A Few Finite Trigonometric Sums

Finite trigonometric sums occur in various branches of physics, mathematics, and their applications. These sums may contain various powers of one or more trigonometric functions. Sums with one trigonometric function are known, however sums with products of trigonometric functions can get complicated and may not have a simple expressions in a number of cases. Some of these sums have interesting properties and can have amazingly simple value. However, only some of them are available in literature. We obtain a number of such sums using method of residues.Comment: 11 pages, added references, corrected typo

Distinguishing different classes of entanglement of three-qubit pure states

Employing the Pauli matrices, we have constructed a set of operators, which can be used to distinguish six inequivalent classes of entanglement under SLOCC (stochastic local operation and classical communication) for three-qubit pure states. These operators have very simple structure and can be obtained from the Mermin's operator with suitable choice of directions. Moreover these operators may be implemented in an experiment to distinguish the types of entanglement present in a state. We show that the measurement of only one operator is sufficient to distinguish GHZ class from rest of the classes. It is also shown that it is possible to detect and classify other classes by performing a small number of measurements. We also show how to construct such observables in any basis. We also consider a few mixed states to investigate the usefulness of our operators. Furthermore, we consider the teleportation scheme of Lee et al. (Phys. Rev. A 72, 024302 (2005)) and show that the partial tangles and hence teleportation fidelity can be measured. We have also shown that these partial tangles can also be used to classify genuinely entangled state, biseparable state and separable state.Comment: 7 pages, 2 figures, comments welcom

Authentication protocol based on collective quantum steering

It is well known that certain quantum correlations like quantum steering exhibit a monogamous relationship. In this paper, we exploit the asymmetric nature of quantum steering and show that there exist states which exhibit a polygamous correlation, known as collective correlation [He and Reid, Phys. Rev. Lett. 111, 250403 (2013)], where the state of one party, Alice, can be steered only by the joint effort of the other two parties, Bob and Charlie. As an example, we explicitly single out a particular set of $3$ qubit states which exhibit this polygamous relationship, known as collective steerability. We provide a recipe to identify the complete set of such states. We also provide a possible application of such states to an information theoretic task, termed as quantum key authentication (QKA) protocol. QKA can also be used in conjunction with other well known cryptography protocols to improve their security and we provide one such example with quantum private comparison (QPC).Comment: 6 pages, 1 figure, comments appreciated :

Two-qubit mixed states and teleportation fidelity: Purity, concurrence, and beyond

To explore the properties of a two-qubit mixed state, we consider quantum teleportation. The fidelity of a teleported state depends on the resource state purity and entanglement, as characterized by concurrence. Concurrence and purity are functions of state parameters. However, it turns out that a state with larger purity and concurrence, may have comparatively smaller fidelity. By computing teleportation fidelity, concurrence and purity for two-qubit X-states, we show it explicitly. We further show that fidelity changes monotonically with respect to functions of parameters - other than concurrence and purity. A state with smaller concurrence and purity, but larger value of one of these functions has larger fidelity. These functions, thus characterize nonlocal classical and/or quantum properties of the state that are not captured by purity and concurrence alone. In particular, concurrence is not enough to characterize the entanglement properties of a two-qubit mixed state

Impact of Capital Adequacy on Profitability Under Basel II Accord: Evidence from Commercial Banks of Bangladesh

This paper explores the effect of several bank specific variables including capital adequacy on the profitability of listed commercial banks operating in Bangladesh. Determinants of banks’ profitability like ROA and ROE have been assessed by the panel data (232 observations) of 29 listed banks out of 30, for the time period of eight years (2007-2014). These sample banks cover approximately 62% of total banking sector asset in the year 2014 in Bangladesh. In this study, profitability has been quantified in terms of regulatory capital, operating efficiency, bank’s asset size, loan structure and leverage. This study found that the regulatory capital held by banks is greater than the minimum capital requirement guided under Basel II accord. Again, it has been showed that explanatory variables like capital adequacy, operating efficiency and loan structure are positively related to profitability of a bank. Keywords: Basel II, bank profitability dimension, Bangladesh