Strong Converse Bounds for Compression of Mixed States

• URL: http://arxiv.org/abs/2206.09415v1
• Date: Sun, 19 Jun 2022 14:38:37 GMT
• Title: Strong Converse Bounds for Compression of Mixed States
• Authors: Zahra Baghali Khanian
• Abstract summary: We consider many copies of a general mixed-state source $rhoAR$ shared between an encoder and an inaccessible reference system $R$. For a bipartite state $rhoAR$, we define a new quantity $E_alpha,p(A:R)_rho$. For any rate below the regularization $lim_alpha to 1+E_alpha,pinfty(A:R)_rho$, the fidelity for the visible compression of ensembles of mixed states exponentially
• Score: 3.04585143845864
• License: http://arxiv.org/licenses/nonexclusive-distrib/1.0/
• Abstract: We consider many copies of a general mixed-state source $\rho^{AR}$ shared between an encoder and an inaccessible reference system $R$. We obtain a strong converse bound for the compression of this source. This immediately implies a strong converse for the blind compression of ensembles of mixed states since this is a special case of the general mixed-state source $\rho^{AR}$. Moreover, we consider the visible compression of ensembles of mixed states. For a bipartite state $\rho^{AR}$, we define a new quantity $E_{\alpha,p}(A:R)_{\rho}$ for $\alpha \in (0,1)\cup (1,\infty)$ as the $\alpha$-R\'enyi generalization of the entanglement of purification $E_{p}(A:R)_{\rho}$. For $\alpha=1$, we define $E_{1,p}(A:R)_{\rho}:=E_{p}(A:R)_{\rho}$. We show that for any rate below the regularization $\lim_{\alpha \to 1^+}E_{\alpha,p}^{\infty}(A:R)_{\rho}:=\lim_{\alpha \to 1^+} \lim_{n \to \infty} \frac{E_{\alpha,p}(A^n:R^n)_{\rho^{\otimes n}}}{n}$ the fidelity for the visible compression of ensembles of mixed states exponentially converges to zero. We conclude that if this regularized quantity is continuous with respect to $\alpha$, namely, if $\lim_{\alpha \to 1^+}E_{\alpha,p}^{\infty}(A:R)_{\rho}=E_{p}^{\infty}(A:R)_{\rho}$, then the strong converse holds for the visible compression of ensembles of mixed states.

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