Related papers: Convex Trace Functions on Quantum Channels and the…
Machine learning techniques are increasingly being used in fundamental research to solve various challenging problems. Here we explore one such technique to address an important problem in quantum communication scenario. While transferring…
The optimal rate at which information can be sent through a quantum channel when the transmitted signal must simultaneously carry some minimum amount of energy is characterized. To do so, we introduce the quantum-classical analogue of the…
We establish a reformulation of the Connes embedding problem in terms of an asymptotic property of factorizable completely positive maps. We also prove that the Holevo-Werner channels W_n^- are factorizable, for all odd integers n different…
In this article, we further explore convex functions by revealing new bounds, resulting from stronger convexity behavior. In particular, we define the so called radical convex functions and study their properties. We will see that such…
The design of error-correcting codes used in modern communications relies on information theory to quantify the capacity of a noisy channel to send information [1]. This capacity can be expressed using the mutual information between input…
We consider the following trace function on n-tuples of positive operators: \Phi_p(A_1,A_2,...,A_n) = Trace (\sum_{j=1}^n A_j^p)^{1/p} and prove that it is jointly concave for 0<p\le 1 and convex for p=2. We then derive from this a…
We give a general solution to the question when the convex hulls of orbits of quantum states on a finite-dimensional Hilbert space under unitary actions of a compact group have a non-empty interior in the surrounding space of all density…
Recently, the projective robustness of quantum states has been introduced in [arXiv:2109.04481(2021)]. It shows that the projective robustness is a useful resource monotone and can comprehensively characterize capabilities and limitations…
One of the most challenging open problems in quantum information theory is to clarify and quantify how entanglement behaves when part of an entangled state is sent through a quantum channel. Of central importance in the description of a…
This article analyzes the algebraic structure of the set of all quantum channels and its subset consisting of quantum channels that have Holevo representation. The regularity of these semigroups under composition of mappings is analyzed. It…
The notion of a valuation on convex bodies is very classical. The notion of a valuation on a class of functions was recently introduced and studied by M. Ludwig and others. We study an explicit relation between continuous valuations on…
Quantum addition channels have been recently introduced in the context of deriving entropic power inequalities for finite dimensional quantum systems. We prove a reverse entropy power equality which can be used to analytically prove an…
Quantum channels can be mathematically represented as completely positive trace-preserving maps that act on a density matrix. A general quantum channel can be written as a convex sum of `extremal' channels. We show that for an $N$-level…
A pair of quantum channels are said to be incompatible if they cannot be realized as marginals of a single channel. This paper addresses the general structure of the incompatibility of completely positive channels with a fixed quantum input…
Quantum channels are not invertible in general. A quasi-inverse allows for a partial recovery of the input state, but its analytical results are found only in a restricted space of its parameters. This work explores the potential of neural…
Quantum transport on structured networks is strongly influenced by interference effects, which can dramatically modify how information propagates through a system. We develop a quantum-information-theoretic framework for scattering on…
We explore complementarity between output and environment of a quantum channel (or, more generally, CP map), making an observation that the output purity characteristics for complementary CP maps coincide. Hence, validity of the…
In this article, we present a new subadditivity behavior of convex and concave functions, when applied to Hilbert space operators. For example, under suitable assumptions on the spectrum of the positive operators $A$ and $B$, we prove that…
In classical information theory, the Doeblin coefficient of a classical channel provides an efficiently computable upper bound on the total-variation contraction coefficient of the channel, leading to what is known as a strong…
As the connection between classical and quantum worlds, quantum measurements play a unique role in the era of quantum information processing. Given an arbitrary function of quantum measurements, how to obtain its optimal value is often…