86 research outputs found
Relations between Entanglement Witnesses and Bell Inequalities
Bell inequalities, considered within quantum mechanics, can be regarded as
non-optimal witness operators. We discuss the relationship between such Bell
witnesses and general entanglement witnesses in detail for the Bell inequality
derived by Clauser, Horne, Shimony, and Holt (CHSH). We derive bounds on how
much an optimal witness has to be shifted by adding the identity operator to
make it positive on all states admitting a local hidden variable model. In the
opposite direction, we obtain tight bounds for the maximal proportion of the
identity operator that can be subtracted from such a CHSH witness, while
preserving the witness properties. Finally, we investigate the structure of
CHSH witnesses directly by relating their diagonalized form to optimal
witnesses of two different classes.Comment: 8 pages, 2 figure
Generation and detection of bound entanglement
We propose a method for the experimental generation of two different families
of bound entangled states of three qubits. Our method is based on the explicit
construction of a quantum network that produces a purification of the desired
state. We also suggest a route for the experimental detection of bound
entanglement, by employing a witness operator plus a test of the positivity of
the partial transposes
Four-qubit entangled symmetric states with positive partial transpositions
We solve the open question of the existence of four-qubit entangled symmetric
states with positive partial transpositions (PPT states). We reach this goal
with two different approaches. First, we propose a
half-analytical-half-numerical method that allows to construct multipartite PPT
entangled symmetric states (PPTESS) from the qubit-qudit PPT entangled states.
Second, we adapt the algorithm allowing to search for extremal elements in the
convex set of bipartite PPT states [J. M. Leinaas, J. Myrheim, and E. Ovrum,
Phys. Rev. A 76, 034304 (2007)] to the multipartite scenario. With its aid we
search for extremal four-qubit PPTESS and show that generically they have ranks
(5,7,8). Finally, we provide an exhaustive characterization of these states
with respect to their separability properties.Comment: 5+4 pages, improved version, title slightly modifie
Parametric amplification of vacuum fluctuations in a spinor condensate
Parametric amplification of vacuum fluctuations is crucial in modern quantum
optics, enabling the creation of squeezing and entanglement. We demonstrate the
parametric amplification of vacuum fluctuations for matter waves using a spinor
F=2 Rb-87 condensate. Interatomic interactions lead to correlated pair creation
in the m_F= +/- 1 states from an initial unstable m_F=0 condensate, which acts
as a vacuum for m_F unequal 0. Although this pair creation from a pure m_F=0
condensate is ideally triggered by vacuum fluctuations, unavoidable spurious
initial m_F= +/- 1 atoms induce a classical seed which may become the dominant
triggering mechanism. We show that pair creation is insensitive to a classical
seed for sufficiently large magnetic fields, demonstrating the dominant role of
vacuum fluctuations. The presented system thus provides a direct path towards
the generation of non-classical states of matter on the basis of spinor
condensates.Comment: 5 pages, 4 figure
Differential atom interferometry beyond the standard quantum limit
We analyze methods to go beyond the standard quantum limit for a class of
atomic interferometers, where the quantity of interest is the difference of
phase shifts obtained by two independent atomic ensembles. An example is given
by an atomic Sagnac interferometer, where for two ensembles propagating in
opposite directions in the interferometer this phase difference encodes the
angular velocity of the experimental setup. We discuss methods of squeezing
separately or jointly observables of the two atomic ensembles, and compare in
detail advantages and drawbacks of such schemes. In particular we show that the
method of joint squeezing may improve the variance by up to a factor of 2. We
take into account fluctuations of the number of atoms in both the preparation
and the measurement stage, and obtain bounds on the difference of the numbers
of atoms in the two ensembles, as well as on the detection efficiency, which
have to be fulfilled in order to surpass the standard quantum limit. Under
realistic conditions, the performance of both schemes can be improved
significantly by reading out the phase difference via a quantum non-demolition
(QND) measurement. Finally, we discuss a scheme using macroscopically entangled
ensembles.Comment: 10 pages, 5 figures; eq. (3) corrected and other minor change
On structural physical approximations and entanglement breaking maps
Very recently a conjecture saying that the so-called structural physical
approximations (SPAa) to optimal positive maps (optimal entanglement witnesses)
give entanglement breaking (EB) maps (separable states) has been posed [J. K.
Korbicz {\it et al.}, Phys. Rev. A {\bf 78}, 062105 (2008)]. The main purpose
of this contribution is to explore this subject. First, we extend the set of
entanglement witnesses (EWs) supporting the conjecture. Then, we ask if SPAs
constructed from other than the depolarizing channel maps also lead to EB maps
and show that in general this is not the case. On the other hand, we prove an
interesting fact that for any positive map there exists an EB channel
such that the SPA of constructed with the aid of is
again an EB channel. Finally, we ask similar questions in the case of
continuous variable systems. We provide a simple way of construction of SPA and
prove that in the case of the transposition map it gives EB channel.Comment: 22 pages, improved version, accepted by Journal of Physics
Experimental detection of entanglement via witness operators and local measurements
In this paper we address the problem of detection of entanglement using only
few local measurements when some knowledge about the state is given. The idea
is based on an optimized decomposition of witness operators into local
operators. We discuss two possible ways of optimizing this local decomposition.
We present several analytical results and estimates for optimized detection
strategies for NPT states of 2x2 and NxM systems, entangled states in 3 qubit
systems, and bound entangled states in 3x3 and 2x4 systems.Comment: 24 pages, 2 figures. Contribution to the proceedings of the
International Conference on Quantum Information in Oviedo, Spain (July 13-18,
2002). Error in W_W1-witness Eq. (35) corrected as well as minor typos.
Reference adde
Optimal entanglement witnesses for continuous-variable systems
This paper is concerned with all tests for continuous-variable entanglement
that arise from linear combinations of second moments or variances of canonical
coordinates, as they are commonly used in experiments to detect entanglement.
All such tests for bi-partite and multi-partite entanglement correspond to
hyperplanes in the set of second moments. It is shown that all optimal tests,
those that are most robust against imperfections with respect to some figure of
merit for a given state, can be constructed from solutions to semi-definite
optimization problems. Moreover, we show that for each such test, referred to
as entanglement witness based on second moments, there is a one-to-one
correspondence between the witness and a stronger product criterion, which
amounts to a non-linear witness, based on the same measurements. This
generalizes the known product criteria. The presented tests are all applicable
also to non-Gaussian states. To provide a service to the community, we present
the documentation of two numerical routines, FULLYWIT and MULTIWIT, which have
been made publicly available.Comment: 14 pages LaTeX, 1 figure, presentation improved, references update
Useful Multiparticle Entanglement and Sub-Shot-Noise Sensitivity in Experimental Phase Estimation
We experimentally demonstrate a general criterion to identify entangled
states useful for the estimation of an unknown phase shift with a sensitivity
higher than the shot-noise limit. We show how to exploit this entanglement on
the examples of a maximum likelihood as well as of a Bayesian phase estimation
protocol. Using an entangled four-photon state we achieve a phase sensitivity
clearly beyond the shot-noise limit. Our detailed comparison of methods and
quantum states for entanglement enhanced metrology reveals the connection
between multiparticle entanglement and sub-shot-noise uncertainty, both in a
frequentist and in a Bayesian phase estimation setting.Comment: 4 pages, 4 figure
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