24 research outputs found
Classification and monogamy of three-qubit biseparable Bell correlations
We strengthen the set of Bell-type inequalities presented by Sun & Fei [Phys.
Rev. A 74, 032335 (2006)] that give a classification for biseparable
correlations and entanglement in tripartite quantum systems. We will
furthermore consider the restriction to local orthogonal spin observables and
show that this strengthens all previously known such tripartite inequalities.
The quadratic inequalities we find indicate a type of monogamy of maximal
biseparable three-particle quantum correlations, although the nonmaximal ones
can be shared. This is contrasted to recently found monogamy inequalities for
bipartite Bell correlations in tripartite systems.Comment: Accepted final version for PRA. 6 page
Partial separability and entanglement criteria for multiqubit quantum states
We explore the subtle relationships between partial separability and
entanglement of subsystems in multiqubit quantum states and give experimentally
accessible conditions that distinguish between various classes and levels of
partial separability in a hierarchical order. These conditions take the form of
bounds on the correlations of locally orthogonal observables. Violations of
such inequalities give strong sufficient criteria for various forms of partial
inseparability and multiqubit entanglement. The strength of these criteria is
illustrated by showing that they are stronger than several other well-known
entanglement criteria (the fidelity criterion, violation of Mermin-type
separability inequalities, the Laskowski-\.Zukowski criterion and the
D\"ur-Cirac criterion), and also by showing their great noise robustness for a
variety of multiqubit states, including N-qubit GHZ states and Dicke states.
Furthermore, for N greater than or equal to 3 they can detect bound entangled
states. For all these states, the required number of measurement settings for
implementation of the entanglement criteria is shown to be only N+1. If one
chooses the familiar Pauli matrices as single-qubit observables, the
inequalities take the form of bounds on the anti-diagonal matrix elements of a
state in terms of its diagonal matrix elements.Comment: 25 pages, 3 figures. v4: published versio
The quantum world is not built up from correlations
It is known that the global state of a composite quantum system can be
completely determined by specifying correlations between measurements performed
on subsystems only. Despite the fact that the quantum correlations thus suffice
to reconstruct the quantum state, we show, using a Bell inequality argument,
that they cannot be regarded as objective local properties of the composite
system in question. It is well known since the work of J.S. Bell, that one
cannot have locally preexistent values for all physical quantities, whether
they are deterministic or stochastic. The Bell inequality argument we present
here shows this is also impossible for correlations among subsystems of an
individual isolated composite system. Neither of them can be used to build up a
world consisting of some local realistic structure. As a corrolary to the
result we argue that entanglement cannot be considered ontologically robust.
The argument has an important advantage over others because it does not need
perfect correlations but only statistical correlations. It can therefore easily
be tested in currently feasible experiments using four particle entanglement.Comment: Published version. Title change
Separability criteria for genuine multiparticle entanglement
We present a method to derive separability criteria for the different classes
of multiparticle entanglement, especially genuine multiparticle entanglement.
The resulting criteria are necessary and sufficient for certain families of
states. Further, the criteria are superior to all known entanglement criteria
for many other families; also they allow the detection of bound entanglement.
We next demonstrate that they are easily implementable in experiments and
discuss applications to the decoherence of multiparticle entangled states.Comment: five pages, one figure, v4: final version plus a remark on
arXiv:0912.187
Addendum to "Sufficient conditions for three-particle entanglement and their tests in recent experiments"
A recent paper [M. Seevinck and J. Uffink, Phys. Rev. A 65, 012107 (2002)]
presented a bound for the three-qubit Mermin inequality such that the violation
of this bound indicates genuine three-qubit entanglement. We show that this
bound can be improved for a specific choice of observables. In particular, if
spin observables corresponding to orthogonal directions are measured at the
qubits (e.g., X and Y spin coordinates) then the bound is the same as the bound
for states with a local hidden variable model. As a consequence, it can
straightforwardly be shown that in the experiment described by J.-W. Pan et al.
[Nature 403, 515 (2000)] genuine three-qubit entanglement was detected.Comment: Two pages, no figures, revtex4; minor changes before publicatio
Sufficient conditions for three-particle entanglement and their tests in recent experiments
We point out a loophole problem in some recent experimental claims to produce
three-particle entanglement. The problem consists in the question whether
mixtures of two-particle entangled states might suffice to explain the
experimental data.
In an attempt to close this loophole, we review two sufficient conditions
that distinguish between N-particle states in which all N particles are
entangled to each other and states in which only M particles are entangled
(with M<N). It is shown that three recent experiments to obtain three-particle
entangled states (Bouwmeester et al., Pan et al., and Rauschenbeutel et al.) do
not meet these conditions. We conclude that the question whether these
experiments provide confirmation of three-particle entanglement remains
unresolved. We also propose modifications of the experiments that would make
such confirmation feasible.Comment: 16 page
Bell inequalities and distillability in N-quantum-bit systems
The relation between Bell inequalities with two two-outcome measurements per
site and distillability is analyzed in systems of an arbitrary number of
quantum bits. We observe that the violation of any of these inequalities by a
quantum state implies that pure-state entanglement can be distilled from it.
The corresponding distillation protocol may require that some of the parties
join into several groups. We show that there exists a link between the amount
of the Bell inequality violation and the size of the groups they have to form
for distillation. Thus, a strong violation is always sufficient for full
N-partite distillability. This result also allows for a security proof of
multi-partite quantum key distribution (QKD) protocols.Comment: REVTEX, 12 pages, two figure