Measures and dynamics of entangled states

We develop an original approach for the quantitative characterisation of the entanglement properties of, possibly mixed, bi- and multipartite quantum states of arbitrary finite dimension. Particular emphasis is given to the derivation of reliable estimates which allow for an efficient evaluation of a specific entanglement measure, concurrence, for further implementation in the monitoring of the time evolution of multipartite entanglement under incoherent environment coupling. The flexibility of the technical machinery established here is illustrated by its implementation for different, realistic experimental scenarios.Comment: Physics Reports, in pres

Entanglement production and decoherence-free subspace of two single-mode cavities embedded in a common environment

A system consisting of two identical single-mode cavities coupled to a common environment is investigated within the framework of algebraic dynamics. Based on the left and right representations of the Heisenberg-Weyl algebra, the algebraic structure of the master equation is explored and exact analytical solutions of this system are obtained. It is shown that for such a system, the environment can produce entanglement in contrast to its commonly believed role of destroying entanglement. In addition, the collective zero-mode eigen solutions of the system are found to be free of decoherence against the dissipation of the environment. These decoherence-free states may be useful in quantum information and quantum computation.Comment: 10 pages, 7 figures, Revtex

Entanglement with phase decoherence

The system of an atom couples to two distinct optical cavities with phase decoherence is studied by making use of a dynamical algebraic method. We adopt the concurrence to characterize the entanglement between atom and cavities or between two optical cavities in the presence of the phase decoherence. It is found that the entanglement between atom and cavities can be controlled by adjusting the detuning parameter. Finally, we show that even if the atom is initially prepared in a maximally mixed state, it can also entangle the two mode cavity fields.Comment: 9 pages, 6 figures, lete

Concurrence of mixed bipartite quantum states in arbitrary dimensions

We derive a lower bound for the concurrence of mixed bipartite quantum states, valid in arbitrary dimensions. As a corollary, a weaker, purely algebraic estimate is found, which detects mixed entangled states with positive partial transpose.Comment: accepted py PR

Genuinely Multipartite Concurrence of N-qubit X-matrices

We find an algebraic formula for the N-partite concurrence of N qubits in an X-matrix. X- matricies are density matrices whose only non-zero elements are diagonal or anti-diagonal when written in an orthonormal basis. We use our formula to study the dynamics of the N-partite entanglement of N remote qubits in generalized N-party Greenberger-Horne-Zeilinger (GHZ) states. We study the case when each qubit interacts with a partner harmonic oscillator. It is shown that only one type of GHZ state is prone to entanglement sudden death; for the rest, N-partite entanglement dies out momentarily. Algebraic formulas for the entanglement dynamics are given in both cases

Entanglement transitions in random definite particle states

Entanglement within qubits are studied for the subspace of definite particle states or definite number of up spins. A transition from an algebraic decay of entanglement within two qubits with the total number $N$ of qubits, to an exponential one when the number of particles is increased from two to three is studied in detail. In particular the probability that the concurrence is non-zero is calculated using statistical methods and shown to agree with numerical simulations. Further entanglement within a block of $m$ qubits is studied using the log-negativity measure which indicates that a transition from algebraic to exponential decay occurs when the number of particles exceeds $m$. Several algebraic exponents for the decay of the log-negativity are analytically calculated. The transition is shown to be possibly connected with the changes in the density of states of the reduced density matrix, which has a divergence at the zero eigenvalue when the entanglement decays algebraically.Comment: Substantially added content (now 24 pages, 5 figures) with a discussion of the possible mechanism for the transition. One additional author in this version that is accepted for publication in Phys. Rev.