A study of two-qubit density matrices with fermionic purifications

TL;DR

This paper analyzes two-qubit density matrices derived from fermionic systems, providing explicit formulas for entanglement measures, exploring their geometry, and confirming their compliance with the generalized Coffman-Kundu-Wootters formula.

Contribution

It introduces a detailed analysis of two-qubit density matrices from fermionic systems, including explicit formulas for entanglement measures and geometric properties.

Findings

Closed-form expressions for concurrence and negativity.

Verification of the generalized Coffman-Kundu-Wootters formula.

Explicit Bures metric for the density matrices.

Abstract

We study 12 parameter families of two qubit density matrices, arising from a special class of two-fermion systems with four single particle states or alternatively from a four-qubit state with amplitudes arranged in an antisymmetric matrix. We calculate the Wooters concurrences and the negativities in a closed form and study their behavior. We use these results to show that the relevant entanglement measures satisfy the generalized Coffman-Kundu-Wootters formula of distributed entanglement. An explicit formula for the residual tangle is also given. The geometry of such density matrices is elaborated in some detail. In particular an explicit form for the Bures metric is given.