Entanglement detection via general SIC-POVMs

@article{Xi2016EntanglementDV,
  title={Entanglement detection via general SIC-POVMs},
  author={Ya Xi and Zhu-Jun Zheng and Chuan-Jie Zhu},
  journal={Quantum Information Processing},
  year={2016},
  volume={15},
  pages={5119-5128}
}
We study separability problem using general symmetric informationally complete measurements and propose separability criteria in $$\mathbb {C}^{d_{1}}\otimes \mathbb {C}^{d_{2}}$$Cd1⊗Cd2 and $$\mathbb {C}^{d_{1}}\otimes \mathbb {C}^{d_{2}}\cdots \otimes \mathbb {C}^{d_{n}}$$Cd1⊗Cd2⋯⊗Cdn. Our criteria just require less local measurements and provide experimental implementation in detecting entanglement of unknown quantum states. 

Informational power of the Hoggar SIC-POVM

Among positive operator valued measures (POVMs) representing general quantum measurements, symmetric informationally complete (SIC) POVMs, called by Christopher Fuchs ‘mysterious entities’, play a

New Separability Criteria Based on Two Classes of Measurements

We investigate entanglement detection using mutually unbiased measurements and general symmetric informationally complete positive operator-valued measurements. Four separability criteria are

Detecting EPR steering via two classes of local measurements

We study the Einstein–Podolsky–Rosen steering and present steerability criteria for arbitrary qubit-qudit (qudit-qubit) systems based on mutually unbiased measurements and general symmetric

Entanglement Witnesses Based on Symmetric Informationally Complete Measurements

TLDR
It can be found this witness detects more entanglement than previous separability method given also by SIC-POVM.

Improved separability criteria via some classes of measurements

TLDR
Based on mutually unbiased measurements and general symmetric informationally complete positive-operator-valued measures, separability criteria for bipartite quantum states are presented, which, by theoretical analysis, are stronger than the related existing criteria via these measurements.

Enhanced entanglement criterion via symmetric informationally complete measurements

We show that a special type of measurements, called symmetric informationally complete positive operator-valued measures (SIC POVMs), provide a stronger entanglement detection criterion than the

Entanglement properties of multipartite informationally complete quantum measurements

We analyze tight informationally complete measurements for arbitrarily large multipartite systems and study their configurations of entanglement. We demonstrate that tight measurements cannot be

Entanglement criterion via general symmetric informationally complete measurements

TLDR
This work studies the quantum separability problem by using general symmetric informationally complete measurements and presents a separability criterion for arbitrary dimensional bipartite systems that is more powerful than the existing ones in entanglement detection.

Construction of general symmetric-informationally-complete–positive-operator-valued measures by using a complete orthogonal basis

A general symmetric informationally complete (GSIC)-positive operator valued measure (POVM) is known to provide an optimal quantum state tomography among minimal IC-POVMs with a fixed average purity.

Entanglement criterion via general symmetric informationally complete measurement

  • Jun LiLin Chen
  • Physics
    Journal of Physics A: Mathematical and Theoretical
  • 2021
We propose entanglement criteria for multipartite systems via symmetric informationally complete measurement and general symmetric informationally complete measurement. We apply these criteria to

References

SHOWING 1-10 OF 59 REFERENCES

Separability Criterion for Density Matrices.

  • Pérès
  • Physics
    Physical review letters
  • 1996
TLDR
It is proved that a necessary condition for separability is that a matrix, obtained by partial transposition of {rho}, has only non-negative eigenvalues.

General SIC measurement-based entanglement detection

TLDR
The criterion for bipartite quantum states is effective in detecting several well-known classes of quantum states, and the criterion for two-qudit states requires less local measurements than the one based on mutually unbiased measurements.

Entanglement detection via some classes of measurements

Based on the mutually unbiased bases, the mutually unbiased measurements and the general symmetric informationally complete positive-operator-valued measures, we propose three separability criteria

Some properties of the computable cross-norm criterion for separability

The computable cross-norm (CCN) criterion is a powerful analytical and computable separability criterion for bipartite quantum states, which is also known to systematically detect bound entanglement.

On quantum information

TLDR
This work investigates the following generalisation of the entropy of quantum measurement and gives a general form of generalised information I.

Notes on general SIC-POVMs

TLDR
It is obtained that for a given density matrix and any general SIC-POVM, the so-called index of coincidence of generated probability distribution is exactly calculated and state-dependent entropic bounds for a single general Sic-PovM are obtained.

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

Optimization of entanglement witnesses

An entanglement witness (EW) is an operator that allows to detect entangled states. We give necessary and sufficient conditions for such operators to be optimal, i.e. to detect entangled states in an

Symmetric informationally complete quantum measurements

TLDR
It is conjecture that a particular kind of group-covariant SIC–POVM exists in arbitrary dimensions, providing numerical results up to dimension 45 to bolster this claim.
...