953 research outputs found
Entanglement witnesses for a class of bipartite states of n x n qubits
We characterize the positive maps detecting the entangled bipartite states of
n x n qubits that are diagonal with respect to the orthonormal basis
constructed by tensor products of Pauli matrices acting on the totally
symmetric state. We then discuss the case n=2 for a class of states completely
determined by the geometric patterns of subsets of a 16 point lattice.Comment: 25 page
Time-evolution of tripartite quantum discord and entanglement under local and non-local random telegraph noise
Few studies explored the dynamics of non-classical correlations besides
entanglement in open multipartite quantum systems. Here, we address the
time-evolution of quantum discord and entanglement in a model of three
non-interacting qubits subject to a classical random telegraph noise in common
and separated environments. Two initial entangled states of the system are
examined, namely the GHZ- and W-type states. The dynamics of quantum
correlations results to be strongly affected by the input configuration of the
qubits, the type of the system-environment interaction, and the memory
properties of the environmental noise. When the qubits are non-locally coupled
to the random telegraph noise, the GHZ-type states partially preserve, at long
times, both discord and entanglement, regardless the correlation time of the
environmental noise. The survived entangled states turn out to be also
detectable by means of suitable entanglement witnesses. On the other hand, in
the same conditions, the decohering effects suppress all the quantum
correlation of the W-type states which are thus less robust than the GHZ-type
ones. The long-time survival of tripartite discord and entanglement opens
interesting perspectives in the use of multipartite entangled states for
practical applications in quantum information science.Comment: 11 pages, 4 figure
Quantum entanglement
All our former experience with application of quantum theory seems to say:
{\it what is predicted by quantum formalism must occur in laboratory}. But the
essence of quantum formalism - entanglement, recognized by Einstein, Podolsky,
Rosen and Schr\"odinger - waited over 70 years to enter to laboratories as a
new resource as real as energy.
This holistic property of compound quantum systems, which involves
nonclassical correlations between subsystems, is a potential for many quantum
processes, including ``canonical'' ones: quantum cryptography, quantum
teleportation and dense coding. However, it appeared that this new resource is
very complex and difficult to detect. Being usually fragile to environment, it
is robust against conceptual and mathematical tools, the task of which is to
decipher its rich structure.
This article reviews basic aspects of entanglement including its
characterization, detection, distillation and quantifying. In particular, the
authors discuss various manifestations of entanglement via Bell inequalities,
entropic inequalities, entanglement witnesses, quantum cryptography and point
out some interrelations. They also discuss a basic role of entanglement in
quantum communication within distant labs paradigm and stress some
peculiarities such as irreversibility of entanglement manipulations including
its extremal form - bound entanglement phenomenon. A basic role of entanglement
witnesses in detection of entanglement is emphasized.Comment: 110 pages, 3 figures, ReVTex4, Improved (slightly extended)
presentation, updated references, minor changes, submitted to Rev. Mod. Phys
Spin squeezing inequalities and entanglement of qubit states
We derive spin squeezing inequalities that generalize the concept of the spin
squeezing parameter and provide necessary and sufficient conditions for genuine
2-, or 3- qubit entanglement for symmetric states, and sufficient condition for
general states of qubits. Our inequalities have a clear physical
interpretation as entanglement witnesses, can be relatively easy measured, and
are given by complex, but {\it elementary} expressions.Comment: formula (24) corrected, minor changes, final versio
Arboreal Bound Entanglement
In this paper, we discuss the entanglement properties of graph-diagonal
states, with particular emphasis on calculating the threshold for the
transition between the presence and absence of entanglement (i.e. the
separability point). Special consideration is made of the thermal states of
trees, including the linear cluster state. We characterise the type of
entanglement present, and describe the optimal entanglement witnesses and their
implementation on a quantum computer, up to an additive approximation. In the
case of general graphs, we invoke a relation with the partition function of the
classical Ising model, thereby intimating a connection to computational
complexity theoretic tasks. Finally, we show that the entanglement is robust to
some classes of local perturbations.Comment: 9 pages + appendices, 3 figure
Entanglement Witnesses for Graph States: General Theory and Examples
We present a general theory for the construction of witnesses that detect
genuine multipartite entanglement in graph states. First, we present explicit
witnesses for all graph states of up to six qubits which are better than all
criteria so far. Therefore, lower fidelities are required in experiments that
aim at the preparation of graph states. Building on these results, we develop
analytical methods to construct two different types of entanglement witnesses
for general graph states. For many classes of states, these operators exhibit
white noise tolerances that converge to one when increasing the number of
particles. We illustrate our approach for states such as the linear and the 2D
cluster state. Finally, we study an entanglement monotone motivated by our
approach for graph states.Comment: 12 pages + appendix, 7 figure
Classification of mixed three-qubit states
We introduce a classification of mixed three-qubit states, in which we define
the classes of separable, biseparable, W- and GHZ-states. These classes are
successively embedded into each other. We show that contrary to pure W-type
states, the mixed W-class is not of measure zero. We construct witness
operators that detect the class of a mixed state. We discuss the conjecture
that all entangled states with positive partial transpose (PPTES) belong to the
W-class. Finally, we present a new family of PPTES "edge" states with maximal
ranks.Comment: 4 pages, 1 figur
Entanglement Detection in the Stabilizer Formalism
We investigate how stabilizer theory can be used for constructing sufficient
conditions for entanglement. First, we show how entanglement witnesses can be
derived for a given state, provided some stabilizing operators of the state are
known. These witnesses require only a small effort for an experimental
implementation and are robust against noise. Second, we demonstrate that also
nonlinear criteria based on uncertainty relations can be derived from
stabilizing operators. These criteria can sometimes improve the witnesses by
adding nonlinear correction terms. All our criteria detect states close to
Greenberger-Horne-Zeilinger states, cluster and graph states. We show that
similar ideas can be used to derive entanglement conditions for states which do
not fit the stabilizer formalism, such as the three-qubit W state. We also
discuss connections between the witnesses and some Bell inequalities.Comment: 15 pages including 2 figures, revtex4; typos corrected, presentation
improved; to appear in PR
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