# A note on perfect quantum state transfers on trees

## TL;DR

This paper proves that, aside from the simple paths P2 and P3, no other tree structures support perfect quantum state transfers, clarifying the limitations of quantum communication on tree graphs.

## Contribution

The paper establishes a negative result showing that only P2 and P3 trees admit perfect quantum state transfers, resolving a previously open question.

## Key findings

- Only P2 and P3 trees admit perfect state transfers.
- Other trees do not support perfect quantum state transfers.
- The result narrows the class of graphs suitable for quantum communication.

## Abstract

It has been asked whether there are trees other than $P_2$ and $P_3$ which can admit perfect state transfers. In this note we show that the answer is negative.