A note on extremal states of composite quantum systems with fixed marginals

TL;DR

This paper constructs a specific extremal mixed and entangled state in a 6-dimensional quantum system with fixed normalized identity marginals, highlighting unique properties of quantum state extremality.

Contribution

It introduces a new extremal state in a bipartite quantum system with fixed marginals, demonstrating its mixed and entangled nature.

Findings

Constructed an extremal state in M_2 ⊗ M_3 with fixed marginals.

Proved the state is both mixed and entangled.

Provides insight into the structure of extremal quantum states with fixed marginals.

Abstract

An extremal element of the convex set of composite quantum states in $M_2\otimes M_3$, whose marginals are all normalised identities has been constructed. It is found to be a mixed state and is entangled as well.