# Separability criterion and inseparable mixed states with positive partial transposition

@article{Horodecki1997SeparabilityCA, title={Separability criterion and inseparable mixed states with positive partial transposition}, author={Paweł Horodecki}, journal={Physics Letters A}, year={1997}, volume={232}, pages={333-339} }

## 711 Citations

### Separability of Mixed Quantum States: Linear Contractions and Permutation Criteria

- MathematicsOpen Syst. Inf. Dyn.
- 2006

This work introduces a family of so called permutation separability criteria for multipartite states, and finds that, somewhat suprisingly, partial realigment (unlike partial transposition) can detect genuinely tri-parite entanglement.

### Is absolute separability determined by the partial transpose?

- MathematicsQuantum Inf. Comput.
- 2015

This work develops an easy-to-use method for showing that an entanglement witness or positive map is unable to detect Entanglement in any such state, and applies this method to many well-known separability criteria.

### On separable decompositions of quantum states with strong positive partial transposes

- Mathematics
- 2013

We analyze a class of positive partial transpose (PPT) states such that the positivity of its partial transposition is recognized with respect to the canonical factorization of the original density…

### Separability Criterion for Arbitrary Multipartite Pure State Based on the Rank of Reduced Density Matrix

- Computer Science
- 2016

It is proved that the rank of reduced density matrices of a multipartite state is closely related to entanglement and can be used to characterizeEntanglement.

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

- Physics
- 2002

### Separability criteria based on the bloch representation of density matrices

- MathematicsQuantum Inf. Comput.
- 2007

The necessary condition is proved to be strong enough to detect bound entangled states and the proofs of the sufficient conditions are constructive, thus providing decompositions in pure product states for the states that satisfy them.

### Separability for Positive Operators on Tensor Product of Hilbert Spaces

- MathematicsActa Mathematica Sinica, English Series
- 2021

The separability and the entanglement (that is, inseparability) of the composite quantum states play important roles in quantum information theory. Mathematically, a quantum state is a trace-class…

### Product Vectors in the Ranges of Multi-Partite States with Positive Partial Transposes and Permanents of Matrices

- Mathematics
- 2015

In this paper, we consider a system of homogeneous algebraic equations in complex variables and their conjugates, which arise naturally from the range criterion for separability of PPT states. We…

### On the Separability Criterion of Bipartite States with Certain Non-Hermitian Operators

- Mathematics
- 2015

We construct a density matrix whose elements are written in terms of expectation values of non-Hermitian operators and their products for arbitrary dimensional bipartite states. We then show that any…

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