Session V10: Invited Session: Quantum Entanglement in Many-Body Systems

Entanglement, teleportation and memory in atomic spin ensembles

Recent experimental progress with entanglement generation and processing in macroscopic atomic spin ensembles will be reviewed. It includes atomic entanglement maintained for an unlimited time via engineered collective dissipation mediated by light and teleportation of collective atomic spin states. A proposal for quantum memory assisted detection of strongly coupled systems will be presented.   

Entanglement and real-space renormalization group methods for quantum field theories

We will demonstrate how the reformulation of the density matrix renormalization group as a variational method within the class of matrix product states has lead to a wide class of novel applications and insights into strongly correlated quantum systems in 1 dimension. The discussion will detail the crucial role of entanglement and area laws, and then focus on the generalization of matrix product state methods to quantum field theories and the prospects of simulating experiments with cold gasses. Joint work with I. Cirac, J. Haegeman, T. Osborne.   

Entangled States of Trapped Ions

Entangled states of the internal degrees of freedom are an important resource in Quantum Information Processing (QIP) and Quantum Simulation (QS) with trapped ions. Most basic requirements for QIP and QS have been demonstrated for trapped ions, with two big challenges remaining: Improving operation fidelity and scaling up to larger numbers of qubits. In the last few years, steady progress has been achieved with laser-based entanglement schemes with demonstrated fidelities of deterministically produced Bell states of 99.3{\%} and up to 14 ion-qubits entangled in generalized GHZ-states. Scalable architectures have been proposed; one scheme, where ion-qubits are moved through a multi-zone trap array, is studied in several laboratories. Sympathetic cooling with a second ion species, which initializes the motional states for multi-qubit operations, has been demonstrated in an experiment where arbitrary operations on two qubits were implemented. Micro-fabrication approaches to ion-trap-arrays have yielded structures that should be capable of holding and manipulating large numbers of ions. Recently, with the use of microwaves, single-qubit rotations with fidelities of 99.998{\%} per gate operation were demonstrated and two ion-qubit gates have been implemented. Microwave control could potentially be easier to scale by directly integrating microwave-lines on micro-fabricated trap devices. It also eliminates several sources of decoherence that are present in laser-based schemes by exclusively coupling to long lived hyperfine ground states.   

Topological order and long range quantum entanglements

What is the origin of fractional charges and fractional statistics in FQH states? What is the origin of light? It turns out that long range entanglement is the reason why fractional charges and fractional statistics can appear FQH state. Long range entanglement is also the reason why waves that satisfy Maxwell equation can appear in some qubit (spin) systems. Long range entanglement also lead to a deeper understanding of gapped quantum phases. It allows us to obtain a classification of interacting topological insulators/superconductors, as well as the much more general symmetry protected topological phases, and intrinsic topological phases.