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… 
View PDF on arXiv
9 Citations
Background Citations
4
Methods Citations
1

Figures from this paper

9 Citations

Citation Type

Citation Type

Mutually Unbiased Quantum Bases : Existence , Entanglement , Information
TLDR
The difficulties of those approaches to the existence problem which employ Hadamard matrices are explored and new general results are derived for the connection between MUBs and Unitary Operator Bases and the role of entanglement is explored.
Witnessing Entanglement In Compton Scattering Processes Via Mutually Unbiased Bases
TLDR
A quantum information theoretic version of the Klein-Nishina formula that singles out the quantity, the a priori visibility, that quantifies the ability to deduce the polarisation property of single photons.
Ju l 2 01 8 Witnessing Entanglement In Compton Scattering Processes Via Mutually Unbiased Bases
We present a quantum information theoretic version of the Klein-Nishina formula. This formulation singles out the quantity, the a priori visibility, that quantifies the ability to deduce the…
Optimization of device-independent witnesses of entanglement depth from two-body correlators
TLDR
The problem of finding the $k$-producible bounds of such DIWEDs under different assumptions is considered, not surprisingly, with the weakest assumptions, only for a relatively small number of parties; however, one can still learn interesting features from these solutions that motivate the search on larger systems under the assumption that these features persist.
Free versus Bound Entanglement: Machine learning tackling a NP-hard problem
TLDR
A large family of magically symmetric states of bipartite qutrits is defined, which shows that this kind of entanglement is not rare, and reveals that there is a strong 2-dimensional (linear) sub-structure in the set of bound entangled states.
Separability of diagonal symmetric states: a quadratic conic optimization problem
We study the separability problem in mixtures of Dicke states i.e., the separability of the so-called Diagonal Symmetric (DS) states. First, we show that separability in the case of DS in $C^d\otimes…
Free versus bound entanglement, a NP-hard problem tackled by machine learning
Entanglement detection in high dimensional systems is a NP-hard problem since it is lacking an efficient way. Given a bipartite quantum state of interest free entanglement can be detected efficiently…
Quantum measurements with prescribed symmetry
We introduce a method to determine whether a given generalised quantum measurement is isolated or it belongs to a family of measurements having the same prescribed symmetry. The technique proposed…
Block-Circulant Complex Hadamard Matrices
A new method of obtaining a sequence of isolated complex Hadamard matrices (CHM) of arbitrary order N > 7 , based on block-circulant structures, is presented. Several analytic and numerical examples…

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…
...
1
2
3
...