Related papers: Relative Entropy for Quantum Channels
We obtained the estimation from below for the output entropy of a tensor product of the quantum phase-damping channel with an arbitrary channel. It is shown that from this estimation immediately follows that the strong superadditivity of…
Quantum channel, as the information transmitter, is an indispensable tool in quantum information theory. In this paper, we study a class of special quantum channels named the mixed-permutation channels. The properties of these channels are…
We revisit the monotonicity of relative entropy under the action of quantum channels, a foundational result in quantum information theory. Among the several available proofs, we focus on those by Petz and Uhlmann, which we reformulate…
We extend the definition of the conditional min-entropy from bipartite quantum states to bipartite quantum channels. We show that many of the properties of the conditional min-entropy carry over to the extended version, including an…
We prove the quantum conditional Entropy Power Inequality for quantum additive noise channels. This inequality lower bounds the quantum conditional entropy of the output of an additive noise channel in terms of the quantum conditional…
We describe analytical properties of the average output entropy of a quantum channel as a function of a pair (channel, input ensemble). In particular, tight semicontinuity bounds for this function with the rank/energy constraints are…
We give a direct proof of the additivity of the minimum output entropy of a particular quantum channel which breaks the multiplicativity conjecture. This yields additivity of the classical capacity of this channel, a result obtained by a…
The R\'enyi and Shannon entropies are information-theoretic measures which have enabled to formulate the position-momentum uncertainty principle in a much more adequate and stringent way than the (variance-based) Heisenberg-like relation.…
Loop quantum gravity can account for the Bekenstein-Hawking entropy of a black hole provided a free parameter is chosen appropriately. Recently, it was proposed that a new choice of the Immirzi parameter could predict both black hole…
Within the unified framework of exploiting the relative entropy as a distance measure of quantum correlations, we make explicit the hierarchical structure of quantum coherence, quantum discord and quantum entanglement in multipartite…
We study quantum measurement retrodiction using the principle of minimum change. For quantum-to-classical measurement channels, we show that all standard quantum divergences select the same retrodictive update, yielding a unique and…
The von Neumann entropy and the subentropy of a mixed quantum state are upper and lower bounds, respectively, on the accessible information of any ensemble consistent with the given mixed state. Here we define and investigate a set of…
We consider a quasi-classical version of the Alicki-Fannes-Winter technique widely used for quantitative continuity analysis of characteristics of quantum systems and channels. This version allows us to obtain continuity bounds under…
We introduce an axiomatic approach to entropies and relative entropies that relies only on minimal information-theoretic axioms, namely monotonicity under mixing and data-processing as well as additivity for product distributions. We find…
Characterizing complexity and criticality in quantum systems requires diagnostics that are both computationally tractable and physically insightful. We apply a measure of quantum state complexity for n-qubit systems, defined as the…
By carrying out appropriate continuous quantum measurements with a family of projection operators, a unitary channel can be approximated in an arbitrary precision in the trace norm sense. In particular, the quantum Zeno effect is described…
We show that the quantum $\alpha$-relative entropies with parameter $\alpha\in (0,1)$ can be represented as generalized cutoff rates in the sense of [I. Csiszar, IEEE Trans. Inf. Theory 41, 26-34, (1995)], which provides a direct…
We propose to quantify the entanglement of pure states of $N \times N$ bipartite quantum system by defining its Husimi distribution with respect to $SU(N)\times SU(N)$ coherent states. The Wehrl entropy is minimal if and only if the pure…
For a $C^{r}$ $(r>1)$ diffeomorphism on a compact manifold that admits a dominated splitting, this paper establishes the upper semi-continuity of the entropy map. More precisely, this paper establishes the upper semi-continuity of the…
We consider a quantum quasi-relative entropy $S_f^K$ for an operator $K$ and an operator convex function $f$. We show how to obtain the error bounds for the monotonicity and joint convexity inequalities from the recent results for the…