# Exchange of quantum states between coupled oscillators

## TL;DR

This paper investigates the conditions under which quantum states can be exchanged between two coupled harmonic oscillators, identifying specific initial states and parameter relations necessary for complete state transfer.

## Contribution

It provides a detailed analysis of the specific initial states and parameter conditions required for perfect quantum state exchange in coupled oscillators.

## Key findings

- Exact exchange occurs only for states of the form C0|0>+Cn|N>
- Complete exchange depends on the relation between coupling and oscillator frequencies
- The study includes qubit components |0> and |1> as special cases

## Abstract

Exchange of quantum states between two interacting harmonic oscillator along their evolution time is discussed. It is analyzed the conditions for such exchange starting from a generic initial state and demonstrating that the effect occurs exactly only for the particular states C0|0>+Cn|N>, which includes the interesting qubits components |0>,|1>. It is also determined the relation between the coupling constant and characteristic frequencies of the oscillators to have the complete exchange.