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arXiv:1208.1068 · Journal of Mathematical Physics

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

H. F. Chau, Chi‐Hang Fred Fung, Chi-Kwong Li, Edward Poon, Nung-Sing Sze

Published Nov 8, 2012• 5 citations
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Abstract

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.

DOI
10.1063/1.4765298

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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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The quantum entanglement is the necessary resource,which could realize some quantum tasks.It is very important to study the algorithm for the entanglement transformation between the quantum states determinately or probability.An algorithm first is presented that transforms one pure bipartite quantum state into a mixed bipartite by Local Operations and Classical Communication(LOCC),this algorithm is much simpler than the original algorithm.The algorithm for the transformation between two pure bipartite states with catalysis by LOCC is then discussed.
We derive a sufficient condition for a set of pure states, each entangled in two remote NNN-dimensional systems, to be transformable to kkk-dimensional-subspace equivalent entangled states (k≤Nk\leq Nk≤N) by same local operations and classical communication. If k=Nk=Nk=N, the condition is also necessary. This condition reveals the function of the relative marginal density operators of the entangled states in the entanglement manipulation without sufficient information of the initial states.