A note on quantum entropy inequalities and channel capacities

A note on "Loophole-free Bell test for continuous variables via wave and particle correlations (Phys. Rev. Lett. 105, 170404 (2010))"

The inequalities proposed in [Phys. Rev. Lett. 105, 170404 (2010)] are not Bell's inequalities in the usual sense: there are local classical models that violate these inequalities. Thus, their violation demonstrates nonlocality only under assumptions about the physical implementation and moreover they cannot be used as a device-independent test of nonlocality.

Group transference techniques for the estimation of the decoherence times and capacities of quantum Markov semigroups

Capacities of quantum channels and decoherence times both quantify the extent to which quantum information can withstand degradation by interactions with its environment. However, calculating capacities directly is known to be intractable in general. Much recent work has focused on upper bounding certain capacities in terms of more tractable quantities such as specific norms from operator theory. In the meantime, there has also been substantial recent progress on estimating decoherence times with techniques from analysis and geometry, even though many hard questions remain open. In this articl…

Arbitrarily varying and compound classical-quantum channels and a note on quantum zero-error capacities

We consider compound as well as arbitrarily varying classical-quantum channel models. For classical-quantum compound channels, we give an elementary proof of the direct part of the coding theorem. A weak converse under average error criterion to this statement is also established. We use this result together with the robustification and elimination technique developed by Ahlswede in order to give an alternative proof of the direct part of the coding theorem for a finite classical-quantum arbitrarily varying channels with the criterion of success being average error probability. Moreover we pro…

A note on the geometric interpretation of Bell's inequalities

Using results of Pitowsky and Gupta, we show in a direct, elementary fashion that, in the case of three spins, Bell's inequalities indeed provide a representation of the tetrahedron of all spin correlation matrices as intersection of half-spaces.

直接信道与互补信道容量的同时超加性

Simultaneous superadditivity of the direct and complementary channel capacities

本文挑战了纠缠单配性直觉，证明了量子信道及其互补信道的相干信息与私密信息在任意多次使用下可同时具有超加性，并研究了最大与总私密信息量在不同信道使用次数下与相干信息的不等式交替关系。

A note on the violation of Bell's inequality

With Bell's inequalities one has a formal expression to show how essentially all local theories of natural phenomena that are formulated within the framework of realism may be tested using a simple experimental arrangement. For the case of entangled pairs of spin-1/2 particles we propose an alternative measurement setup which is consistent to the necessary assumptions corresponding to the derivation of the Bell inequalities. We find that the Bell inequalities are never violated with respect to our suggested measurement process.

Note on the saturation of the norm inequalities between diamond and nuclear norm

The diamond norm plays an important role in quantum information and operator theory. Recently, it has also been proposed as a regularizer for low-rank matrix recovery. The norm constants that bound the diamond norm in terms of the nuclear norm (also known as trace norm) are explicitly known. This note provides a simple characterization of all operators saturating the upper and the lower bound.

A simple derivation of the strong subadditivity inequalities

In this short note, we give a simple derivation of the strong subadditivity inequalities: S(13) + S(23) \ge S(1) + S(2) and S(12) + S(23) \ge S(2) + S(123). The simplicity is due to the way we represent the quantum systems. We make a few remarks about such a representation.

关于一些不等式、由此产生的不确定性关系和相关性的注释。1. 一般的数学形式主义

Notes on some inequalities, resulting uncertainty relations and correlations

本文分析Schwarz不等式及其推广，以及由Jensen不等式导出的不等式，用于量子理论中推导两个非对易可观测量的Heisenberg-Robertson和Schroedinger-Robertson不确定性关系及其推广。

Limits on classical communication from quantum entropy power inequalities

Almost all modern communication systems rely on electromagnetic fields as a means of information transmission, and finding the capacities of these systems is a problem of significant practical importance. The Additive White Gaussian Noise (AWGN) channel is often a good approximate description of such systems, and its capacity is given by a simple formula. However, when quantum effects are important, estimating the capacity becomes difficult: a lower bound is known, but a similar upper bound is missing. We present strong new upper bounds for the classical capacity of quantum additive noise chan…