Detection of multiparticle entanglement: quantifying the search for symmetric extensions.

@article{Brando2012DetectionOM,
  title={Detection of multiparticle entanglement: quantifying the search for symmetric extensions.},
  author={Fernando G. S. L. Brand{\~a}o and Matthias Christandl},
  journal={Physical review letters},
  year={2012},
  volume={109 16},
  pages={
          160502
        }
}
We provide quantitative bounds on the characterization of multiparticle separable states by states that have locally symmetric extensions. The bounds are derived from two-particle bounds and relate to recent studies on quantum versions of de Finetti's theorem. We discuss algorithmic applications of our results, in particular a quasipolynomial-time algorithm to decide whether a multiparticle quantum state is separable or entangled (for constant number of particles and constant error in the norm… 

Figures from this paper

Applications of differential geometry and representation theory to description of quantum correlations
One of the most important questions in quantum information theory is the so-called separability problem. It involves characterizing the set of separable (or, equivalently entangled) states among
Quantum de finetti theorems under local measurements with applications
TLDR
Two new quantum de Finetti theorems are proved, both showing that under tests formed by local measurements in each of the subsystems one can get an exponential improvement in the error dependence on the dimension ofThe subsystems.
Extendibility of Bosonic Gaussian States.
TLDR
A simple semidefinite program is derived, whose size scales linearly with the number of local modes, to efficiently decide k-extendibility of any given bosonic Gaussian state.
Linking entanglement detection and state tomography via quantum 2-designs
TLDR
An experimentally feasible and efficient method for detecting entangled states with measurements that extend naturally to a tomographically complete set, and is twice as effective as standard witnesses in the sense that both upper and lower bounds can be derived.
Generation and Detection of Quantum Correlations and Entanglement on a Spin-Based Quantum Information Processor
This thesis focuses on the experimental creation and detection of a variety of quantum correlations using nuclear magnetic resonance hardware. Quantum entanglement, being most common and
Entanglement and the shareability of quantum states
This brief review discusses the problem of determining whether a given quantum state is separable or entangled. I describe an established approach to this problem that is based on the monogamy of
Quantum Interactive Proofs and the Complexity of Separability Testing
TLDR
Strong hardness results are obtained by employing prior work on entanglement purification protocols to prove that for each n-qubit maximally entangled state there exists a fixed one-way LOCC measurement that distinguishes it from any separable state with error probability that decays exponentially in n.
Quantum interactive proofs and the complexity of entanglement detection
This paper identifies a formal connection between physical problems related to entanglement detection and complexity classes in theoretical computer science. In particular, we show that to nearly
Experimental detection of non-local correlations using a local measurement-based hierarchy on an NMR quantum processor
The non-local nature of the correlations possessed by quantum systems may be revealed by experimental demonstrations of the violation of Bell-type inequalities. Recent work has placed bounds on the
Designing quantum information processing via structural physical approximation.
  • J. Bae
  • Physics
    Reports on progress in physics. Physical Society
  • 2017
TLDR
A comprehensive review on quantum information processing with structural physical approximations and their applications toward practical information applications is presented.
...
...

References

SHOWING 1-10 OF 38 REFERENCES
"J."
however (for it was the literal soul of the life of the Redeemer, John xv. io), is the peculiar token of fellowship with the Redeemer. That love to God (what is meant here is not God’s love to men)
Phys
  • Rev. A 69, 022308
  • 2004
Commun
  • Math. Phys. 273, 473
  • 2007
Comm
  • Math. Phys. 273, 473
  • 2007
Theory Comput
  • 7, 101
  • 2011
Phys
  • (N.Y.) 50, 042104
  • 2009
Inf
  • Theory 48, 580
  • 2002
Commun
  • Math. Phys. 306, 579 (2011). PRL 109, 160502
  • 2012
Phys
  • Rev. Lett. 86, 5807
  • 2001
...
...