Given a bipartite density matrix ρ of a quantum state, the Quantum Separability problem (QUSEP) asks — is ρ entangled, or separable? In this thesis, we first strengthen Gurvits’ 2003 NP-hardness result for QUSEP by showing that the Weak Membership problem over the set of separable bipartite quantum states is strongly NP-hard, meaning it is NP-hard even when the error margin is as large as inverse polynomial in the dimension, i.e. is “moderately large”. Previously, this NP-hardness was known only to hold in the case of inverse exponential error. We observe the immediate implication of NP-hardness of the Weak Membership problem over the set of entanglement-breaking maps, as well as lower bounds on the maximum (Euclidean) distance possible between a bound entangled state and the separable set of quantum states (assuming P ≠ NP). We next investigate the entanglement-detecting capabilities of locally invariant unitary operations, as proposed by Fu in 2006. Denoting the subsystems of ρ as A and B, such that ρ_B = Tr_A(ρ), a locally invariant unitary operation U^B is one with the property U^B ρ_B (U^B)^† = ρ_B. We investigate the maximum shift (in Euclidean distance) inducible in ρ by applying I⊗U^B, over all locally invariant choices of U^B. We derive closed formulae for this quantity for three cases of interest: (pseudo)pure quantum states of arbitrary dimension, Werner states of arbitrary dimension, and two-qubit states. Surprisingly, similar to recent anomalies detected for non-locality measures, the first of these formulae demonstrates the existence of non-maximally entangled states attaining shifts as large as maximally entangled ones. Using the latter of these formulae, we demonstrate for certain classes of two-qubit states an equivalence between the Fu criterion and the CHSH inequality. Among other results, we investigate the ability of locally invariant unitary operations to detect bound entanglement.

This study is to research the ¡§Corruption Prevention and Profits Promotion of Corporate Governance in our country¡¨. Recently, companies have encountered the corporate governance problems globally and indicate that corporate governance have not been fulfilled exactly. It not only failed to maximize the profit of shareholders and stakeholders, and even worse, unable to make the investment money get back. Furthermore, it will also cause bad effects that associate with the social instability and weaken the economic development. In view of the reasons that contribute to the occurrence of company scandals, most of people will think it¡¦s due to lack of monitoring and supervision of companies. But this should be merely the direct reasons. Apart form this, it has to be added with indirect causes of inability of company strategy leadership and cause financial problems to occur consequently. It¡¦s obvious that monitoring with corruption prevention and leadership work to profit promotion are two essential features of corporate governance. In the aspect of monitoring system enhancement, this paper has investigated the current supervision problems of corporate governance and provided improvement suggestions accordingly. To the issue of evaluating these two systems regarding independent directors and existing supervisors, several fundamental but important points have been reviewed and recommendations have been provided. In consideration of increasing leadership management performance and building a multi-purposes board, we recommend taking British mode of a balancing board as a good reference example. It¡¦s recommended that both characteristics of independent monitoring and excellent ability of promoting company¡¦s profit should be taken into account simultaneously when choosing directors. It¡¦s expected that the board can fulfill the duties of monitoring the company efficiently and playing the role as excellent navigator successfully to lead the company going forward continuously. It¡¦s all wish that owing to these dual functions have been stressed and developed; it can bring a new era to our corporate governance.

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Polarization division multiplexing (PolDM) is a promising way to improve the spectral efficiency of fiber-optic communication systems. However, PolDM systems suffer greatly from polarization mode dispersion (PMD), especially in long-haul systems. PMD is time-varying and is intrinsically hard to compensate. Current PMD compensators are complicated and expensive to build, adding to the cost and complexity of practical PolDM systems. We propose a new differential polarization time coding scheme combined with controlled polarization rotation to increase the system tolerance to PMD. An encoding algorithm, a differential receiver design, and a decoding algorithm are described in detail. Controlled polarization rotation is achievable using conventional Mach-Zehnder interferometers that are used to modulate the signal. Simulation results show that significant improvement in PMD tolerance can be achieved with little added complexity. Given a certain transmission distance, our proposed system can also increase the achievable data rate compared to a PolDM differential quadrature phase shift keying system.

Polarization division multiplexing (PolDM) is a promising way to improve the spectral efficiency of fiber-optic communication systems. However, PolDM systems suffer greatly from polarization mode dispersion (PMD), especially in long-haul systems. PMD is time-varying and is intrinsically hard to compensate. Current PMD compensators are complicated and expensive to build, adding to the cost and complexity of practical PolDM systems. We propose a new differential polarization time coding scheme combined with controlled polarization rotation to increase the system tolerance to PMD. An encoding algorithm, a differential receiver design, and a decoding algorithm are described in detail. Controlled polarization rotation is achievable using conventional Mach-Zehnder interferometers that are used to modulate the signal. Simulation results show that significant improvement in PMD tolerance can be achieved with little added complexity. Given a certain transmission distance, our proposed system can also increase the achievable data rate compared to a PolDM differential quadrature phase shift keying system.

This dissertation examines multi-antenna transceiver design over flat-fading wireless channels. Bit Interleaved Coded Modulation (BICM) and MultiLevel Coded Modulation (MLCM) transmitter structures are considered, as well as the used of an optional spatial precoder under slow and quasi-static fading conditions. At the receiver, MultiStage Decoder (MSD) and Iterative Detection and Decoding (IDD) strategies are applied. Precoder, mapper and subcode designs are optimized for different receiver structures over the different antenna and fading scenarios. Under slow and quasi-static channel conditions, fade resistant multi-antenna transmission is achieved through a combination of linear spatial precoding and non-linear multi-dimensional mapping. A time-varying random unitary precoder is proposed, with significant performance gains over spatial interleaving. The fade resistant properties of multidimensional random mapping are also analyzed. For MLCM architectures, a group random labelling strategy is proposed for large antenna systems. The use of complexity constrained receivers in BICM and MLCM transmissions is explored. Two multi-antenna detectors are proposed based on a group detection strategy, whose complexity can be adjusted through the group size parameter. These detectors show performance gains over the the Minimum Mean Squared Error (MMSE)detector in spatially multiplexed systems having an excess number of transmitter antennas. A class of irregular convolutional codes is proposed for use in BICM transmissions. An irregular convolutional code is formed by encoding fractions of bits with different puncture patterns and mother codes of different memory. The code profile is designed with the aid of extrinsic information transfer charts, based on the channel and mapping function characteristics. In multi-antenna applications, these codes outperform convolutional turbo codes under independent and quasi-static fading conditions. For finite length transmissions, MLCM-MSD performance is affected by the mapping function. Labelling schemes such as set partitioning and multidimensional random labelling generate a large spread of subcode rates. A class of generalized Low Density Parity Check (LDPC) codes is proposed, to improve low-rate subcode performance. For MLCM-MSD transmissions, the proposed generalized LDPC codes outperform conventional LDPC code construction over a wide range of channels and design rates.

Integrations over the unitary group are required in many applications including the joint eigenvalue distributions of the Wishart matrices. In this thesis, a universal integration framework is proposed to use the character expansions for any unitary integral with general rectangular complex matrices in the integrand. The proposed method is applied to solve some of the well--known but not solved in general form unitary integrals in their general forms, such as the generalized Harish--Chandra--Itzykson--Zuber integral. These integrals have applications in quantum chromodynamics and color--flavor transformations in physics. The unitary integral results are used to obtain new expressions for the joint eigenvalue distributions of the semi--correlated and full--correlated central Wishart matrices, as well as the i.i.d. and uncorrelated noncentral Wishart matrices, in a unified approach. Compared to the previous expressions in the literature, these new expressions are much easier to compute and also to apply for further analysis. In addition, the joint eigenvalue distribution of the full--correlated case is a new result in random matrix theory. The new distribution results are employed to obtain the individual eigenvalue densities of Wishart matrices, as well as the capacity of multiple--input multiple--output (MIMO) wireless channels. The joint eigenvalue distribution of the i.i.d. case is used to obtain the largest eigenvalue density and the bit error rate (BER) of the optimal beamforming in finite--series expressions. When complete channel state information is not available at the transmitter, a codebook of beamformers is used by the transmitter and the receiver. In this thesis, a codebook design method using the genetic algorithm is proposed, which reduces the design complexity and achieves large minimum--distance codebooks. Exploiting the specific structure of these beamformers, an order and bound algorithm is proposed to reduce the beamformer selection complexity at the receiver side. By employing a geometrical approach, an approximate BER for limited feedback beamforming is derived in finite--series expressions.

The Formulary Approach to the Taxation of Transnational Corporations: A Realistic Alternative? Synopsis The central hypotheses of this thesis are: that global formulary apportionment is the most appropriate method for the taxation of transnational corporations (TNCs) in lieu of the present system commonly referred to as the separate accounting/arm's length method; and that it is essential, in order to implement the proposed global formulary model, to create an international organisation which would fulfil, in the taxation field, a role equivalent to that of the World Trade Organisation (WTO) in international trade. The world economy is fast integrating and is increasingly dominated by the activities of transnational enterprises. These activities create a dual tax problem for various revenue authorities seeking to tax gains derived thereon: Firstly, when two or more countries entertain conflicting tax claims on the same base, there arises what is commonly referred to as a double taxation problem. Secondly, an allocation problem arises when different jurisdictions seek to determine the quantum of the gains to be allocated to each jurisdiction for taxation purposes. The traditional regime for solving both the double taxation and the allocation problem is enshrined in a series of bilateral treaties signed between various nations. These are, in general, based on the Organisation for Economic Co-operation and Development (OECD) Model Treaty.1 It is submitted, in this thesis, that while highly successful in an environment characterised by the coexistence of various national taxation systems, the traditional regime lacks the essential attributes suitable to the emerging 'borderless world'. The central theme of this thesis is the allocation problem. The OECD Model attempts to deal with this issue on a bilateral basis. Currently, the allocation problem is resolved through the application of Articles 7 and 9 of the OECD Model. In both instances the solution is based on the 'separate enterprise' standard, also known as the separate entity theory. This separate accounts/arm's length system was articulated in the 1930s when international trade consisted of flows of raw materials and other natural products as well as flows of finished manufactured goods. Such trade is highly visible and may be adequately valued both at the port of departure or at the port of entry in a country. It follows that within this particular system of international trade the application of the arm's length principle was relatively easy and proved to be extremely important in resolving both the double taxation and apportionment problems. Today, however, the conditions under which international trade is conducted are substantially different from those that prevailed until the 1960s. * Firstly, apart from the significant increase in the volume of traditionally traded goods, trade in services now forms the bulk of international exchanges. In addition, the advent of the information age has dramatically increased the importance of specialised information whose value is notoriously difficult to ascertain for taxation purposes. * Secondly, the globalisation phenomenon which gathered momentum over the last two decades has enabled existing TNCs to extend their global operations and has favoured the emergence of new transnational firms. Thus, intra-firm trade conducted outside market conditions accounts for a substantial part of international trade. * Thirdly, further economic integration has been achieved following the end of the Cold War and the acceleration of the globalisation phenomenon. In this new world economic order only TNCs have the necessary resources to take advantage of emerging opportunities. The very essence of a TNC is 'its ability to achieve higher revenues (or lower costs) from its different subsidiaries as a whole compared to the results that would be achieved under separate management on an arm's length basis.'2 Yet, the prevailing system for the taxation of TNCs overlooks this critical characteristic and is therefore incapable of fully capturing, for taxation purposes, the aggregate gains of TNCs. The potential revenue loss arising from the inability of the present system to account for and to allocate synergy gains is substantial. It follows that the perennial questions of international taxation can no longer be addressed within the constraints of the separate entity theory and a narrow definition of national sovereignty. Indeed, in order to mirror the developments occurring in the economic field, taxation needs to move from a national to an international level. Moreover, a profound reform of the system is imperative in order to avoid harmful tax competition between nations and enhance compliance from TNCs. Such a new international tax system needs to satisfy the test of simplicity, equity, efficiency, and administrative ease. To achieve these objectives international cooperation is essential. The hallmark of international cooperation has been the emergence, after World War II, of a range of international organisations designed to facilitate the achievement of certain goals deemed essential by various nations. The need for an organisation to deal specifically with taxation matters is now overwhelming. Consequently, this thesis recommends the creation of an international organisation to administer the proposed system. The main objective of this international organisation would be to initiate and coordinate the multilateral application of a formulary apportionment system which, it is suggested, would deal in a more realistic way with 'the difficult problems of determining the tax base and allocating it appropriately between jurisdictions'.3 The global formulary apportionment methodology is derived from the unitary entity theory. The unitary theory considers a TNC as a single business which, for convenience, is divided into 'purely formal, separately-incorporated subsidiaries'.4 Under the unitary theory the global income of TNCs needs to be computed, then such income is apportioned between the various component parts of the enterprise by way of a formula which reflects the economic contribution of each part to the derivation of profits. The question that arises is whether the world of international taxation is ready for such a paradigm shift. It is arguable that this shift has already occurred albeit cautiously and in very subtle ways. Thus, the latest of the OECD Guidelines on the transfer pricing question provides that 'MNE [Multinational Enterprise] groups retain the freedom to apply methods not described in this Report to establish prices provided those prices satisfy the arm's length principle in accordance with these Guidelines.'5 Arguably, the globalisation process has created 'the specific situation' allowed for by the OECD. This thesis, therefore, explores the relative obsolescence of the bilateral approach to the taxation of TNCs and then suggests that a multilateral system is better adapted to the emerging globalised economy. The fundamental building blocks of the model proposed in this thesis are the following: * First, the administration and coordination of the proposed system is to be achieved by the creation of a specialised tax organisation, called Intertax, to which member countries would devolve a limited part of their fiscal sovereignty. * Second, in order to enable the centralised calculation of TNC's profits, the proposed system requires the formulation of harmonised methods for the measurement of the global profits of TNCs. Therefore, the efforts of the International Accounting Standards Committee (IASC) to produce international accounting standards and harmonised consolidation rules must be recognised and, if needs be, refined and ultimately implemented. * Third, the major function of Intertax would be to determine the commercial profits of TNCs on a standardised basis and to apportion the latter to relevant countries by way of an appropriate formula/formulas. Once this is achieved, each country would be free, starting from its share of commercial profits, to determine the taxable income in accordance with the particular tax base that it adopts and, ultimately, the tax payable within its jurisdiction. In the proposed system, therefore, a particular country would be able to independently set whatever depreciation schedules or investment tax credits it chooses, and adopt whatever tax accounting rules it deems fit relative to its policy objectives. Moreover, this thesis argues that the global formulary apportionment model it proposes is not dramatically opposed to the arm's length principle. Indeed, it suggests that the constant assumption to the contrary, even with regard to the usual formulary apportionment methodology, is extravagant because both methodologies are based on a common endeavour, that is, to give a substantially correct reflex of a TNC's true profits. It has often been objected that global formulary apportionment is arbitrary and ignores market conditions. This thesis addresses such concerns by rejecting the application of a single all-purpose formula. Rather, it recognises that TNCs operating in different industries require different treatment and, therefore, suggests the adoption of different formulas to satisfy specific industry requirements. For example, the formula applicable to a financial institution would be different to that applicable to the pharmaceutical industry. Each formula needs to be based on the fundamental necessity to capture the functions, taking into consideration assets used, and risks assumed within that industry. In addition, if the need arises, each formula should be able to be fine-tuned to fit specific situations. Moreover, it is also pertinent to note that the OECD already accepts 'the selected application of a formula developed by both tax administrations in cooperation with a specific taxpayer or MNE group...such as it might be used in a mutual agreement procedure, advance transfer pricing agreement, or other bilateral or multilateral determination.'6 The system proposed in this thesis can thus be easily reconciled with the separate accounting/arm's length which the OECD so vehemently advocates. Both models have the same preoccupations so that what is herein proposed may simply be characterised as an institutionalised version of the system advocated by the OECD. Multilateral formulary apportionment addresses both the double taxation and the allocation problems in international taxation. It resolves the apportionment question 'without depending on an extraordinary degree of goodwill or compliance from taxpayers.'7 It is therefore submitted that, if applied on a multilateral basis with a minimum of central coordination, it also seriously addresses the double taxation problem. Indeed, it is a flexible method given that different formulas may be devised to suit the needs of TNCs operating in different sectors. Consequently, formulary apportionment understood in this sense, is a realistic alternative to the limitations of the present system.