Geometry of two-qubit states with negative conditional entropy

TL;DR

This paper explores the geometric structure of two-qubit states with negative conditional entropy, revealing their relation to entanglement and nonlocality, and analyzing the effectiveness of the Cerf-Adami operator as an entanglement witness.

Contribution

It characterizes the region of negative conditional entropy in the state space and compares the Cerf-Adami operator's effectiveness with the Peres-Horodecki criterion.

Findings

Negative conditional entropy implies entanglement and nonlocality within the tetrahedron.

The Cerf-Adami operator acts as an entanglement witness equivalent to the Peres-Horodecki criterion inside the tetrahedron.

Outside the tetrahedron, the equivalence between the Cerf-Adami operator and entanglement detection does not hold.

Abstract

We review the geometric features of negative conditional entropy and the properties of the conditional amplitude operator proposed by Cerf and Adami for two qubit states in comparison with entanglement and nonlocality of the states. We identify the region of negative conditional entropy in the tetrahedron of locally maximally mixed two-qubit states. Within this set of states, negative conditional entropy implies nonlocality and entanglement, but not vice versa, and we show that the Cerf-Adami conditional amplitude operator provides an entanglement witness equivalent to the Peres-Horodecki criterion. Outside of the tetrahedron this equivalence is generally not true.