Quantum systems engineering

Abstract:

We develop a concept of entanglement percolation for long-distance singlet generation in quantum networks with neighboring nodes connected by partially entangled bipartite mixed states. We give a necessary and sufficient condition on the class of mixed network states for the generation of singlets. States beyond this class are insufficient for entanglement percolation. We find that neighboring nodes are required to be connected by multiple partially entangled states and devise a rich variety of distillation protocols for the conversion of these states into singlets. These distillation protocols are suitable for a variety of network geometries and have a sufficiently high success probability even for significantly impure states. In addition to this, we discuss possible further improvements achievable by using quantum strategies including generalized forms of entanglement swapping. © Europhysics Letters Association.

Abstract:

We propose a Bell inequality for high-dimensional bipartite systems obtained by binning local measurement outcomes and show that it is tight. We find a binning method for even d -dimensional measurement outcomes for which this Bell inequality is maximally violated by maximally entangled states. Furthermore, we demonstrate that the Bell inequality is applicable to continuous variable systems and yields strong violations for two-mode squeezed states. © 2009 The American Physical Society.

Abstract:

We derive a Bell inequality based on a generalized quasiprobability function, which is parametrized by one nonpositive real value. Two types of known Bell inequalities formulated in terms of the Wigner and the Q functions are included as limiting cases. We investigate violations of our Bell inequalities for single-photon entangled states and two-mode squeezed vacuum states when varying the detector efficiency. We show that the Bell inequality for the Q function allows the lowest detection efficiency for violations of local realism. © 2009 The American Physical Society.

Abstract:

In recent work Hartmann et al [Phys. Rev. Lett. 102, 057202 (2009)] demonstrated that the classical simulation of the dynamics of open 1D quantum systems with matrix product algorithms can often be dramatically improved by performing time evolution in the Heisenberg picture. For a closed system this was exemplified by an exact matrix product operator solution of the time-evolved creation operator of a quadratic fermi chain with a matrix dimension of just two. In this work we show that this exact solution can be significantly generalized to include the case of an open quadratic fermi chain subjected to master equation evolution with Lindblad operators that are linear in the fermionic operators. Remarkably even in this open system the time-evolution of operators continues to be described by matrix product operators with the same fixed dimension as that required by the solution of a coherent quadratic fermi chain for all times. Through the use of matrix product algorithms the dynamical behaviour of operators in this non-equilibrium open quantum system can be computed with a cost that is linear in the system size. We present some simple numerical examples which highlight how useful this might be for the more detailed study of open system dynamics. Given that Heisenberg picture simulations have been demonstrated to offer significant accuracy improvements for other open systems that are not exactly solvable our work also provides further insight into how and why this advantage arises.

Abstract:

We investigate the effect of a rotating Bose-Einstein condensate on a system of immersed impurity atoms trapped by an optical lattice. We analytically show that for a one-dimensional, ring-shaped setup the coupling of the impurities to the Bogoliubov phonons of the condensate leads to a non-trivial phase in the impurity hopping. The presence of this phase can be tested by observing a drift in the transport properties of the impurities. These results are quantitatively confirmed by a numerically exact simulation of a two-mode Bose-Hubbard model. We also give analytical expressions for the occurring phase terms for a two-dimensional setup. The phase realises an artificial magnetic field and can, for instance, be used for the simulation of the quantum Hall effect using atoms in an optical lattice. © Europhysics Letters Association, 2009.