# Capacity of a quantum memory channel correlated by matrix product states

## TL;DR

This paper investigates the quantum capacity of a memory channel influenced by correlated spin chain environments modeled as matrix product states, providing exact formulas for specific models like AKLT and Majumdar-Ghosh.

## Contribution

It derives exact formulas for the quantum capacity of a correlated quantum memory channel using matrix product states, including specific models like AKLT and Majumdar-Ghosh.

## Key findings

- Capacity formulas are analytic over parameter ranges.
- Exact capacity results for AKLT and Majumdar-Ghosh models.
- Demonstrates the impact of environment correlations on quantum channel capacity.

## Abstract

We study the capacity of a quantum channel where channel acts like controlled phase gate with the control being provided by a one-dimensional quantum spin chain environment. Due to the correlations in the spin chain, we get a quantum channel with memory. We derive formulas for the quantum capacity of this channel when the spin state is a matrix product state. Particularly, we derive exact formulas for the capacity of the quantum memory channel when the environment state is the ground state of the AKLT model and the Majumdar-Ghosh model. We find that the behavior of the capacity for the range of the parameters is analytic.