703 research outputs found
Classical spin systems and the quantum stabilizer formalism: general mappings and applications
We present general mappings between classical spin systems and quantum
physics. More precisely, we show how to express partition functions and
correlation functions of arbitrary classical spin models as inner products
between quantum stabilizer states and product states, thereby generalizing
mappings for some specific models established in [Phys. Rev. Lett. 98, 117207
(2007)]. For Ising- and Potts-type models with and without external magnetic
field, we show how the entanglement features of the corresponding stabilizer
states are related to the interaction pattern of the classical model, while the
choice of product states encodes the details of interaction. These mappings
establish a link between the fields of classical statistical mechanics and
quantum information theory, which we utilize to transfer techniques and methods
developed in one field to gain insight into the other. For example, we use
quantum information techniques to recover well known duality relations and
local symmetries of classical models in a simple way, and provide new classical
simulation methods to simulate certain types of classical spin models. We show
that in this way all inhomogeneous models of q-dimensional spins with pairwise
interaction pattern specified by a graph of bounded tree-width can be simulated
efficiently. Finally, we show relations between classical spin models and
measurement-based quantum computation.Comment: 24 pages, 5 figures, minor corrections, version as accepted in JM
Persistent entanglement in arrays of interacting particles
We study the entanglement properties of a class of quantum states that can be generated in arrays of two-state particles (qubits) with simple next-neighbor interactions. Examples of such systems are optical lattices for neutral atoms and arrays of ion traps for charged particles. We show that, by simple interferometric operations, entangled states of large "clusters" of particles can be created which have the following properties: Any chosen pair of particles of a cluster can be projected into a Bell state by local measurements on the other particles. Different from so-called GHZ states, these cluster states have a high {\em persistency of entanglement}, defined as the required number of local (1-particle) measurements to completely disentangle a cluster
Graph states as ground states of many-body spin-1/2 Hamiltonians
We consider the problem whether graph states can be ground states of local
interaction Hamiltonians. For Hamiltonians acting on n qubits that involve at
most two-body interactions, we show that no n-qubit graph state can be the
exact, non-degenerate ground state. We determine for any graph state the
minimal d such that it is the non-degenerate ground state of a d-body
interaction Hamiltonian, while we show for d'-body Hamiltonians H with d'<d
that the resulting ground state can only be close to the graph state at the
cost of H having a small energy gap relative to the total energy. When allowing
for ancilla particles, we show how to utilize a gadget construction introduced
in the context of the k-local Hamiltonian problem, to obtain n-qubit graph
states as non-degenerate (quasi-)ground states of a two-body Hamiltonian acting
on n'>n spins.Comment: 10 pages, 1 figur
Quantum random walks in optical lattices
We propose an experimental realization of discrete quantum random walks using
neutral atoms trapped in optical lattices. The random walk is taking place in
position space and experimental implementation with present day technology
--even using existing set-ups-- seems feasible. We analyze the influence of
possible imperfections in the experiment and investigate the transition from a
quantum random walk to the classical random walk for increasing errors and
decoherence.Comment: 8 pages, 4 figure
Observation of the Vacuum-Rabi Spectrum for One Trapped Atom
The transmission spectrum for one atom strongly coupled to the field of a
high-finesse optical resonator is observed to exhibit a clearly resolved
vacuum-Rabi splitting characteristic of the normal modes in the eigenvalue
spectrum of the atom-cavity system. A new Raman scheme for cooling atomic
motion along the cavity axis enables a complete spectrum to be recorded for an
individual atom trapped within the cavity mode, in contrast to all previous
measurements in cavity QED that have required averaging over many atoms.Comment: 5 pages with 4 figure
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