Tradeoff Between Multiple-copy Transformation and Entanglement Catalysis with Limited Resources

Yuan Feng, Rui Duan

Mingsheng Ying, Yuan Feng, Rui Duan

Runyao Duan, Yuan Feng, Xin Li +1 more

We demonstrate that multiple copies of a bipartite entangled pure state may serve as a catalyst for certain entanglement transformations while a single copy cannot. Such a state is termed a ``multiple-copy catalyst'' for the transformations. A trade-off between the number of copies of source state and that of the catalyst is also observed. These results can be generalized to probabilistic entanglement transformations directly.

Ray Ganardi

Entanglement is a key quantum resource in various quantum protocols, with a rich set of laws governing its manipulation. In this context, catalysis refers to the possibility of an auxiliary state that enables a previously forbidden manipulation, while being completely returned at the end. While the catalytic setting has been thoroughly examined in the single-copy regime, much less is known in the asymptotically many copy regime. In this work, we focus on the entanglement cost of preparing asymptotically many copies of a given state exactly. We show that catalysis can significantly lower the exact entanglement cost by constructing an explicit catalytic protocol. Additionally, these findings generalize readily to other resource theories, showing a general catalytic advantage in the resource dilution task.

Runyao Duan, Yuan Feng, Xin Li +1 more

We prove that any multiple-copy entanglement transformation [S. Bandyopadhyay, V. Roychowdhury, and U. Sen, Phys. Rev. A 65, 052315 (2002)] can be implemented by a suitable entanglement-assisted local transformation [D. Jonathan and M. B. Plenio, Phys. Rev. Lett. 83, 3566 (1999)]. Furthermore, we show that the combination of multiple-copy entanglement transformation and the entanglement-assisted one is still equivalent to the pure entanglement-assisted one. The mathematical structure of multiple-copy entanglement transformations then is carefully investigated. Many interesting properties of multiple-copy entanglement transformations are presented, which exactly coincide with those satisfied by the entanglement-assisted ones. Most interestingly, we show that an arbitrarily large number of copies of state should be considered in multiple-copy entanglement transformations.

Zheng-Wei Zhou, Guang‐Can Guo