We use a disordered anti-ferromagnetic spin-1/2 chain with anisotropic exchange coupling to model an array of interacting qubits. All qubits have the same level spacing, except two, which are called the defects of the chain. The level spacings of the defects are equal and much larger than all the others. We investigate how the entanglement between the two defects depends on the anisotropy of the system. When the anisotropy coupling is much larger than the energy difference between a defect and an ordinary qubit, the two defects become strongly entangled. Small anisotropies, on the contrary, may decrease the entanglement, which is, in this case, also much affected by the number of excitations. The analysis is made for nearest neighbor and next-nearest neighbor defects. The decrease in the entanglement for nearest neighbor defects is not very significant, especially in large chains.
This thesis explores ways in which quantum channels and correlations (of both classical and quantum types) manifest themselves, and also studies the interplay between these two aspects in various physical settings. Quantum channels represent all possible evolutions of states allowed by quantum mechanics while correlations are intrinsic (nonlocal) properties of composite systems. There are four main problems that are addressed (i) the role played by initial system-bath correlations on the subsystem dynamics of an open quantum system, (ii) computation of correlations for two-qubit X-states, (iii…
The distribution of entanglement of typical multiparty quantum states is not uniform over the range of the measure utilized for quantifying the entanglement. We intend to find the response to disorder in the state parameters on this non-uniformity for typical states. We find that the typical entanglement, averaged over the disorder, is taken farther away from uniformity, as quantified by decreased standard deviation, in comparison to the clean case. The feature is seemingly generic, as we see it for Gaussian and non-Gaussian disorder distributions, for varying strengths of the disorder, and fo…
We prove an upper bound proportional to the surface area for the bipartite entanglement of the ground state and thermal states of harmonic oscillator systems with disorder, as measured by the logarithmic negativity. Our assumptions are satisfied for some standard models that are almost surely gapless in the thermodynamic limit.
Using a non-Hermitian Hamiltonian approach to open systems, we study the interplay of disorder and superradiance in a one-dimensional Anderson model. Analyzing the complex eigenvalues of the non-Hermitian Hamiltonian, a transition to a superradiant regime is shown to occur. As an effect of openness the structure of eigenstates undergoes a strong change in the superradiant regime: we show that the sensitivity to disorder of the superradiant and the subradiant subspaces is very different; superradiant states remain delocalized as disorder increases, while subradiant states are sensitive to the d…
We propose an exactly solvable model to reveal the physics of the interplay between interaction and disorder in bosonic systems. Considering interacting bosons in a double-well potential, in which disorder is mimicked by taking the energy level mismatch between the two wells to be randomly distributed, we find "two negatives make a positive" effect. While disorder or interaction by itself suppresses the phase coherence between the two wells, both together enhance the phase coherence. This model also captures several striking features of the disordered Bose-Hubbard model found in recent numeric…
Using a non-Hermitian Hamiltonian approach to open systems, we study the interplay of disorder and superradiance in a one- and three-dimensional Anderson model. Analyzing the complex eigenvalues of the non-Hermitian Hamiltonian, a transition to a superradiant regime is shown to occur. As an effect of openness the structure of eigenstates undergoes a strong change in the superradiant regime: we show that the sensitivity to disorder of the superradiant and the subradiant subspaces is very different; superradiant states remain delocalized as disorder increases, while subradiant states are sensiti…
Many types of dissipative processes can be found in nature or be engineered, and their interplay with a system can give rise to interesting phases of matter. Here we study the interplay among interaction, tunneling, and disorder in the steady state of a spin chain coupled to a tailored bath. We consider a dissipation which, in contrast to disorder, tends to generate a homogeneously polarized steady state. We find that the steady state can be highly sensitive even to weak disorder. We also establish that, in the presence of such dissipation, even in the absence of interaction, a finite amount o…
We study the emergence of bipartite entanglement between a pair of spins weakly connected to the ends of a linear disordered $XY$ spin-1/2 channel. We analyze how their concurrence responds to structural and on-site fluctuations embodied by long-range spatially-correlated sequences. We show that the end-to-end entanglement is very robust against disorder and asymmetries in the channel provided that the degree of correlations are strong enough and both entangling parties are tuned accordingly. Our results offer further alternatives in the design of stable quantum communication protocols via imp…
We investigate the trends of information backflow associated with the dynamics of a sub-part of a disordered spin-1/2 transverse field Heisenberg chain for different regimes of the Hamiltonian. Towards this aim, the decay profile of bipartite entanglement shared between a probe-qubit and a system-qubit (sub-part) of the chain is monitored in time. A clear shift in the trends of the decay profiles of the bipartite entanglement from monotonic in the low-disorder limit to non-monotonic in the moderately large disorder limit occurs due to strong information backflow from the environment (complemen…
The time-dynamics of quantum correlations in the quantum transverse anisotropic XY spin chain of infinite length is studied at zero as well as finite temperatures. The evolution occurs due to the instantaneous quenching of the coupling constant between the nearest-neighbor spins of the model, which is either performed within the same phase or across the quantum phase transition point connecting the order-disorder phases of the model. We characterize the time-evolved quantum correlations, entanglement and quantum discord, which exhibit varying behavior depending on the initial state and the que…
Understanding the interplay between disorder, environment and interactions is key to elucidating the transport properties of open quantum systems, from excitons in photosynthetic networks to qubits in ion traps. This interplay is studied here theoretically in the context of environment-assisted quantum transport (ENAQT), a unique situation in open system where an environment-induced dephasing can, counter-intuitively, enhance transport. First, we show a surprising situation where the particle current grows with increasing disorder, even without dephasing. Then, we suggest a specific mechanism …
The interplay among topology, disorder, and non-Hermiticity can induce some exotic topological and localization phenomena. Here we investigate this interplay in a two-dimensional non-Hermitian disordered Chern-insulator model with two typical kinds of non-Hermiticities, the nonreciprocal hopping and on-site gain-and-loss effects. The topological phase diagrams are obtained by numerically calculating two topological invariants in the real space, which are the disorder-averaged open-bulk Chern number and the generalized Bott index, respectively. We reveal that the nonreciprocal hopping (the gain…
Disordered systems form one of the centrestages of research in many body sciences and lead to a plethora of interesting phenomena and applications. A paradigmatic disordered system consists of an one-dimensional array of quantum spin-1/2 particles, governed by the Heisenberg spin glass Hamiltonian with natural or engineered quenched disordered couplings in an external magnetic field. These systems allow disorder-induced enhancement for bipartite and multipartite observables. Here we show that simultaneous application of independent quenched disorders results in disorder-induced enhancement, wh…
We investigate bipartite entanglement in random quantum $XY$ models at equilibrium. Depending on the intrinsic time scales associated with equilibration of the random parameters and measurements associated with observation of the system, we consider two distinct kinds of disorder, namely annealed and quenched disorders. We conduct a comparative study of the effects of disorder on nearest-neighbor entanglement, when the nature of randomness changes from being annealed to quenched. We find that entanglement properties of the annealed and quenched disordered systems are drastically different from…
