# 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.

## 11 Citations

### Informational power of the Hoggar SIC-POVM

- Physics
- 2015

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

- Physics
- 2018

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

- PhysicsQuantum Inf. Process.
- 2020

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

- Computer Science
- 2020

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

- MathematicsQuantum Inf. Process.
- 2018

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

- PhysicsPhysical Review A
- 2018

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

- MathematicsJournal of Physics A: Mathematical and Theoretical
- 2018

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

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

- MathematicsPhysical Review A
- 2022

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

- PhysicsQuantum Inf. Process.
- 2018

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.

### Separability discrimination and decomposition of m -partite quantum mixed states

- Computer Science
- 2020

An E-truncated and semidefinite relaxations method and an algorithm for detecting the separability of mixed states are proposed and it is found that not all symmetric separable states have symmetric decompositions.

## References

SHOWING 1-10 OF 33 REFERENCES

### Separability Criterion for Density Matrices.

- PhysicsPhysical review letters
- 1996

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

- PhysicsQuantum Inf. Process.
- 2015

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

- Physics
- 2015

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

- Mathematics
- 2003

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

- MathematicsArXiv
- 2012

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

- Computer Science
- 2014

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

- Physics
- 2012

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…

### Symmetric informationally complete quantum measurements

- Mathematics
- 2003

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.

### The generalized partial transposition criterion for separability of multipartite quantum states

- Physics
- 2002

### Inequalities Detecting Quantum Entanglement for 2 ⊗ d Systems

- Physics
- 2011

We present a set of inequalities for detecting quantum entanglement of 2 x d quantum states. For 2 x 2 and 2 x 3 systems, the inequalities give rise to sufficient and necessary separability…