Stability theorem of depolarizing channels for the minimal output quantum R\'enyi entropies

TL;DR

This paper extends the stability theorem of depolarizing channels to output quantum p-Rényi entropies for p ≥ 2 or p=1, enabling protocols to verify quantum state preparations based on entropy estimates.

Contribution

It generalizes the stability theorem to a broader range of quantum Rényi entropies, providing a new method for verifying quantum state preparations.

Findings

Stability theorem holds for p ≥ 2 and p=1 cases.

Protocol enables Bob to verify Alice’s state preparation using entropy estimates.

Extension of known stability results to new entropy measures.

Abstract

We show that the stability theorem of the depolarizing channel holds for the output quantum $p$-R\'enyi entropy for $p \ge 2$ or $p=1$, which is an extension of the well known case $p=2$. As an application, we present a protocol in which Bob determines whether Alice prepares a pure quantum state close to a product state. In the protocol, Alice transmits to Bob multiple copies of a pure state through a depolarizing channel, and Bob estimates its output quantum $p$-R\'enyi entropy. By using our stability theorem, we show that Bob can determine whether her preparation is appropriate.