# Quantum Information Capsule in Multiple-Qudit Systems and Continuous-Variable Systems

## TL;DR

This paper extends the concept of quantum information capsules (QICs) from qubit systems to multiple-qudit and continuous-variable systems, providing analytical constructions and analyzing information dynamics in these broader contexts.

## Contribution

It formulates and proves the existence of QICs in multi-qudit and CV systems, including explicit constructions for Gaussian states and analysis of information diffusion.

## Key findings

- QICs can be constructed for general write operations in multi-qudit systems.
- Explicit QIC construction for Gaussian states under shift operations.
- Demonstration of information diffusion in CV system dynamics.

## Abstract

Quantum correlations in an entangled many-body system are capable of storing information. Even when the information is injected by a local unitary operation to the system, the entanglement delocalizes it. In a recent study on multiple-qubit systems, it is shown that a virtual qubit defined in the correlation space plays a role of perfect storage of delocalized information, which is called a quantum information capsule (QIC). In order to enhance the capacity of quantum information storage, it is crucial to formulate the cases for multiple-qudit systems and continuous-variable (CV) systems. We analytically prove that it is possible to construct a QIC for general write operations of the systems. It turns out that the extension to quantum field theory is achievable. For Gaussian states, we explicitly construct a QIC for shift write operations. We analyze the time-evolution of QIC in a CV system to demonstrate the diffusion of information in entangled pure states.