arXiv subjects
Publications and source records attributed to Markus Tiersch.
We derive an explicit analytic estimate for the entanglement of a large class of bipartite quantum states which extends into bound entanglement regions. This is done by using an efficiently computable concurrence lower bound, which is further employed to numerically construct a volume of $3 \times 3$ bound entangled states.
We derive analytical upper bounds for the entanglement of generalized Greenberger-Horne-Zeilinger states coupled to locally depolarizing and dephasing environments, and for local thermal baths of arbitrary temperature. These bounds apply for any convex quantifier of entanglement, and exponential entanglement decay with the number of constituent particles is found. The bounds are tight for depolarizing and dephasing channels. We also show that randomly generated initial states tend to violate these bounds, and that this discrepancy grows with the number of particles.
We provide a relation which describes how the entanglement of two d-level systems evolves as either system undergoes an arbitrary physical process. The dynamics of the entanglement turns out to be of a simple form, and is fully captured by a single quantity.
We present a simple and general factorization law for quantum systems shared by two parties, which describes the time evolution of entanglement upon passage of either component through an arbitrary noisy channel. The robustness of entanglement-based quantum information processing protocols is thus easily and fully characterized by a single quantity.
We consider an adiabatic quantum algorithm (Grover's search routine) weakly coupled to a rather general environment, i.e., without using the Markov approximation. Markovian errors generally require high-energy excitations (of the reservoir) and tend to destroy the scalability of the adiabatic quantum algorithm. We find that, under appropriate conditions (such as low temperatures), the low-energy (i.e., non-Markovian) modes of the bath are most important. Hence the scalability of the adiabatic quantum algorithm depends on the infra-red behavior of the environment: a reasonably small coupling to the three-dimensional electromagnetic field does not destroy the scaling behavior, whereas phonons or localized degrees of freedom can be problematic. PACS: 03.67.Pp, 03.67.Lx, 03.67.-a, 03.65.Yz.
By means of two simple examples: phase and amplitude damping, the impact of decoherence on the dynamical Casimir effect is investigated. Even without dissipating energy (i.e., pure phase damping), the amount of created particles can be diminished significantly via the coupling to the environment (reservoir theory) inducing decoherence. For a simple microscopic model, it is demonstrated that spontaneous decays within the medium generate those problems -- Rabi oscillations are far more advantageous in that respect. These findings are particularly relevant in view of a recently proposed experimental verification of the dynamical Casimir effect. PACS: 42.50.Lc, 03.65.Yz, 03.70.+k, 42.50.Dv.