相关论文: Another Short and Elementary Proof of Strong Subad…
The joint convexity of the map $(X,A) \mapsto X^* A^{-1} X$, an integral representation of operator convex functions, and an observation of Ando are used to obtain a simple proof of both the joint convexity of relative entropy and a trace…
Arguably the deepest fact known about the von Neumann entropy, the strong subadditivity inequality is a potent hammer in the quantum information theorist's toolkit. This short tutorial describes a simple proof of strong subadditivity due to…
We derive the monotonicity of the quantum relative entropy by an elementary operational argument based on Stein's lemma in quantum hypothesis testing. For the latter we present an elementary and short proof that requires the law of large…
This paper presents self-contained proofs of the strong subadditivity inequality for quantum entropy and some related inequalities for the quantum relative entropy, most notably its convexity and its monotonicity under stochastic maps.…
The familiar second derivative test for convexity, combined with resolvent calculus, is shown to yield a useful tool for the study of convex matrix-valued functions. We demonstrate the applicability of this approach on a number of theorems…
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…
We introduce quantum weighted entropy in analogy to an earlier notion of (classical) weighted entropy and derive many of its properties. These include the subadditivity, concavity and strong subadditivity property of quantum weighted…
We give a simple proof of a strengthened version of a theorem of Lieb that played a key role in the proof of strong subadditivity of the quantum entropy.
The goal of this note is to show that Hastings' counterexample to the additivity of minimal output von Neumann entropy can be readily deduced from a sharp version of Dvoretzky's theorem on almost spherical sections of convex bodies.
When a quantum system is divided into subsystems, their entanglement entropies are subject to an inequality known as "strong subadditivity". For a field theory this inequality can be stated as follows: given any two regions of space $A$ and…
The strong subadditivity of entropy plays a key role in several areas of physics and mathematics. It states that the entropy S[\rho]= - Tr (\rho \ln \rho) of a density matrix \rho_{123} on the product of three Hilbert spaces satisfies…
Some of the important inequalities associated with quantum entropy are immediate algebraic consequences of the Hansen-Pedersen-Jensen inequality. A general argument is given using matrix perspectives of operator convex functions. A matrix…
Many trace inequalities can be expressed either as concavity/convexity theorems or as monotonicity theorems. A classic example is the joint convexity of the quantum relative entropy which is equivalent to the Data Processing Inequality. The…
We give an elementary proof of an inequality of Lin, Kim and Hsieh that implies strong subadditivity of the non Neumann entropy.
Integral representations of quantum relative entropy, and of the directional second and higher order derivatives of von Neumann entropy, are established, and used to give simple proofs of fundamental, known data processing inequalities: the…
We prove an entropic uncertainty relation for two quantum channels, extending the work of Frank and Lieb for quantum measurements. This is obtained via a generalized strong super-additivity (SSA) of quantum entropy. Motivated by Petz's…
We exhibit infinitely many new, constrained inequalities for the von Neumann entropy, and show that they are independent of each other and the known inequalities obeyed by the von Neumann entropy (basically strong subadditivity). The new…
We give an explicit characterisation of the quantum states which saturate the strong subadditivity inequality for the von Neumann entropy. By combining a result of Petz characterising the equality case for the monotonicity of relative…
We study the interplay between additivity (as in the Cauchy functional equation), subadditivity and linearity. We obtain automatic continuity results in which additive or subadditive functions, under minimal regularity conditions, are…
Fundamental properties for the Tsallis relative entropy in both classical and quantum systems are studied. As one of our main results, we give the parametric extension of the trace inequality between the quantum relative entropy and the…