Abstract:
We quantify various possible entanglement measures for the four particles GHZ entangled state that has been produced experimentally [C. Sackett et al, Nature 404, 256-259 (2000)].

Abstract:
The adiabatic theorem states that if we prepare a quantum system in one of the instantaneous eigenstates then the quantum number is an adiabatic invariant and the state at a later time is equivalent to the instantaneous eigenstate at that time apart from phase factors. Recently, Marzlin and Sanders have pointed out that this could lead to apparent violation of unitarity. We resolve the Marzlin-Sanders inconsistency within the quantum adiabatic theorem. Yet, our resolution points to another inconsistency, namely, that the cyclic as well as non-cyclic adiabatic Berry phases may vanish under strict adiabatic condition. We resolve this inconsistency and develop an unitary operator decomposition method to argue for the validity of the adiabatic approximation.

Abstract:
We prove a new sum uncertainty relation in quantum theory which states that the uncertainty in the sum of two or more observables is always less than or equal to the sum of the uncertainties in corresponding observables. This shows that the quantum mechanical uncertainty in any observable is a convex function. We prove that if we have a finite number $N$ of identically prepared quantum systems, then a joint measurement of any observable gives an error $\sqrt N$ less than that of the individual measurements. This has application in quantum metrology that aims to give better precision in the parameter estimation. Furthermore, this proves that a quantum system evolves slowly under the action of a sum Hamiltonian than the sum of individuals, even if they are non-commuting.

Abstract:
We consider W-states and generalized W-states for $n$-qubit systems. We obtain conditions to use these states as quantum resources to teleport unknown states. Only a limited class of multi-qubit states can be teleported. For $one$-qubit states, we use protocols which are simple extensions of the conventional teleportation protocol. We also show that these resource states can be used to transmit {\em at most} $n + 1$ classical bits by sending $n$ qubits if the appropriate conditions are met. Therefore these states are not suitable for maximal teleportation or superdense coding when $ n > 3$.

Abstract:
We discuss the exact remote state preparation protocol of special ensembles of qubits at multiple locations. We also present generalization of this protocol for higher dimensional Hilbert space systems for multiparties. Using the `dark states', the analogue of singlet EPR pair for multiparties in higher dimension as quantum channel, we show several instances of remote state preparation protocol using multiparticle measurement and classical communication.

Abstract:
We investigate the usefulness of different classes of genuine quadripartite entangled states as quantum resources for teleportation and superdense coding. We examine the possibility of teleporting unknown one, two and three qubit states. We show that one can use the teleportation protocol to send any general one and two qubit states. A restricted class of three qubit states can also be faithfully teleported. We also explore superdense coding protocol in single-receiver and multi-receiver scenarios. We show that there exist genuine quadripartite entangled states that can be used to transmit four cbits by sending two qubits. We also discuss some interesting features of multi-receiver scenario under LOCC paradigm.

Abstract:
We show that the quadratic short time behaviour of transition probability is a natural consequence of the inner product of the Hilbert space of the quantum system. We prove that Schr\"odinger time evolution between two successive measurements is not a necessary but only a sufficient condition for predicting quantum Zeno effect. We provide a relation between the survival probability and the underlying geometric structure such as the Fubini-Study metric defined on the projective Hilbert space of the quantum system. This predicts the quantum Zeno effect even for systems described by non-linear and non-unitary evolution equations, within the collapse mechanism of the wavefunction during measurement process. Two examples are studied, one is non-linear Schr\"odinger equation and other is Gisin's equation and it is shown that one can observe quantum Zeno effect for systems described by these equations.

Abstract:
We explore the possibility of performing super dense coding with non-maximally entangled states as a resource. Using this we find that one can send two classical bits in a probabilistic manner by sending a qubit. We generalize our scheme to higher dimensions and show that one can communicate 2log_2 d classical bits by sending a d-dimensional quantum state with a certain probability of success. The success probability in super dense coding is related to the success probability of distinguishing non-orthogonal states. The optimal average success probabilities are explicitly calculated. We consider the possibility of sending 2 log_2 d classical bits with a shared resource of a higher dimensional entangled state (D X D, D > d). It is found that more entanglement does not necessarily lead to higher success probability. This also answers the question as to why we need log_2 d ebits to send 2 log_2 d classical bits in a deterministic fashion.

Abstract:
It is known that the stronger no-cloning theorem and the no-deleting theorem taken together provide the permanence property of quantum information. Also, it is known that the violation of the no-deletion theorem would imply signalling. Here, we show that the violation of the stronger no-cloning theorem could lead to signalling. Furthermore, we prove the stronger no-cloning theorem from the conservation of quantum information. These observations imply that the permanence property of quantum information is connected to the no-signalling and the conservation of quantum information.

Abstract:
We investigate if physical laws can impose limit on computational time and speed of a quantum computer built from elementary particles. We show that the product of the speed and the running time of a quantum computer is limited by the type of fundamental interactions present inside the system. This will help us to decide as to what type of interaction should be allowed in building quantum computers in achieving the desired speed.