# Non-negativity of conditional von Neumann entropy and global unitary operations

## TL;DR

This paper investigates how global unitary operations affect the non-negativity of conditional von Neumann entropy in quantum states, characterizing states that preserve or become negative under such operations, with implications for quantum information tasks.

## Contribution

It introduces the class ACVENN of states with non-negative conditional entropy preserved under global unitaries and characterizes these states for 2x2 systems, also exploring their detection and applications.

## Key findings

- ACVENN states form a convex, compact set.
- Hermitian witness operators can detect states with negative conditional entropy after unitaries.
- Connections to absolute separable and local states are discussed.

## Abstract

Conditional von Neumann entropy is an intriguing concept in quantum information theory. In the present work, we examine the effect of global unitary operations on the conditional entropy of the system. We start with the set containing states with non-negative conditional entropy and find that some states preserve the non-negativity under unitary operations on the composite system. We call this class of states as Absolute Conditional von Neumann entropy Non Negative class (\textbf{ACVENN}). We are able to characterize such states for $2\otimes 2$ dimensional systems. On a different perspective the characterization accentuates the detection of states whose conditional entropy becomes negative after the global unitary action. Interestingly, we are able to show that this \textbf{ACVENN} class of states forms a set which is convex and compact. This feature enables for the existence of hermitian witness operators the measurement of which could distinguish unknown states which will have negative conditional entropy after the global unitary operation. This has immediate application in super dense coding and state merging as negativity of conditional entropy plays a key role in both these information processing tasks. Some illustrations are also provided to probe the connection of such states with Absolute separable (AS) states and Absolute local (AL) states.