# Entropy Production in Quantum Is Different

## TL;DR

This paper reviews recent advances in understanding entropy evolution in quantum information theory, highlighting the novel 'multiple parallel world' formalism that introduces a form of 'time' and reveals new types of correlations.

## Contribution

It introduces the 'multiple parallel world' formalism for entropy evaluation, connecting quantum information theory with quantum physics and revealing new correlation phenomena.

## Key findings

- Entropy can flow internally between subsystems without physical correlations.
- The 'multiple parallel world' formalism enables the study of entropy evolution over time.
- New types of correlations arise due to nonlinear dependence of entropy on the density matrix.

## Abstract

Currently, 'time' does not play any essential role in quantum information theory. In this sense, quantum information theory is underdeveloped similarly to how quantum physics was underdeveloped before Erwin Schrodinger introduced his famous equation for the evolution of a quantum wave function. In this review article, we cope with the problem of time for one of the central quantities in quantum information theory: entropy. Recently, a replica trick formalism, the so-called 'multiple parallel world' formalism, has been proposed that revolutionizes entropy evaluation for quantum systems. This formalism is one of the first attempts to introduce 'time evolution' in quantum information theory. With the total entropy being conserved in a closed system, entropy can flow internally between subsystems; however, we show that this flow is not limited only to physical correlations as the literature suggest. The nonlinear dependence of entropy on the density matrix introduces new types of correlations with no analogue in physical quantities. Evolving a number of replicas simultaneously makes it possible for them to exchange particles between different replicas. We will summarize some of the recent news about entropy in some example quantum devices. Moreover, we take a quick look at a new correspondence that was recently proposed that provides an interesting link between quantum information theory and quantum physics. The mere existence of such a correspondence allows for exploring new physical phenomena as the result of controlling entanglement in a quantum device.