Related papers: Majorization and additivity for multimode bosonic …
The long-standing conjectures of the optimality of Gaussian inputs for Gaussian channel and Gaussian additivity are solved for a broad class of covariant or contravariant Bosonic Gaussian channels (which includes in particular thermal,…
We prove multiplicativity of maximal output $p$ norm of classical noise channels and thermal noise channels of arbitrary modes for all $p>1$ under the assumption that the input signal states are Gaussian states. As a direct consequence, we…
We give a survey of the two remarkable analytical problems of quantum information theory. The main part is a detailed report of the recent (partial) solution of the quantum Gaussian optimizers problem which establishes an optimal property…
The additivity problem asks if the use of entanglement can boost the information-carrying capacity of a given channel beyond what is achievable by coding with simple product states only. This has recently been shown not to be the case for…
The Amosov-Holevo-Werner conjecture implies the additivity of the minimum Re'nyi entropies at the output of a channel. The conjecture is proven true for all Re'nyi entropies of integer order greater than two in a class of Gaussian bosonic…
The additivity of the minimal output entropy and that of the $\chi$-capacity are known to be equivalent for finite-dimensional irreducibly covariant channels. In this paper we formulate a list of conditions allowing to establish similar…
We show the existence of a majorization ladder in bosonic Gaussian channels, that is, we prove that the channel output resulting from the $n\text{th}$ energy eigenstate (Fock state) majorizes the channel output resulting from the…
Quantum communication theory explores the implications of quantum mechanics to the tasks of information transmission. Many physical channels can be formally described as quantum Gaussian operations acting on bosonic quantum states.…
In this paper we prove two results related to the Gaussian optimizers conjecture for multimode bosonic system with gauge symmetry. First, we argue that the classical capacity of a Gaussian observable is attained on a Gaussian ensemble of…
Recently de Palma et al. [IEEE Trans. Inf. Theory 63, 728 (2017)] proved---using Lagrange multiplier techniques---that under a non-zero input entropy constraint, a thermal state input minimizes the output entropy of a pure-loss bosonic…
We address the question of the multiplicativity of the maximal p-norm output purities of bosonic Gaussian channels under Gaussian inputs. We focus on general Gaussian channels resulting from the reduction of unitary dynamics in larger…
A longstanding open problem in quantum information theory is to find the classical capacity of an optical communication link, modeled as a Gaussian bosonic channel. It has been conjectured that this capacity is achieved by a random coding…
Optimization methods aimed at estimating the capacities of a general Gaussian channel are developed. Specifically evaluation of classical capacity as maximum of the Holevo information is pursued over all possible Gaussian encodings for the…
We determine the p->q norms of the Gaussian one-mode quantum-limited attenuator and amplifier and prove that they are achieved by Gaussian states, extending to noncommutative probability the seminal theorem "Gaussian kernels have only…
A complete analysis of multi-mode bosonic Gaussian channels is proposed. We clarify the structure of unitary dilations of general Gaussian channels involving any number of bosonic modes and present a normal form. The maximum number of…
The quantum Gaussian optimizers conjecture says that q-p norm of a Bosonic Gaussian channel is attained on "Gaussian" operators. Recently R.L. Frank and E.H. Lieb confirmed the hypothesis in the case q=p for gauge-covariant channels with…
An ordering between the quantum states emerging from a single mode gauge-covariant bosonic Gaussian channel is proven. Specifically, we show that within the set of input density matrices with the same given spectrum, the element passive…
We derive explicit formulas for the capacity of multimode quantum Gaussian channels which serve as a fundamental model for optical version of multiple-input multiple-output channels. We show that it is always optimal to increase the number…
In this paper we consider the classical capacity problem for Gaussian measurement channels without imposing any kind of threshold condition. We prove Gaussianity of the average state of the optimal ensemble in general and discuss the…
We consider a quantum bosonic channel that couples the input mode via a beam splitter or two-mode squeezer to an environmental mode that is prepared in an arbitrary state. We investigate the classical capacity of this channel, which we call…