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Suppose that two distant parties Alice and Bob share an entangled state$\rho_{AB}$, and they want to exchange the subsystems of $\rho_{AB}$ by localoperations and classical communication (LOCC). In general, this LOCC task (i.e.the LOCC transformation of $\rho_{AB} \to V\rho_{AB} V$ with $V$ being a swapoperator) is impossible deterministically, but becomes possibleprobabilistically. In this paper, we study how the optimal probability isrelated to the amount of entanglement in the framework of positive partialtransposed (PPT) operations, and numerically show a remarkable class of stateswhose probability is the smallest among every state in two quantum bits.

Entanglement and swap of quantum states in two qubits