382 research outputs found
Delocalized Entanglement of Atoms in optical Lattices
We show how to detect and quantify entanglement of atoms in optical lattices
in terms of correlations functions of the momentum distribution. These
distributions can be measured directly in the experiments. We introduce two
kinds of entanglement measures related to the position and the spin of the
atoms
Quantum simulators, continuous-time automata, and translationally invariant systems
The general problem of finding the ground state energy of lattice
Hamiltonians is known to be very hard, even for a quantum computer. We show
here that this is the case even for translationally invariant systems. We also
show that a quantum computer can be built in a 1D chain with a fixed,
translationally invariant Hamitonian consisting of nearest--neighbor
interactions only. The result of the computation is obtained after a prescribed
time with high probability.Comment: partily rewritten and important references include
Counterexample to an additivity conjecture for output purity of quantum channels
A conjecture arising naturally in the investigation of additivity of
classical information capacity of quantum channels states that the maximal
purity of outputs from a quantum channel, as measured by the p-norm, should be
multiplicative with respect to the tensor product of channels. We disprove this
conjecture for p>4.79. The same example (with p=infinity) also disproves a
conjecture for the multiplicativity of the injective norm of Hilbert space
tensor products.Comment: 3 pages, 3 figures, revte
Quantum Metropolis Sampling
The original motivation to build a quantum computer came from Feynman who
envisaged a machine capable of simulating generic quantum mechanical systems, a
task that is believed to be intractable for classical computers. Such a machine
would have a wide range of applications in the simulation of many-body quantum
physics, including condensed matter physics, chemistry, and high energy
physics. Part of Feynman's challenge was met by Lloyd who showed how to
approximately decompose the time-evolution operator of interacting quantum
particles into a short sequence of elementary gates, suitable for operation on
a quantum computer. However, this left open the problem of how to simulate the
equilibrium and static properties of quantum systems. This requires the
preparation of ground and Gibbs states on a quantum computer. For classical
systems, this problem is solved by the ubiquitous Metropolis algorithm, a
method that basically acquired a monopoly for the simulation of interacting
particles. Here, we demonstrate how to implement a quantum version of the
Metropolis algorithm on a quantum computer. This algorithm permits to sample
directly from the eigenstates of the Hamiltonian and thus evades the sign
problem present in classical simulations. A small scale implementation of this
algorithm can already be achieved with today's technologyComment: revised versio
Quantum state engineering, purification, and number resolved photon detection with high finesse optical cavities
We propose and analyze a multi-functional setup consisting of high finesse
optical cavities, beam splitters, and phase shifters. The basic scheme projects
arbitrary photonic two-mode input states onto the subspace spanned by the
product of Fock states |n>|n> with n=0,1,2,.... This protocol does not only
provide the possibility to conditionally generate highly entangled photon
number states as resource for quantum information protocols but also allows one
to test and hence purify this type of quantum states in a communication
scenario, which is of great practical importance. The scheme is especially
attractive as a generalization to many modes allows for distribution and
purification of entanglement in networks. In an alternative working mode, the
setup allows of quantum non demolition number resolved photodetection in the
optical domain.Comment: 14 pages, 10 figure
Ensemble Quantum Computation with atoms in periodic potentials
We show how to perform universal quantum computation with atoms confined in
optical lattices which works both in the presence of defects and without
individual addressing. The method is based on using the defects in the lattice,
wherever they are, both to ``mark'' different copies on which ensemble quantum
computation is carried out and to define pointer atoms which perform the
quantum gates. We also show how to overcome the problem of scalability on this
system
Entanglement in SU(2)-invariant quantum systems: The positive partial transpose criterion and others
We study entanglement in mixed bipartite quantum states which are invariant
under simultaneous SU(2) transformations in both subsystems. Previous results
on the behavior of such states under partial transposition are substantially
extended. The spectrum of the partial transpose of a given SU(2)-invariant
density matrix is entirely determined by the diagonal elements of
in a basis of tensor-product states of both spins with respect to a common
quantization axis. We construct a set of operators which act as entanglement
witnesses on SU(2)-invariant states. A sufficient criterion for having a
negative partial transpose is derived in terms of a simple spin correlator. The
same condition is a necessary criterion for the partial transpose to have the
maximum number of negative eigenvalues. Moreover, we derive a series of sum
rules which uniquely determine the eigenvalues of the partial transpose in
terms of a system of linear equations. Finally we compare our findings with
other entanglement criteria including the reduction criterion, the majorization
criterion, and the recently proposed local uncertainty relations.Comment: 7 pages, no figures, version to appear in Phys. Rev.
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