# Entanglement in block-scalable and block-scaled states

## TL;DR

This paper investigates how entanglement behaves in special initial states of spin chains that produce scaled versions of themselves at the receiver, revealing that entanglement generally decreases after scaling and is affected by state perturbations.

## Contribution

It introduces the concept of block-scalable states and analyzes their entanglement properties compared to block-scaled states, including effects of perturbations and chain length.

## Key findings

- Entanglement in block-scaled states is usually less than in block-scalable states.
- Perturbations tend to increase entanglement in initial states and decrease it in scaled states.
- Chain length influences entanglement dynamics, demonstrated with chains of 6 and 42 spins.

## Abstract

There is a special class of so-called block-scalable initial states of the sender whose transfer to the receiver through the spin chain results in multiplying {their} MQ-coherence matrices by scalar factors (block-scaled receiver's states). We study the entanglement in block-scalable and block-scaled states and show that, generically, the entanglement in block scaled states is less than the entanglement in the corresponding block-scalable states, although the balance between these entanglements depends on particular values of parameters characterizing these states. Using the perturbations of the sender's block-scalable initial states we show that generically the entanglement in the block-scalable states is bigger, while the entanglement in the block-scaled states is less than the entanglements in the appropriate states from their neighborhoods. A short chain of 6 and a long chain of 42 spin-1/2 particles are considered as examples.}