471 research outputs found
Spectral decomposition of Bell's operators for qubits
The spectral decomposition is given for the N-qubit Bell operators with two
observables per qubit. It is found that the eigenstates (when non-degenerate)
are N-qubit GHZ states even for those operators that do not allow the maximal
violation of the corresponding inequality. We present two applications of this
analysis. In particular, we discuss the existence of pure entangled states that
do not violate any Mermin-Klyshko inequality for .Comment: 12 pages, 1 figure
Entanglement, which-way measurements, and a quantum erasure
We present a didactical approach to the which-way experiment and the
counterintuitive effect of the quantum erasure for one-particle quantum
interferences. The fundamental concept of entanglement plays a central role and
highlights the complementarity between quantum interference and knowledge of
which path is followed by the particle.Comment: 5 pages, 4 figures; with some clarifications and added reference
Device independent state estimation based on Bell's inequalities
The only information available about an alleged source of entangled quantum
states is the amount by which the Clauser-Horne-Shimony-Holt (CHSH)
inequality is violated: nothing is known about the nature of the system or the
measurements that are performed. We discuss how the quality of the source can
be assessed in this black-box scenario, as compared to an ideal source that
would produce maximally entangled states (more precisely, any state for which
). To this end, we introduce several inequivalent notions of
fidelity, each one related to the use one can make of the source after having
assessed it; and we derive quantitative bounds for each of them in terms of the
violation . We also derive a lower bound on the entanglement of the source
as a function of only.Comment: 8 pages, 2 figures. Added appendices containing proof
Finite-key security against coherent attacks in quantum key distribution
The work by Christandl, K\"onig and Renner [Phys. Rev. Lett. 102, 020504
(2009)] provides in particular the possibility of studying unconditional
security in the finite-key regime for all discrete-variable protocols. We spell
out this bound from their general formalism. Then we apply it to the study of a
recently proposed protocol [Laing et al., Phys. Rev. A 82, 012304 (2010)]. This
protocol is meaningful when the alignment of Alice's and Bob's reference frames
is not monitored and may vary with time. In this scenario, the notion of
asymptotic key rate has hardly any operational meaning, because if one waits
too long time, the average correlations are smeared out and no security can be
inferred. Therefore, finite-key analysis is necessary to find the maximal
achievable secret key rate and the corresponding optimal number of signals.Comment: 9 pages, 4 figure
A Witness of Multipartite Entanglement Strata
We describe an entanglement witness for -qubit mixed states based on the
properties of -point correlation functions. Depending on the degree of
violation, this witness can guarantee that no more than qubits are
separable from the rest of the state for any , or that there is some
genuine -party or greater multipartite entanglement present. We illustrate
the use our criterion by investigating the existence of entanglement in thermal
stabilizer states, where we demonstrate that the witness is capable of
witnessing bound-entangled states. Intriguingly, this entanglement can be shown
to persist in the thermodynamic limit at arbitrary temperature.Comment: 7 pages, 1 figur
de Finetti reductions for correlations
When analysing quantum information processing protocols one has to deal with
large entangled systems, each consisting of many subsystems. To make this
analysis feasible, it is often necessary to identify some additional structure.
de Finetti theorems provide such a structure for the case where certain
symmetries hold. More precisely, they relate states that are invariant under
permutations of subsystems to states in which the subsystems are independent of
each other. This relation plays an important role in various areas, e.g., in
quantum cryptography or state tomography, where permutation invariant systems
are ubiquitous. The known de Finetti theorems usually refer to the internal
quantum state of a system and depend on its dimension. Here we prove a
different de Finetti theorem where systems are modelled in terms of their
statistics under measurements. This is necessary for a large class of
applications widely considered today, such as device independent protocols,
where the underlying systems and the dimensions are unknown and the entire
analysis is based on the observed correlations.Comment: 5+13 pages; second version closer to the published one; new titl
- …