Highly efficient transfer of quantum resources including quantum excitations, states, and information on coupled bosonic networks is an important task in quantum physics and quantum information science. Here we propose a bipartite-graph framework to characterize quantum excitation transfer in coupled bosonic networks. This is achieved by diagonalizing the intermediate subnetwork between the sender and the receiver to construct a bipartite-graph configuration, and hence this treatment can be understood from the viewpoint of network deformation. We examine the covariance matrix of the coupled bosonic networks in both the original and bipartite-graph representations. In particular, we investigate quantum excitation transfer in both the finite and infinite intermediate-normal-mode cases and show the dependence of the transfer efficiency on the network configurations and system parameters. We find the bounds of maximally transferred excitations for various network configurations and reveal the underlying physical mechanisms. We also discover that the dark-mode effect will degrade the excitation transfer efficiency. Our findings provide a new insight for the design and optimization of networks in physics, information theory, and complex system science.
Highly efficient transfer of quantum resources including quantum excitations, states, and information on coupled bosonic networks is an important task in quantum physics and quantum information science. Here we propose a bipartite-graph framework to characterize quantum excitation transfer in coupled bosonic networks. This is achieved by diagonalizing the intermediate subnetwork between the sender and the receiver to construct a bipartite-graph configuration, and hence this treatment can be understood from the viewpoint of network deformation. We examine the covariance matrix of the coupled bosonic networks in both the original and bipartite-graph representations. In particular, we investigate quantum excitation transfer in both the finite and infinite intermediate-normal-mode cases and show the dependence of the transfer efficiency on the network configurations and system parameters. We find the bounds of maximally transferred excitations for various network configurations and reveal the underlying physical mechanisms. We also discover that the dark-mode effect will degrade the excitation transfer efficiency. Our findings provide a new insight for the design and optimization of networks in physics, information theory, and complex system science.
We propose and prove two theorems for determining the number of dark modes in linear two-component quantum networks composed of two types of bosonic modes. This is achieved by diagonalizing the two sub-networks of the same type of modes, mapping the networks to either a standard or a thick arrowhead matrix, and analyzing the linear dependence and independence between the column vectors associated with degenerate normal modes in the coupling matrix. We confirm the two theorems by checking the simultaneous ground-state cooling of the mechanical modes in linearized optomechanical networks. These results also work for linear fermionic networks and other networks described by quadratic coupled-mode Hamiltonian. The present method can be extended to study the dark-state effect in driven atom systems and to construct large decoherence-free subspaces for processing quantum information. This work will initiate the studies on dynamical, transport, and statistical properties of linear networks with decoupled subspaces.
Abstract We study the excitation transfer across a fully connected quantum network whose sites energies can be artificially designed. Starting from a simplified model of a broadly-studied physical system, we systematically optimize its local energies to achieve high excitation transfer for various environmental conditions, using an adaptive Gradient Descent technique and Automatic Differentiation. We show that almost perfect transfer can be achieved with and without local dephasing, provided that the dephasing rates are not too large. We investigate our solutions in terms of resilience against variations in either the network connection strengths, or size, as well as coherence losses. We highlight the different features of a dephasing-free and dephasing-driven transfer. Our work gives further insight into the interplay between coherence and dephasing effects in excitation-transfer phenomena across fully connected quantum networks. In turn, this will help designing optimal transfer in artificial open networks through the simple manipulation of local energies.
Controlling the dynamics of quantum states is a common demand in quantum technology. We theoretically study quantum transport and switching in long-range coupled quantum networks possessing a single excitation. The qubit networks of our study are affected by Markovian environments while one qubit is irreversibly connected to an additional site. Different goals are studied towards controlling quantum transport such as efficient single excitation transfer, switching quantum transport,and manipulating the quantum states of qubit networks. These goals have been previously investigated using different mechanisms, however in this thesis we approach them by proposing appropriate geometrical arrangements of sites. Regarding efficient single excitation transfer we follow two approaches: Checking if there exist a spatial dimension preference for qubit arrangements towards optimal quantum transport, and whether the efficient network designs are robust against geometrical variations. For dimension analysis a random walk optimization method is used to compare the transport efficiency of networks expanded in one and two spatial dimensions. We find that for some choices of network parameters the two-dimensional networks are slightly more efficient than the one dimensional equivalent networks. This assures that designing one-dimensional qubit channels are adequate for efficient transport and the two-dimensional networks should only be considered where the two-dimensional spatial expansion is more compatible with the surrounding architecture. To design a network, after deciding about the network dimensionality, one may attempt to optimize the channel geometry which might result in a non-robust optimal configuration against the geometrical errors. To achieve robust optimal configurations we follow two approaches: We investigate the efficient configurations of sites in both one and two dimensional arrangements and present some patterns of robust geometric arrangements of sites in geometrical parameter space. Another approach to achieve robust efficient transport is defining a quantity as the geometrical robustness (georobustness) of qubit networks. By optimising geo-robustness against the network-environment parameters one can efficiently transfer a single excitation with many arbitrary arrangements of the network sites. Switching of quantum states is another goal towards controlled quantum dynamics. We study the transport characteristics of highly symmetric three-dimensional networks and analytically prove that a fraction of the initially injected excitation can trap for long durations via the creation of dark states. Using this characteristic we suggest switching devices which are robust against environmental noises.
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.
Quantum teleportation plays a key role in modern quantum technologies. Thus, it is of much interest to generate alternative approaches or representations that are aimed at allowing us a better understanding of the physics involved in the process from different perspectives. With this purpose, here an approach based on graph theory is introduced and discussed in the context of some applications. Its main goal is to provide a fully symbolic framework for quantum teleportation from a dynamical viewpoint, which makes explicit at each stage of the process how entanglement and information swap among the qubits involved in it. In order to construct this dynamical perspective, it has been necessary to define some auxiliary elements, namely virtual nodes and edges, as well as an additional notation for nodes describing potential states (against nodes accounting for actual states). With these elements, not only the flow of the process can be followed step by step, but they also allow us to establish a direct correspondence between this graph-based approach and the usual state vector description. To show the suitability and versatility of this graph-based approach, several particular teleportation examples are examined in detail, which include bipartite, tripartite, and tetrapartite maximally entangled states as quantum channels. From the analysis of these cases, a general protocol is devised to describe the sharing of quantum information in presence of maximally entangled multi-qubit system.
Abstract Continuous-time quantum walks (CTQW) becoming more significant for quantum information and quantum computation. The perfect state transfer (PST) on graphs is a specific phenomena of CTQW which is widely used in quantum communication of small system, and be found critical for quantum algorithm design recently, such as quantum approximate optimization algorithms and quantum search. If a network G contains 2N vertices, and PST occurs between N pairs of vertices at the same time T, then we say G admits symmetric PST (SPST). In this work, we will study the SPST on bipartite graphs via spectra. And then, we will present how to set couplings of special bipartite graphs such as cycles, grids and chains to admit SPST is given. For cycles with 6, 8, 10, 12 vertices, we give the analytical method to obtain the couplings to admit SPST. Analogously, the couplings for chains and grids to admit SPST are analytical obtained. We also present a typical approach by using the graph tensor product to construct new quantum networks that admit SPST, in which the new quantum networks are derived from special kinds of integral graphs, such as complete graphs, strongly regular graphs and distance regular graphs.