Mutually unbiased bases and bound entanglement

@article{Hiesmayr2013MutuallyUB,
  title={Mutually unbiased bases and bound entanglement},
  author={Beatrix C. Hiesmayr and Wolfgang Loffler},
  journal={Physica Scripta},
  year={2013},
  volume={2014},
  pages={014017}
}
In this contribution we relate two different key concepts: mutually unbiased bases (MUBs) and entanglement. We provide a general toolbox for analyzing and comparing entanglement of quantum states for different dimensions and numbers of particles. In particular we focus on bound entanglement, i.e. highly mixed states which cannot be distilled by local operations and classical communications. For a certain class of states—for which the state-space forms a 'magic' simplex—we analyze the set of… 

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References

SHOWING 1-10 OF 26 REFERENCES
Entanglement detection via mutually unbiased bases
We investigate correlations among complementary observables. In particular, we show how to take advantage of mutually unbiased bases (MUBs) for the detection of entanglement in arbitrarily
Two distinct classes of bound entanglement: PPT-bound and `multi-particle'-bound
TLDR
By a general construction of W simplices, novel classes of multipartite and multidimensional states are introduced which have the same geometry concerning separability and entanglement independent of the number of involved particle pairs.
Complementarity reveals bound entanglement of two twisted photons
We demonstrate the detection of bipartite bound entanglement as predicted by the Horodecki's in 1998. Bound entangled states, being heavily mixed entangled quantum states, can be produced by
Simplex of bound entangled multipartite qubit states
We construct a simplex for multipartite qubit states of even number n of qubits, which has the same geometry concerning separability, mixedness, kind of entanglement, amount of entanglement and
State space for two qutrits has a phase space structure in its core
We investigate the state space of bipartite qutrits. For states which are locally maximally mixed we obtain an analog of the 'magic' tetrahedron for bipartite qubits - a magic simplex W. This is
Experimental bound entanglement in a four-photon state.
TLDR
This work considers a one-parameter family of four-qubit Smolin states and experimentally produces these states in the polarization of four optical photons produced from parametric down-conversion, showing that they are entangled and undistillable, and thus bound entangled.
Mixed-State Entanglement and Distillation: Is there a “Bound” Entanglement in Nature?
It is shown that if a mixed state can be distilled to the singlet form it must violate partial transposition criterion [A. Peres, Phys. Rev. Lett. 76, 1413 (1996)]. It implies that there are two
A special simplex in the state space for entangled qudits
The focus is on two parties with Hilbert spaces of dimension d, i.e. 'qudits'. In the state space of these two possibly entangled qudits an analogue to the well-known tetrahedron with the four qubit
Four-party unlockable bound entangled state
I present a four-party unlockable bound entangled state, that is, a four-party quantum state which cannot be written in a separable form and from which no pure entanglement can be distilled by local
Detection and typicality of bound entangled states
We derive an explicit analytic estimate for the entanglement of a large class of bipartite quantum states, which extends into bound entanglement regions. This is done by using an efficiently
...
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3
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