Entanglement degree of electron pairs out of Andreev reflection

We study the entanglement degree of electron pairs emitted from an s-wave Superconductor, which Couples to two normal leads via a single-level quantum dot. Within the framework of scattering matrix theory. the concurrence is used to quantify the entanglement. And the result shows that the entanglement degree is generally influenced by the initial separation of the two electrons in a Cooper pair and the normal transmission eigenvalues T-1, T-2. But it is only determined by the eigenvalues in the tunnelling limit, T-1. T-2 << 1, what is more. it is measurable. (C) 2008 Elsevier B.V. All rights reserved.

Characterization of entanglement transformation via group representation theory

Entanglement transformation of composite quantum systems is investigated in the context of group representation theory. Representation of the direct product group SL(2, C) circle times SL(2, C), composed of local operators acting on the binary composite system, is realized in the four-dimensional complex space in terms of a set of novel bases that are pseudo-orthonormalized. The two-to-one homomorphism is then established for the group SL(2, C) circle times SL(2, C) onto the SO(4, C). It is shown that the resulting representation theory leads to the complete characterization for the entanglement transformation of the binary composite system.

Method for measuring two-qubit entanglement of formation by local operations and classical communication

We present a parametrically efficient method for measuring the entanglement of formation E-f in an arbitrarily given unknown two-qubit state rho(AB) by local operations and classical communication. The two observers, Alice and Bob, first perform some local operations on their composite systems separately, by which the desired global quantum states can be prepared. Then they estimate seven functions via two modified local quantum networks supplemented a classical communication. After obtaining these functions, Alice and Bob can determine the concurrence C and the entanglement of formation E-f.

Thermal entanglement in a two-qubit Heisenberg XXZ spin chain under an inhomogeneous magnetic field

The thermal entanglement in a two-qubit Heisenberg XXZ spin chain is investigated under an inhomogeneous magnetic field b. We show that the ground-state entanglement is independent of the interaction of z-component J(z). The thermal entanglement at the fixed temperature can be enhanced when J(z) increases. We strictly show that for any temperature T and J(z), the entanglement is symmetric with respect to zero inhomogeneous magnetic field, and the critical inhomogeneous magnetic field b(c) is independent of J(z). The critical magnetic field B-c increases with the increasing parallel to b parallel to but the maximum entanglement value that the system can arrive at becomes smaller.

Thermal entanglement in two qutrits system

The thermal entanglement in a two-qutrit system with two spins coupled by exchange interaction is investigated in terms of the measure of entanglement called "negativity". It is found that the thermal entanglement is present and evolvements symmetrically between both ferromagnetic and antiferromagnetic exchange couplings with the temperature. Moreover the critical temperature at which the negativity vanishes increases with the exchange coupling constant J. From the temperature and magnetic field dependences we demonstrate that the temperature and the magnetic field can affect the feature of the thermal entanglement significantly.

Double hydrogenic impurities in double quantum dots

The ground states and degree of entanglement of double hydrogenic impurities in a pair of vertically stacked InGaAs/GaAs quantum dots are studied with a proposed diagonalization technique. It is found that at short barrier widths, the entanglement is small due to the coupling between the intra- and interdot orbitals. At large barrier widths, large entanglement occurs.

Entanglement in a spin-one spin chain

The thermal entanglement in a two-spin-qutrit system with two spins coupled by exchange interaction is investigated in terms of the measure of entanglement called 'negativity'. We strictly show that for any temperature the entanglement is symmetric with respect to zero magnetic field. The behavior of negativity is presented for four different cases. We find that the entanglement may be enhanced under a nonuniform magnetic field. Because there is not any necessary and sufficient condition for quantum separability in systems of dimension 3 circle times 3, our results are qualitative, not quantitative. (c) 2006 Elsevier Ltd. All rights reserved.

Thermal entanglement in a two-spin-qutrit system under a nonuniform external magnetic field

The thermal entanglement in a two-spin-qutrit system with two spins coupled by exchange interaction under a magnetic field in an arbitrary direction is investigated. Negativity, the measurement of entanglement is calculated. We find that for any temperature the evolvement of negativity is symmetric with respect to magnetic field. The behavior of negativity is presented for four different cases. The results show that for different temperature; different magnetic field give maximum entanglement. Both the parallel and antiparallel magnetic field cases are investigated qualitatively (not quantitatively) in detail, we find that the entanglement may be enhanced under an antiparallel magnetic field.

Quantum computation with coupled quantum dots embedded in optical microcavities

Based on an idea that spatial separation of charge states can enhance quantum coherence, we propose a scheme for a quantum computation with the quantum bit (qubit) constructed from two coupled quantum dots. Quantum information is stored in the electron-hole pair state with the electron and hole located in different dots, which enables the qubit state to be very long-lived. Universal quantum gates involving any pair of qubits are realized by coupling the quantum dots through the cavity photon which is a hopeful candidate for the transfer of long-range information. The operation analysis is carried out by estimating the gate time versus the decoherence time.

Quantum behavior in mesoscopic systems

In this thesis I present the work done during my PhD. The Thesis is divided into two parts; in the first one I present the study of mesoscopic quantum systems whereas in the second one I address the problem of the definition of Markov regime for quantum system dynamics. The first work presented is the study of vortex patterns in (quasi) two dimensional rotating Bose Einstein condensates (BECs). I consider the case of an anisotropy trapping potential and I shall show that the ground state of the system hosts vortex patterns that are unstable. In a second work I designed an experimental scheme to transfer entanglement from two entangled photons to two BECs. This work is meant to propose a feasible experimental set up to bring entanglement from microscopic to macroscopic systems for both the study of fundamental questions (quantum to classical transition) and technological applications. In the last work of the first part another experimental scheme is presented in order to detect coherences of a mechanical oscillator which is assumed to have been previously cooled down to the quantum regime. In this regime in fact the system can rapidly undergo decoherence so that new techniques have to be employed in order to detect and manipulate their states. In the scheme I propose a micro-mechanical oscillator is coupled to a BEC and the detection is performed by monitoring the BEC with a negligible back-action on the cantilever. In the second part of the thesis I give a definition of Markov regime for open quantum dynamics. The importance of such definition comes from both the mathematical description of the system dynamics and from the understanding of the role played by the environment in the evolution of an open system. In the Markov regime the mathematical description can be simplified and the role of the environment is a passive one.

Correlations in low dimensional quantum systems

In this thesis I present the work done during my PhD in the area of low dimensional quantum gases. The chapters of this thesis are self contained and represent individual projects which have been peer reviewed and accepted for publication in respected international journals. Various systems are considered, the first of which is a two particle model which possesses an exact analytical solution. I investigate the non-classical correlations that exist between the particles as a function of the tunable properties of the system. In the second work I consider the coherences and out of equilibrium dynamics of a one-dimensional Tonks-Girardeau gas. I show how the coherence of the gas can be inferred from various properties of the reduced state and how this may be observed in experiments. I then present a model which can be used to probe a one-dimensional Fermi gas by performing a measurement on an impurity which interacts with the gas. I show how this system can be used to observe the so-called orthogonality catastrophe using modern interferometry techniques. In the next chapter I present a simple scheme to create superposition states of particles with special emphasis on the NOON state. I explore the effect of inter-particle interactions in the process and then characterise the usefulness of these states for interferometry. Finally I present my contribution to a project on long distance entanglement generation in ion chains. I show how carefully tuning the environment can create decoherence-free subspaces which allows one to create and preserve entanglement.

Pyramidal quantum dots: single and entangled photon sources and correlation studies

Practical realisation of quantum information science is a challenge being addressed by researchers employing various technologies. One of them is based on quantum dots (QD), usually referred to as artificial atoms. Being capable to emit single and polarization entangled photons, they are attractive as sources of quantum bits (qubits) which can be relatively easily integrated into photonic circuits using conventional semiconductor technologies. However, the dominant self-assembled QD systems suffer from asymmetry related problems which modify the energetic structure. The main issue is the degeneracy lifting (the fine-structure splitting, FSS) of an optically allowed neutral exciton state which participates in a polarization-entanglement realisation scheme. The FSS complicates polarization-entanglement detection unless a particular FSS manipulation technique is utilized to reduce it to vanishing values, or a careful selection of intrinsically good candidates from the vast number of QDs is carried out, preventing the possibility of constructing vast arrays of emitters on the same sample. In this work, site-controlled InGaAs QDs grown on (111)B oriented GaAs substrates prepatterned with 7.5 μm pitch tetrahedrons were studied in order to overcome QD asymmetry related problems. By exploiting an intrinsically high rotational symmetry, pyramidal QDs were shown as polarization-entangled photon sources emitting photons with the fidelity of the expected maximally entangled state as high as 0.721. It is the first site-controlled QD system of entangled photon emitters. Moreover, the density of such emitters was found to be as high as 15% in some areas: the density much higher than in any other QD system. The associated physical phenomena (e.g., carrier dynamic, QD energetic structure) were studied, as well, by different techniques: photon correlation spectroscopy, polarization-resolved microphotoluminescence and magneto-photoluminescence.

Entanglement distribution with global control in a star-shaped multi-splitter

Distributed quantum information processing (QIP) is a promising way to bypass problems due to unwanted interactions between elements. However, this strategy presupposes the engineering of protocols for remote processors. In many of them, pairwise entanglement is a key resource. We study a model which distributes entanglement among elements of a delocalized network without local control. The model is efficient both in finite- and infinite-dimensional Hilbert spaces. We suggest a setup of electromechanical systems to implement our proposal.

Correspondence between continuous-variable and discrete quantum systems of arbitrary dimensions

We establish a mapping between a continuous-variable (CV) quantum system and a discrete quantum system of arbitrary dimension. This opens up the general possibility to perform any quantum information task with a CV system as if it were a discrete system. The Einstein-Podolsky-Rosen state is mapped onto the maximally entangled state in any finite-dimensional Hilbert space and thus can be considered as a universal resource of entanglement. An explicit example of the map and a proposal for its experimental realization are discussed.

Quantum-information processing for a coherent superposition state via a mixed entangled coherent channel

An entangled two-mode coherent state is studied within the framework of 2 x 2-dimensional Hilbert space. An entanglement concentration scheme based on joint Bell-state measurements is worked out. When the entangled coherent state is embedded in vacuum environment, its entanglement is degraded but not totally lost. It is found that the larger the initial coherent amplitude, the faster entanglement decreases. We investigate a scheme to teleport a coherent superposition state while considering a mixed quantum channel. We find that the decohered entangled coherent state may be useless for quantum teleportation as it gives the optimal fidelity of teleportation less than the classical limit 2/3.