We investigated the dissipative dynamics of quantum discord for correlated qubits under Markovian environments. The basic idea in the present scheme is that quantum discord is more general, and possibly more robust and fundamental, than entanglement.We provide three initially correlated qubits in pure Greenberger-Horne-Zeilinger (GHZ) or W state and analyse the time evolution of the quantum discord under various dissipative channels such as: Pauli channels σ x , σ y , and σ z , as well as depolarising channels.Surprisingly, we find that under the action of Pauli channel σ x , the quantum discord of GHZ state is not affected by decoherence. For the remaining dissipative channels, the W state is more robust than the GHZ state against decoherence. Moreover, we compare the dynamics of entanglement with that of the quantum discord under the conditions in which disentanglement occurs and show that quantum discord is more robust than entanglement except for phase flip coupling of the three qubits system to the environment. * Mahdian@tabrizu.ac.ir † R.yousefjany@uok.ac.ir ‡ shsalimi@uok.ac.ir

One of the important approaches to detect quantum entanglement is using linear entanglement witnesses (EW s). In this paper, by determining the envelope of the boundary hyper-planes defined by a family of linear EW s, a set of powerful nonlinear optimal EW s is manipulated. These EW s enable us to detect some three qubits bound MUB (mutually unbiased bases) diagonal entangled states, i.e., the PPT (positive partial transpose) entangled states. Also, in some particular cases, the introduced nonlinear optimal EW s are powerful enough to separate the bound entangled regions from the separable ones.Finally, we present numerical examples to demonstrate the practical accessibility of this approach.

In a recent paper, it was shown that the projections of a relativistic spin operator (RSO) massive spin-1 2 particle on a world-vector which can be in timelike or null tetrad direction are proportional to the helicity or Bargman-Wigner (BW) qubit, respectively. Here we consider Lorentz transformations of two-particle states, which have been constructed both in helicity basis. For convenience, instead of using the superposition of momenta we use only two momentum eigenstates ( p 1 and p 2 ) for each particle. Consequently, in 2D momentum subspace we describe the structure of one particle in terms of the four-qubit system. We present a new approach to quantification of relativistic entanglement based on entanglement witness (EW), which is obtained by a new method of convex optimization. In addition, Lorentz invariance of entanglement using BW qubit is also studied.

Here we consider a class of 2 ⊗ 2 ⊗ d chessboard density matrices starting with threequbit ones which have positive partial transposes with respect to all subsystems. To investigate the entanglement of these density matrices, we use the entanglement witness approach. For constructing entanglement witnesses (EWs) detecting these density matrices, we attempt to convert the problem to an exact convex optimization problem. To this aim, we map the convex set of separable states into a convex region, named feasible region, and consider cases that the exact geometrical shape of feasible region can be obtained. In this way, various linear and non-linear EWs are constructed. The optimality and decomposability of some of introduced EWs are also considered. Furthermore, the detection of the density matrices by introduced EWs are discussed analytically and numerically.

Recently, the dynamics simulation of light-harvesting complexes as an open quantum system, in the weak and strong coupling regimes, has received much attention. In this paper, we investigate a digital quantum simulation approach of the Fenna–Matthews–Olson (FMO) photosynthetic pigment-protein complex surrounded with a Markovian bath, i.e. memoryless, based on a nuclear magnetic resonance (NMR) quantum computer. For this purpose, we apply the decoupling (recoupling) method, which is turn off (on) the couplings, and also Solovay–Kitaev techniques to decompose Hamiltonian and Lindbladians into efficient elementary gates on an NMR simulator. Finally, we design the quantum circuits for the unitary and nonunitary part due to the system-environment interactions of the open system dynamics.