One-way deficit of SU(2) invariant states

TL;DR

This paper analytically computes the one-way quantum deficit for SU(2) invariant states involving spin systems, revealing its relation to quantum discord and entanglement, and highlighting differences based on the spin quantum number.

Contribution

It provides the first analytical calculation of the one-way deficit for SU(2) invariant states and compares it with quantum discord and entanglement.

Findings

One-way deficit equals quantum discord for half-integer spins.

One-way deficit exceeds quantum discord for integer spins.

One-way deficit remains large even as entanglement vanishes.

Abstract

We calculate analytically the one-way deficit for systems consisting spin-$j$ and spin-${1}{2}$ subsystems with SU(2) symmetry. Comparing our results with the quantum discord of SU(2) invariant states, we show that the one-way deficit is equal to the quantum discord for half-integer $j$, and is larger than the quantum discord for integer $j$. Moreover, we also compare the one-way deficit with entanglement of formation. The quantum entanglement tends to zero as $j$ increases, while the one-way deficit can remain significantly large.