# Entanglement classification via integer partitions

@article{Li2019EntanglementCV, title={Entanglement classification via integer partitions}, author={Dafa Li}, journal={Quantum Information Processing}, year={2019}, volume={19} }

In Walter et al. (Science 340:1205, 2013), they gave a sufficient condition for genuinely entangled pure states and discussed SLOCC classification via polytopes and the eigenvalues of the single-particle states. In this paper, for 4n qubits, we show the invariance of algebraic multiplicities (AMs) and geometric multiplicities (GMs) of eigenvalues and the invariance of sizes of Jordan blocks (JBs) of the coefficient matrices under SLOCC. We explore properties of spectra, eigenvectors…

## One Citation

### Entanglement Quantification and Classification: A Systematic Literature Review

- PhysicsInternational Journal of Advanced Computer Science and Applications
- 2022

—Quantum entanglement is one of the essences of quantum mechanics and quantum information theory. It is a physical phenomenon in which entangled particles remain correlated with each other regardless…

## References

SHOWING 1-10 OF 48 REFERENCES

### Polynomial invariants for discrimination and classification of four-qubit entanglement

- Physics
- 2011

The number of entanglement classes in stochastic local operations and classical communication (SLOCC) classifications increases with the number of qubits and is already infinite for four qubits.…

### Method for classifying multiqubit states via the rank of the coefficient matrix and its application to four-qubit states

- Mathematics
- 2012

We construct coefficient matrices of size 2^l by 2^{n-l} associated with pure n-qubit states and prove the invariance of the ranks of the coefficient matrices under stochastic local operations and…

### On polynomial invariants of several qubits

- Physics, Mathematics
- 2009

It is a recent observation that entanglement classification for qubits is closely related to local SL(2,C)-invariants including the invariance under qubit permutations [Dur, et al., Phys. Rev. A 62,…

### Constructing N-qubit entanglement monotones from antilinear operators (4 pages)

- Mathematics
- 2005

We present a method to construct entanglement measures for pure states of multipartite qubit systems. The key element of our approach is an antilinear operator that we call ``comb''. For qubits (or…

### Quantifying entanglement of arbitrary-dimensional multipartite pure states in terms of the singular values of coefficient matrices

- Physics, Computer Science
- 2013

The so-called Manhattan distance ($l_1$ norm) of averaged partial entropies (MAPE) is proved to be an entanglement measure for pure states and the relation between the rank of the coefficient matrix and the degree ofEntanglement is demonstrated for symmetric states by two examples.

### Classification of multipartite entanglement of all finite dimensionality.

- MathematicsPhysical review letters
- 2013

We provide a systematic classification of multiparticle entanglement in terms of equivalence classes of states under stochastic local operations and classical communication (SLOCC). We show that such…

### SLOCC classification of n qubits invoking the proportional relationships for spectrums and standard Jordan normal forms

- PhysicsQuantum Inf. Process.
- 2018

Invoking the proportional relationships for spectrums and SJNFs, pure states of n qubits are partitioned into 12 groups or less and 34 families or less under SLOCC, respectively.

### Classification of general n-qubit states under stochastic local operations and classical communication in terms of the rank of coefficient matrix.

- PhysicsPhysical review letters
- 2012

The entanglement classification under stochastic local operations and classical communication (SLOCC) for general n-qubit states is solved and it is revealed that all the Dicke states |ℓ,n> with ℓ=1,…,[n/2] are inequivalent under SLOCC.

### Entanglement in the symmetric sector of n qubits.

- PhysicsPhysical review letters
- 2011

The manifold of maximally entangled 3 qubit state, both in the symmetric and generic case, is analyzed and a cross ratio of related Möbius transformations are shown to play a central role.

### Classification of multipartite entanglement via negativity fonts

- Physics
- 2012

Partial transposition of state operator is a well known tool to detect quantum correlations between two parts of a composite system. In this letter, the global partial transpose (GPT) is linked to…