Noise robustness of the nonlocality of entangled quantum states.

@article{Almeida2007NoiseRO,
  title={Noise robustness of the nonlocality of entangled quantum states.},
  author={Mafalda L. Almeida and Stefano Pironio and Jonathan Barrett and G{\'e}za T{\'o}th and Antonio Ac{\'i}n},
  journal={Physical review letters},
  year={2007},
  volume={99 4},
  pages={
          040403
        }
}
We study the nonlocal properties of states resulting from the mixture of an arbitrary entangled state rho of two d-dimensional systems and completely depolarized noise, with respective weights p and 1-p. We first construct a local model for the case in which rho is maximally entangled and p at or below a certain bound. We then extend the model to arbitrary rho. Our results provide bounds on the resistance to noise of the nonlocal correlations of entangled states. For projective measurements… 

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References

SHOWING 1-10 OF 59 REFERENCES
Quantum nonlocality in two three-level systems
Recently a new Bell inequality has been introduced (CGLMP,KKCZO) that is strongly resistant to noise for maximally entangled states of two d-dimensional quantum systems. We prove that a larger
Grothendieck's constant and local models for noisy entangled quantum states
We relate the nonlocal properties of noisy entangled states to Grothendieck's constant, a mathematical constant appearing in Banach space theory. For two-qubit Werner states rho p W
SEPARABILITY OF VERY NOISY MIXED STATES AND IMPLICATIONS FOR NMR QUANTUM COMPUTING
TLDR
Though this result raises questions about NMR quantum computation, further analysis would be necessary to assess the power of the general unitary transformations, which are indeed implemented in these experiments, in their action on separable states.
Robustness of entanglement
In the quest to completely describe entanglement in the general case of a finite number of parties sharing a physical system of finite-dimensional Hilbert space an entanglement magnitude is
Genuine tripartite entangled states with a local hidden-variable model
We present a family of three-qubit quantum states with a basic local hidden-variable model. Any von Neumann measurement can be described by a local model for these states. We show that some of these
Nonsequential positive-operator-valued measurements on entangled mixed states do not always violate a Bell inequality
We present a local-hidden-variable model for positive-operator-valued measurements (an LHVPOV model) ) on a class of entangled generalized Werner states, thus demonstrating that such measurements do
Steering, entanglement, nonlocality, and the Einstein-Podolsky-Rosen paradox.
TLDR
An operational definition is provided, from which it is proved that steerable states are a strict subset of the entangled states, and a strict superset of the states that can exhibit Bell nonlocality.
Volume of the set of separable states
The question of how many entangled or, respectively, separable states there are in the set of all quantum states is considered. We propose a natural measure in the space of density matrices %
Conditions for a Class of Entanglement Transformations
Suppose Alice and Bob jointly possess a pure state, |ψ〉. Using local operations on their respective systems and classical communication it may be possible for Alice and Bob to transform |ψ〉 into
Efficient classical simulation of slightly entangled quantum computations.
  • G. Vidal
  • Computer Science, Physics
    Physical review letters
  • 2003
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The results imply that a necessary condition for an exponential computational speedup is that the amount of entanglement increases with the size n of the computation, and provide an explicit lower bound on the required growth.
...
1
2
3
4
5
...