85 research outputs found
Low-dimensional quite noisy bound entanglement with cryptographic key
We provide a class of bound entangled states that have positive distillable
secure key rate. The smallest state of this kind is 4 \bigotimes 4. Our class
is a generalization of the class presented in [1] (IEEE Trans. Inf. Theory 54,
2621 (2008); arXiv:quant-ph/0506203). It is much wider, containing, in
particular, states from the boundary of PPT entangled states (all of the states
in the class in [1] were of this kind) but also states inside the set of PPT
entangled states, even, approaching the separable states. This generalization
comes with a price: for the wider class a positive key rate requires, in
general, apart from the one-way Devetak-Winter protocol (used in [1]) also the
recurrence preprocessing and thus effectively is a two-way protocol. We also
analyze the amount of noise that can be admixtured to the states of our class
without losing key distillability property which may be crucial for
experimental realization. The wider class contains key-distillable states with
higher entropy (up to 3.524, as opposed to 2.564 for the class in [1]).Comment: 10 pages, final version for J. Phys. A: Math. Theo
Robust entanglement
It is common belief among physicists that entangled states of quantum systems
loose their coherence rather quickly. The reason is that any interaction with
the environment which distinguishes between the entangled sub-systems collapses
the quantum state. Here we investigate entangled states of two trapped Ca
ions and observe robust entanglement lasting for more than 20 seconds
Realization of the quantum Toffoli gate with trapped ions
Algorithms for quantum information processing are usually decomposed into
sequences of quantum gate operations, most often realized with single- and two-
qubit gates[1]. While such operations constitute a universal set for quantum
computation, gates acting on more than two qubits can simplify the
implementation of complex quantum algorithms[2]. Thus, a single three-qubit
operation can replace a complex sequence of two-qubit gates, which in turn
promises faster execution with potentially higher Fidelity. One important
three-qubit operation is the quantum Toffoli gate which performs a NOT
operation on a target qubit depending on the state of two control qubits. Here
we present the first experimental realization of the quantum Toffoli gate in an
ion trap quantum computer. Our implementation is particular effcient as we
directly encode the relevant logic information in the motion of the ion string.
[1] DiVincenzo, D. P. Two-bit gates are universal for quantum computation.
cond-mat/9407022, Phys.Rev. A 51, 1015-1022 (1995). [2] Chiaverini, J. et al.
Realization of quantum error correction. Nature 432, 602-605 (2004).Comment: 11 pages, 2 figure
Precision spectroscopy with two correlated atoms
We discuss techniques that allow for long coherence times in laser
spectroscopy experiments with two trapped ions. We show that for this purpose
not only entangled ions prepared in decoherence-free subspaces can be used but
also a pair of ions that are not entangled but subject to the same kind of
phase noise. We apply this technique to a measurement of the electric
quadrupole moment of the 3d D5/2 state of 40Ca+ and to a measurement of the
linewidth of an ultrastable laser exciting a pair of 40Ca+ ions
'Designer atoms' for quantum metrology
Entanglement is recognized as a key resource for quantum computation and
quantum cryptography. For quantum metrology, the use of entangled states has
been discussed and demonstrated as a means of improving the signal-to-noise
ratio. In addition, entangled states have been used in experiments for
efficient quantum state detection and for the measurement of scattering
lengths. In quantum information processing, manipulation of individual quantum
bits allows for the tailored design of specific states that are insensitive to
the detrimental influences of an environment. Such 'decoherence-free subspaces'
protect quantum information and yield significantly enhanced coherence times.
Here we use a decoherence-free subspace with specifically designed entangled
states to demonstrate precision spectroscopy of a pair of trapped Ca+ ions; we
obtain the electric quadrupole moment, which is of use for frequency standard
applications. We find that entangled states are not only useful for enhancing
the signal-to-noise ratio in frequency measurements - a suitably designed pair
of atoms also allows clock measurements in the presence of strong technical
noise. Our technique makes explicit use of non-locality as an entanglement
property and provides an approach for 'designed' quantum metrology
An Open-System Quantum Simulator with Trapped Ions
The control of quantum systems is of fundamental scientific interest and
promises powerful applications and technologies. Impressive progress has been
achieved in isolating the systems from the environment and coherently
controlling their dynamics, as demonstrated by the creation and manipulation of
entanglement in various physical systems. However, for open quantum systems,
engineering the dynamics of many particles by a controlled coupling to an
environment remains largely unexplored. Here we report the first realization of
a toolbox for simulating an open quantum system with up to five qubits. Using a
quantum computing architecture with trapped ions, we combine multi-qubit gates
with optical pumping to implement coherent operations and dissipative
processes. We illustrate this engineering by the dissipative preparation of
entangled states, the simulation of coherent many-body spin interactions and
the quantum non-demolition measurement of multi-qubit observables. By adding
controlled dissipation to coherent operations, this work offers novel prospects
for open-system quantum simulation and computation.Comment: Pre-review submission to Nature. For an updated and final version see
publication. Manuscript + Supplementary Informatio
Trapped Rydberg Ions: From Spin Chains to Fast Quantum Gates
We study the dynamics of Rydberg ions trapped in a linear Paul trap, and
discuss the properties of ionic Rydberg states in the presence of the static
and time-dependent electric fields constituting the trap. The interactions in a
system of many ions are investigated and coupled equations of the internal
electronic states and the external oscillator modes of a linear ion chain are
derived. We show that strong dipole-dipole interactions among the ions can be
achieved by microwave dressing fields. Using low-angular momentum states with
large quantum defect the internal dynamics can be mapped onto an effective spin
model of a pair of dressed Rydberg states that describes the dynamics of
Rydberg excitations in the ion crystal. We demonstrate that excitation transfer
through the ion chain can be achieved on a nanosecond timescale and discuss the
implementation of a fast two-qubit gate in the ion chain.Comment: 26 pages, 9 figure
Additivity and non-additivity of multipartite entanglement measures
We study the additivity property of three multipartite entanglement measures,
i.e. the geometric measure of entanglement (GM), the relative entropy of
entanglement and the logarithmic global robustness. First, we show the
additivity of GM of multipartite states with real and non-negative entries in
the computational basis. Many states of experimental and theoretical interests
have this property, e.g. Bell diagonal states, maximally correlated generalized
Bell diagonal states, generalized Dicke states, the Smolin state, and the
generalization of D\"{u}r's multipartite bound entangled states. We also prove
the additivity of other two measures for some of these examples. Second, we
show the non-additivity of GM of all antisymmetric states of three or more
parties, and provide a unified explanation of the non-additivity of the three
measures of the antisymmetric projector states. In particular, we derive
analytical formulae of the three measures of one copy and two copies of the
antisymmetric projector states respectively. Third, we show, with a statistical
approach, that almost all multipartite pure states with sufficiently large
number of parties are nearly maximally entangled with respect to GM and
relative entropy of entanglement. However, their GM is not strong additive;
what's more surprising, for generic pure states with real entries in the
computational basis, GM of one copy and two copies, respectively, are almost
equal. Hence, more states may be suitable for universal quantum computation, if
measurements can be performed on two copies of the resource states. We also
show that almost all multipartite pure states cannot be produced reversibly
with the combination multipartite GHZ states under asymptotic LOCC, unless
relative entropy of entanglement is non-additive for generic multipartite pure
states.Comment: 45 pages, 4 figures. Proposition 23 and Theorem 24 are revised by
correcting a minor error from Eq. (A.2), (A.3) and (A.4) in the published
version. The abstract, introduction, and summary are also revised. All other
conclusions are unchange
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