Entanglement and swap of quantum states in two qubits

TL;DR

This paper investigates the probabilistic exchange of quantum subsystems between two distant parties using LOCC, revealing how entanglement influences the success probability and identifying states with minimal swap probability.

Contribution

It analyzes the relationship between entanglement and the optimal probability of swapping quantum states under PPT operations, introducing a class of states with minimal swap success probability.

Findings

Optimal swap probability is linked to entanglement levels.

Identifies states with the lowest swap success probability.

Numerical analysis of two-qubit states.

Abstract

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 local operations 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 swap operator) is impossible deterministically, but becomes possible probabilistically. In this paper, we study how the optimal probability is related to the amount of entanglement in the framework of positive partial transposed (PPT) operations, and numerically show a remarkable class of states whose probability is the smallest among every state in two quantum bits.