Entanglement transformation between sets of bipartite pure quantum states using local operations

@article{Chau2012EntanglementTB,
  title={Entanglement transformation between sets of bipartite pure quantum states using local operations},
  author={Hoi Fung Chau and Chi-Hang Fred Fung and Chi-Kwong Li and Edward Poon and Nung-Sing Sze},
  journal={Journal of Mathematical Physics},
  year={2012},
  volume={53},
  pages={122201-122201}
}
Alice and Bob are given an unknown initial state chosen from a set of pure quantum states. Their task is to transform the initial state to a corresponding final pure state using local operations only. We prove necessary and sufficient conditions on the existence of such a transformation. We also provide efficient algorithms that can quickly rule out the possibility of transforming a set of initial states to a set of final states. 

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References

SHOWING 1-10 OF 26 REFERENCES
Conditions for a Class of Entanglement Transformations
Suppose Alice and Bob jointly possess a pure state, |ψ〉. Using local operations on their respective systems and classical communication it may be possible for Alice and Bob to transform |ψ〉 into
Separable operations on pure states
We show that the possible ensembles produced when a separable operation acts on a single pure bipartite entangled state are completely characterized by a majorization condition, a collection of
MINIMAL CONDITIONS FOR LOCAL PURE-STATE ENTANGLEMENT MANIPULATION
We find a minimal set of necessary and sufficient conditions for the existence of a local procedure that converts a finite pure state into one of a set of possible final states. This result provides
Quantum operations, state transformations and probabilities
In quantum operations, probabilities characterize both the degree of the success of a state transformation and, as density operator eigenvalues, the degree of mixedness of the final state. We give a
Physical transformations between quantum states
Given two sets of quantum states {A1, …, Ak} and {B1, …, Bk}, represented as sets as density matrices, necessary and sufficient conditions are obtained for the existence of a physical transformation
ON THE EXISTENCE OF PHYSICAL TRANSFORMATIONS BETWEEN SETS OF QUANTUM STATES
Let A={ρ1,…,ρn} be a given set of quantum states. We consider the problem of finding necessary and sufficient conditions on another set B={σ1,…,σn} that guarantee the existence of a physical
Entanglement transformation with no classical communication
We present an optimal scheme to realize the transformations between single copies of two bipartite entangled states without classical communication between the sharing parties. The scheme achieves
Concentrating entanglement by local actions: Beyond mean values
TLDR
It is proved that one-way communications is necessary and sufficient for entanglement manipulations of a pure bipartite state and the supremum probability of obtaining a maximally entangled state (of any dimension) from an arbitrary state is determined.
Concentrating partial entanglement by local operations.
TLDR
Any pure or mixed entangled state of two systems can be produced by two classically communicating separated observers, drawing on a supply of singlets as their sole source of entanglement.
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