# Effects of quantum noises and noisy quantum operations on entanglement and special dense coding

## TL;DR

This paper investigates how quantum noises and noisy operations can cause entanglement sudden death and reduce the effectiveness of special dense coding in quantum communication, highlighting practical challenges.

## Contribution

It demonstrates the effects of non-commuting quantum noises on entanglement and dense coding, revealing new insights into noise-induced failures in quantum communication protocols.

## Key findings

- Quantum noises can cause entanglement sudden death (ESD).
- Noisy quantum operations can impair dense coding capacity.
- Entanglement may persist without enabling effective information transfer.

## Abstract

We show how, in the presence of quantum noises generated by non-commuting Lindblad operators, a maximally entangled Bell state may suffer entanglement sudden death (ESD). Similarly, ESD may occur when a Bell state is under the action of a quantum operation generated by a Hamiltonian in the presence of a quantum noise, provided that the Hamiltonian does not commute with the corresponding Lindblad operator. Practically this means noisy quantum operations could cause ESD during the encoding process in quantum communication protocols like special dense coding ($\cal S$). Next, we show how in the presence of quantum noises which cause ESD, a Bell state may lose its capacity for $\cal S$ before ESD occurs. Finally, we show that a Bell state may indeed fail to yield information transfer better than classically possible when the encoding operations of $\cal S$ are noisy, even though entanglement is not totally destroyed in the process.