Fidelity Tradeoff in Estimation of Partial Entanglement State with Local Operation and Classic Communication**Supported by the National Natural Science Foundation of China under Grant Nos U1304613, 11204197, 11204379 and 11074244, the National Basic Research Program of China under Grant No 2011CBA00200, and the Doctor Science Research Foundation of the Ministry of Education of China under Grant No 20113402110059.

Abstract

In quantum mechanics, there is no measurement process that could gain some information of an unknown quantum state without causing any disturbance. A tradeoff bound between the amount of information gain and the concomitant disturbance in the measurement process of a bipartite entangled state is actually ingrained. Such a bound is fundamental and closely connected with the entangled degree b. In this work, the bound for estimation of a partial entangled state with a local strategy is investigated. It is shown that, with local operation with classical communication, a monotonic change in the picture will be spotted. This is due to the fact that the partial entanglement gradually becomes two individual qubits and, consequently, the optimal operation boils down to local operations. A quantum circuit which achieves the optimal tradeoff is also obtained.