480 research outputs found
Viable entanglement detection of unknown mixed states in low dimensions
We explore procedures to detect entanglement of unknown mixed states, which
can be experimentally viable. The heart of the method is a hierarchy of simple
feasibility problems, which provides sufficient conditions to entanglement. Our
numerical investigations indicate that the entanglement is detected with a cost
which is much lower than full state tomography. The procedure is applicable to
both free and bound entanglement, and involves only single copy measurements.Comment: 8 pages, 9 figures, 4 table
Witnessed Entanglement
We present a new measure of entanglement for mixed states. It can be
approximately computable for every state and can be used to quantify all
different types of multipartite entanglement. We show that it satisfies the
usual properties of a good entanglement quantifier and derive relations between
it and other entanglement measures.Comment: Revised version. 7 pages and one figur
Quantum Correlations and Coherence in Spin-1 Heisenberg Chains
We explore quantum and classical correlations along with coherence in the
ground states of spin-1 Heisenberg chains, namely the one-dimensional XXZ model
and the one-dimensional bilinear biquadratic model, with the techniques of
density matrix renormalization group theory. Exploiting the tools of quantum
information theory, that is, by studying quantum discord, quantum mutual
information and three recently introduced coherence measures in the reduced
density matrix of two nearest neighbor spins in the bulk, we investigate the
quantum phase transitions and special symmetry points in these models. We point
out the relative strengths and weaknesses of correlation and coherence measures
as figures of merit to witness the quantum phase transitions and symmetry
points in the considered spin-1 Heisenberg chains. In particular, we
demonstrate that as none of the studied measures can detect the infinite order
Kosterlitz-Thouless transition in the XXZ model, they appear to be able to
signal the existence of the same type of transition in the biliear biquadratic
model. However, we argue that what is actually detected by the measures here is
the SU(3) symmetry point of the model rather than the infinite order quantum
phase transition. Moreover, we show in the XXZ model that examining even single
site coherence can be sufficient to spotlight the second-order phase transition
and the SU(2) symmetry point.Comment: 8 pages. 5 figure
Separable Multipartite Mixed States - Operational Asymptotically Necessary and Sufficient Conditions
We introduce an operational procedure to determine, with arbitrary
probability and accuracy, optimal entanglement witness for every multipartite
entangled state. This method provides an operational criterion for separability
which is asymptotically necessary and sufficient. Our results are also
generalized to detect all different types of multipartite entanglement.Comment: 4 pages, 2 figures, submitted to Physical Review Letters. Revised
version with new calculation
A Robust Semidefinite Programming Approach to the Separability Problem
We express the optimization of entanglement witnesses for arbitrary bipartite
states in terms of a class of convex optimization problems known as Robust
Semidefinite Programs (RSDP). We propose, using well known properties of RSDP,
several new sufficient tests for the separability of mixed states. Our results
are then generalized to multipartite density operators.Comment: Revised version (minor spell corrections) . 6 pages; submitted to
Physical Review
Schmidt balls around the identity
Robustness measures as introduced by Vidal and Tarrach [PRA, 59, 141-155]
quantify the extent to which entangled states remain entangled under mixing.
Analogously, we introduce here the Schmidt robustness and the random Schmidt
robustness. The latter notion is closely related to the construction of Schmidt
balls around the identity. We analyse the situation for pure states and provide
non-trivial upper and lower bounds. Upper bounds to the random Schmidt-2
robustness allow us to construct a particularly simple distillability
criterion. We present two conjectures, the first one is related to the radius
of inner balls around the identity in the convex set of Schmidt number
n-states. We also conjecture a class of optimal Schmidt witnesses for pure
states.Comment: 7 pages, 1 figur
Optimal measurement bases for Bell-tests based on the CH-inequality
The Hardy test of nonlocality can be seen as a particular case of the Bell
tests based on the Clauser-Horne (CH) inequality. Here we stress this
connection when we analyze the relation between the CH-inequality violation,
its threshold detection efficiency, and the measurement settings adopted in the
test. It is well known that the threshold efficiencies decrease when one
considers partially entangled states and that the use of these states,
unfortunately, generates a reduction in the CH violation. Nevertheless, these
quantities are both dependent on the measurement settings considered, and in
this paper we show that there are measurement bases which allow for an optimal
situation in this trade-off relation. These bases are given as a generalization
of the Hardy measurement bases, and they will be relevant for future Bell tests
relying on pairs of entangled qubits.Comment: 8 pages, 6 figure
Experimental implementation of a NMR entanglement witness
Entanglement witnesses (EW) allow the detection of entanglement in a quantum
system, from the measurement of some few observables. They do not require the
complete determination of the quantum state, which is regarded as a main
advantage. On this paper it is experimentally analyzed an entanglement witness
recently proposed in the context of Nuclear Magnetic Resonance (NMR)
experiments to test it in some Bell-diagonal states. We also propose some
optimal entanglement witness for Bell-diagonal states. The efficiency of the
two types of EW's are compared to a measure of entanglement with tomographic
cost, the generalized robustness of entanglement. It is used a GRAPE algorithm
to produce an entangled state which is out of the detection region of the EW
for Bell-diagonal states. Upon relaxation, the results show that there is a
region in which both EW fails, whereas the generalized robustness still shows
entanglement, but with the entanglement witness proposed here with a better
performance
Quantifying Quantum Correlations in Fermionic Systems using Witness Operators
We present a method to quantify quantum correlations in arbitrary systems of
indistinguishable fermions using witness operators. The method associates the
problem of finding the optimal entan- glement witness of a state with a class
of problems known as semidefinite programs (SDPs), which can be solved
efficiently with arbitrary accuracy. Based on these optimal witnesses, we
introduce a measure of quantum correlations which has an interpretation
analogous to the Generalized Robust- ness of entanglement. We also extend the
notion of quantum discord to the case of indistinguishable fermions, and
propose a geometric quantifier, which is compared to our entanglement measure.
Our numerical results show a remarkable equivalence between the proposed
Generalized Robustness and the Schliemann concurrence, which are equal for pure
states. For mixed states, the Schliemann con- currence presents itself as an
upper bound for the Generalized Robustness. The quantum discord is also found
to be an upper bound for the entanglement.Comment: 7 pages, 6 figures, Accepted for publication in Quantum Information
Processin
Recombinant proteins in plants.
Edição do Congress of the Brazilian Biotechnology Society, Florianópolis, 2013
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