# Bounds on bipartite entanglement from fixed marginals

## TL;DR

This paper investigates the limits of bipartite entanglement given fixed marginal states, proposing candidate states that are extremal and quasidistillable, supported by numerical evidence.

## Contribution

It introduces a family of candidate maximally entangled states for two qudits with fixed marginals, extending the two-qubit case and analyzing their properties.

## Key findings

- Proposed candidate states are extremal in the set with fixed marginals.
- Such states are always quasidistillable.
- Numerical analysis supports the theoretical observations.

## Abstract

We discuss the problem of characterizing upper bounds on entanglement in a bipartite quantum system when only the reduced density matrices (marginals) are known. In particular, starting from the known two-qubit case, we propose a family of candidates for maximally entangled mixed states with respect to fixed marginals for two qudits. Interestingly, it turns out such states are always quasidistillable. Moreover, they are extremal in the convex set of two qudit states with fixed marginals. Our observations are supported by numerical analysis.