Fidelity Tradeoff in Estimation of Partial Entanglement State with Local Operation and Classic Communication

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 G and the concomitant disturbance F 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 F-G 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.