both theoretical and experimental efforts have been devoted to study problems regarding the transfer of quantum correlations, quantum memories, entanglement protection against decoherence and new regimes accessible in cQED. One of the fundamental model underlying these topics is the well known Jaynes-Cummings (JC) one for light-matter interaction, introduced in quantum optics already in 1963. This paradigmatic model describes the coherent exchange of a single excitation between a qubit (a two-level system) and a mode of a quantized harmonic oscillator. The JC model describes a lot of purely quantum effects such as Rabi oscillations and generation of entangled quantum states, which were confirmed by several sophisticated experiments in CQED. This model has been then applied in many other frameworks. Analytical results can be derived only under the so-called rotating wave approximation (RWA), which allows to neglect the energy contributions coming from the counter-rotating terms, which describe the simultaneous excitation (or de-excitation) of the qubit and the field mode. In this Thesis a first interesting investigation, based on the JC model, is related to the realization of quantum memories. The main aspect is the transfer of generic quantum entangled states of a propagating radiation to some qubits, such as two-level atoms placed in separated optical cavities. Generalizing previous results for bipartite entangled systems, I investigated the more complex case of tripartite systems, where the very quantification of entanglement is still an open problem. This issue is broadened to open systems in contact with a common environment which induces decoherence effects unavoidable in realistic implementations. The main result of this analysis is that it is possible to map in an optimal way a quantum state from radiation to qubits in the unitary dynamics, and even in the presence of a dissipative environment a significative amount of entanglement can be transferred. This study has been carried on with either theoretical calculations or numerical simulations performed adopting the powerful Monte Carlo wave function method. A second important problem for quantum memories faced in this PhD Thesis, regards the protection of qubits entanglement for long enough times in order to implement quantum information tasks. A possible way to obtain this goal is to add an external coherent field driving two or more two-level atoms interacting with a common mode of a cavity electromagnetic field. In fact it is possible to demonstrate that, under certain conditions, an effective Hamiltonian of the whole system involves, together with the familiar JC terms, also the counter-rotating ones. The main feature that comes out from this analysis is the possibility to freeze, during system dynamics, peculiar quantum entangled states of the atomic qubits in so called decoherence-free subspaces. This important property allows to store the entanglement in matter qubits, isolating the quantum state from environment induced decoherence. Though the system includes dissipation, analytical results have been obtained for multipartite entanglement and decoherence by solving the master equation through a projection on a suitable basis and using the method of characteristics. In particular it is possible to monitor the rate of decoherence via measurements of joint atomic probabilities, shading light on the fascinating border between the quantum and the classical world. A last topic investigated in this Thesis concerns the recently developed and quite promising implementation of the JC model well outside CQED, that is cQED. Here superconductive circuits, which play the role of artificial atoms, interact on-chip with transmission line resonators, instead of the usual electromagnetic cavities. These systems have the advantage of being quite easily engineered exploiting the most advanced available technologies. Moreover they allow a great flexibility in handling the relevant parameters, since the inter-system coupling is here of capacitive or inductive nature, instead of the usual electric dipole interaction in CQED. In this way a strong and ultrastrong coupling regime have become available, giving a direct access to the physics beyond the JC model and its possible applications. I first performed a detailed characterization of system dynamics in order to test the main approximations usually introduced to describe superconductive circuits as qubits. Then I described, both analytically and numerically, the dissipative dynamics of a superconductive qubit coupled to a resonator mode in the deep strong regime.
During the last decade the field of quantum information has seen considerable progress both
theoretically and experimentally. The building block of this theory is the so-called qubit,
the quantum counterpart of the classical bit. It turns out that spin degrees of freedom
of quantum particles are among the most promising candidates for quantum information
processing and computation. Thus, a deep understanding of the different processes that
govern the dynamics of these objects is of fundamental importance. For instance, the decoherence
process, caused the coupling of the qubits to their surrounding environment, is
the main obstacle to quantum information processing: it leads them to lose their quantum
coherence and thus behave classically. In addition, quantum systems exhibit correlations
that have no classical counterpart. This phenomenon is called entanglement and is the
vital resource for quantum teleportation and quantum computing. Decoherence and entanglement
dynamics were extensively studied within the framework of the Markovian
approximation using the master equation approach. However, due to the non-commuting
character of quantum observables, only few models are known to be exactly solvable.
Moreover, many spin systems display a strongly non-Markovian behavior. This thesis is
devoted to the development of new techniques for deriving the exact dynamics of spin
qubits, coupled through Heisenberg and/or Ising interactions to spin environments that
have internal dynamics. The basic idea behind these techniques is to use the underlying
symmetries exhibited by the Hamitonian operators of the composite systems. This allows
for the study of problems related to decoherence and entanglement.
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.
We consider an entangled but non-interacting qubit pair a 1 and b 1 that is independently coupled to a set of local qubit systems, a I and b J , of 0 bit value, respectively. We derive rules for the transfer of entanglement from the pair a 1 – b 1 to an arbitrary pair a I – b J , for the case of qubit-number conserving local interactions. It is shown that the transfer rule depends strongly on the initial entangled state. If the initial entanglement is in the form of the Bell state corresponding to anti-correlated qubits, the sum of the square of the nonlocal pairwise concurrences is conserved. If the initial state is the Bell state with correlated qubits, this sum can be reduced, even to zero in some cases, to reveal a complete and abrupt loss of all nonlocal pairwise entanglement. We also identify that for the nonlocal bipartitions A – b J involving all qubits at one location, with one qubit b J at the other location, the concurrences satisfy a simple addition rule for both cases of the Bell states that the sum of the square of the nonlocal concurrences is conserved.
The title of the present dissertation Decoherence in Quantum Network sounds very general and all-inclusive. Indeed it embraces two topics (decoherence and quantum network) from the area of Quantum Mechanics each of which is described in all respects by a huge literature developed in the last three decades [...]. Quantum decoherence, as the name lets it mean, is the mechanism that makes a quantum system loose its coherence properties, and with them the capability of giving rise to interference phenomena or to other interesting quantum effects [...]. The key idea promoted by decoherence is the insight that realistic quantum systems are never isolated, but are immersed in the surrounding environment and interact continuously with it [...]. As an example one may consider a two-level quantum system (i.e. a quantum bit, usually shortened with a terminology from information science to \\qubit" ) in contact with a wide environment. Hence, quantum systems are open systems, and continuously interact or exchange information with an external environment whose degrees of freedom are too numerous to be monitored. The resulting correlation between the system and the environment spoils quantum coherence and brings about the transition from a pure quantum state to a mixture of quantum state resulting a classical state. To describe decoherence different kind of approaches can be used (for example Master equation, random matrix, etc). A quantum network typically consists of a number of quantum objects (e.g., atoms, ions, quantum dots, cavities, etc.), to be referred to hereafter as the sites or the nodes of the network. They can interact and the interactions (or their correlations) will be usually described by the edges of a graph. Quantum networks can address different information processing tasks. For instance a quantum state can be transferred from qubit to qubit down a chain solely due to the interactions, that is according to the laws of quantum physics [...]. Quantum networks offer us new opportunities and phenomena as compared to classical networks. An extension to large scale of the idea of a quantum network could lead to a futurible quantum internet [...]. The study of networks has traditionally been the territory of graph theory [...], also with the advent of their quantum versions. Within simple quantum network model information processing is usually described by assuming perfect control of the underlying graph. However, this is not much realistic since randomness is often present and it leads to decoherence effects [...]. In contrast, the conservation of coherence is essential for any quantum information process [...], hence there is a persistent interest in decoherence effects in quantum networks, which motivate us to study models for describing such noisy effects. We consider a simple model of quantum network, employing qubits (spin-1/2 particles) attached to the nodes of an underlying graph and we study the simplest task, namely information storage (on a single and two qubits), when the graph randomly changes in time. Actually we randomly add edges to an initially disconnected graph according to the Gilbert model characterized by a weighting parameter ex [...] and in an identically and independent way at each time step. We find that by increasing ex the dynamics of relevant quantities like fidelity, entropy or concurrence, gradually transforms from damped to damped oscillatory and finally to purely oscillatory. That leads to the paper [see, Information dissipation in random quantum networks, by U. Farooq and S. Mancini, OSID 21(3), 1450004, 2014]. We also study a system composed by pairs of qubits attached to each node of a linear chain, a model that stems from quantum dot arrays. Here we use the approach of evolution with a stochastic Hamiltonian to describe the noisy effects. We then evaluate the effect of two most common disorders, namely exchange coupling and hyperfine interaction fluctuations, in adiabatic preparation of ground state in such model. We show that the adiabatic ground state preparation is highly robust against these disorders making the chain a good analog simulator. Moreover, we also study the adiabatic information transfer, using singlet-triplet states, across the chain. In contrast to ground state preparation the transfer mechanism is highly affected by disorders. This suggested that for communication tasks across such chains adiabatic evolution is not as effective and quantum quenches would be preferable. That leads to the paper [see, Adiabatic many-body state preparation and information transfer in quantum dot arrays, by U. Farooq, A. Bayat, S. Mancini and S. Bose Phys. Rev. B 91, 134303, 2015]. The present work is organized as follows. In chapter 1, we shall give a survey of the various types of approach which can be employed to analyse the dynamics of open quantum systems that leads to decoherence effects. In chapter 2, we shall give a general description about quantum network and its possible applications. In chapter 3, we shall discuss the problem of quantum state transfer in qubit network and shall give a brief overview of some scheme that enable nearly prefect state transfer. In chapter 4, we shall discuss singlet-triplet networks, that is networks having on each site a pair of (generally entangled) qubit. Then within this framework we propose a model stemming from quantum dot array. There we shall address the problem of ground state preparation and state transfer. Finally we shall describe the inherent entanglement of the ground state of strongly correlated systems can be exploited for both classical and quantum communications. In chapter 5, we shall propose a decoherence model for qubit networks based on edges representing XY interactions randomly added to a disconnected graph accordingly to a suitable probability distribution. In this way we shall describe dissipation of information initially localize in single or two qubits all over the network. In chapter 6 we shall model the noisy effects in the quantum dot array introduced in chapter 4 and investigate their consequences on the preparation of ground state and quantum state transfer mechanism. Finally we shall draw conclusions.
Although the concept of quantum entanglement has been known for about seventy years, it only recently quit the realms of meta-theoretical discussions when it was discovered how entanglement can be exploited to compute and communicate with an unprecedented power. The primary motivation of the work presented in this thesis has been to contribute to the big e#ort that has been done during the last decade to understand and quantify quantum entanglement. We have developed advanced techniques of linear and multilinear algebra to investigate and classify entangled pure and mixed quantum states, and discussed some novel applications in the field of quantum information theory. The results presented in this thesis are mainly of interest from a fundamental point a view: entanglement is the characteristic trait of quantum mechanics, the one that enforces its entire departure from classical lines of thought [186]. It is however a real privilege that fundamental research in quantum information theory bears the tools of tomorrow's electrical engineers: the ongoing miniaturization of electronic components will soon reach a scale where quantum mechanical e#ects play a major role.