# The decompositions of Werner and isotropic states

@article{Yang2021TheDO, title={The decompositions of Werner and isotropic states}, author={Ma-Cheng Yang and Jun-Li Li and Cong-Feng Qiao}, journal={Quantum Inf. Process.}, year={2021}, volume={20}, pages={1-11} }

The decompositions of separable Werner state, and also isotropic state, are well-known tough issues in quantum information theory, in this work we investigate them in the Bloch vector representation, exploring the symmetric informationally complete positive operator-valued measure (SIC-POVM) in the Hilbert space. We successfully get the decomposition for arbitrary $N\times N$ Werner state in terms of regular simplexes. Meanwhile, the decomposition of isotropic state is found to be related to…

## References

SHOWING 1-10 OF 39 REFERENCES

Quantum Computation and Quantum Information

- Physics, Computer Science
- 2000

This chapter discusses quantum information theory, public-key cryptography and the RSA cryptosystem, and the proof of Lieb's theorem.

Quantum states with Einstein-Podolsky-Rosen correlations admitting a hidden-variable model.

- PhysicsPhysical review. A, General physics
- 1989

Any classically correlated state can be modeled by a hidden-variable theory and hence satisfies all generalized Bell's inequalities and the converse of this statement is false.

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.

Distillability and partial transposition in bipartite systems

- Mathematics
- 2000

Institut fu¨r Theoretische Physik, Universit¨at Hannover, D-30167 Hannover, Germany(February 1, 2008)We study the distillability of a certain class of bipartitedensity operators which can be obtained…

Matrix analysis

- Mathematics
- 1985

This new edition of the acclaimed text presents results of both classic and recent matrix analyses using canonical forms as a unifying theme, and demonstrates their importance in a variety of applications.

Quantum Entanglement

- Physics, Computer ScienceDo We Really Understand Quantum Mechanics?
- 2019

A brief overview of the concept of entanglement in quantum mechanics is given, and the major results and open problems related to the recent scientific progress in this field are discussed.

A Necessary and Sufficient Criterion for the Separability of Quantum State

- MathematicsScientific Reports
- 2018

In this work, an operational necessary and sufficient criterion for the separability of an arbitrary bipartite mixed state is proposed, by virtue of the multiplicative Horn’s problem.

A necessary and sufficient criterion for the separability of quantum state, Sci

- Rep. 8,
- 2018

Separable decompositions of bipartite mixed states

- MathematicsQuantum Inf. Process.
- 2018

We present a practical scheme for the decomposition of a bipartite mixed state into a sum of direct products of local density matrices, using the technique developed in Li and Qiao (Sci. Rep. 8:1442,…