Irreversibility of Entanglement Concentration for Pure State

TL;DR

This paper proves that entanglement concentration for pure states cannot be perfectly reversed even asymptotically, and analyzes the asymptotic loss in entanglement during the process, highlighting fundamental irreversibility.

Contribution

It demonstrates the fundamental irreversibility of entanglement concentration for pure states in the asymptotic limit, contrary to previous assumptions of reversibility.

Findings

Reversibility of entanglement concentration is impossible asymptotically.

Quantitative evaluation of entanglement loss during concentration.

Insights into entanglement compression in distributed quantum systems.

Abstract

For a pure state $\psi$ on a composite system $\mathcal{H}_A\otimes\mathcal{H}_B$, both the entanglement cost $E_C(\psi)$ and the distillable entanglement $E_D(\psi)$ coincide with the von Neumann entropy $H(\mathrm{Tr}_{B}\psi)$. Therefore, the entanglement concentration from the multiple state $\psi^{\otimes n}$ of a pure state $\psi$ to the multiple state $\Phi^{\otimes L_n}$ of the EPR state $\Phi$ seems to be able to be reversibly performed with an asymptotically infinitesimal error when the rate ${L_n}/{n}$ goes to $H(\mathrm{Tr}_{B}\psi)$. In this paper, we show that it is impossible to reversibly perform the entanglement concentration for a multiple pure state even in asymptotic situation. In addition, in the case when we recover the multiple state $\psi^{\otimes M_n}$ after the concentration for $\psi^{\otimes n}$, we evaluate the asymptotic behavior of the loss number $n-M_n$ of $\psi$. This evaluation is thought to be closely related to the entanglement compression in distant parties.