One-Way Deficit and Holevo Quantity of Generalized $n$-qubit Werner State

Abstract: Originated from the work extraction in quantum systems coupled to a heat bath, quantum deficit is a kind of significant quantum correlations like quantum entanglement. It links quantum thermodynamics with quantum information. We analytically calculate the one-way deficit of the generalized $n$-qubit Werner state. We find that the one-way deficit increases as the mixing probability $p$ increases for any $n$. For fixed $p$, we observe that the one-way deficit increases as $n$ increases. For any $n$, the maximum of one-way deficit is attained at $p=1$. Furthermore, for large $n$ ($2^n \rightarrow \infty$), we prove that the curve of one-way deficit versus $p$ approaches to a straight line with slope $1$. We also calculate the Holevo quantity for the generalized $n$-qubit Werner state, and show that it is zero.