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It is known that random quantum channels exhibit significant violations of multiplicativity of maximum output p-norms for any p>1. In this work, we show that a weaker variant of multiplicativity nevertheless holds for these channels. For…

Quantum Physics · Physics 2015-06-03 Ashley Montanaro

Recently there has been considerable activity on the subject of additivity of various quantum channel capacities. Here, we construct a family of channels with sharply bounded classical, hence private capacity. On the other hand, their…

Quantum Physics · Physics 2017-08-01 Ke Li , Andreas Winter , XuBo Zou , GuangCan Guo

We derive a novel chain rule for a family of channel conditional entropies, covering von Neumann and sandwiched R\'{e}nyi entropies. In the process, we show that these channel conditional entropies are equal to their regularized version,…

Quantum Physics · Physics 2025-07-29 Amir Arqand , Ernest Y. -Z. Tan

In a previous paper, we proved that the limit of the collection of possible eigenvalues of output states of a random quantum channel is a deterministic, compact set K_{k,t}. We also showed that the set K_{k,t} is obtained, up to an…

Mathematical Physics · Physics 2016-09-06 Serban T. Belinschi , Benoit Collins , Ion Nechita

The additivity of minimal output entropy is proved for the Weyl channel obtained by the deformation of a q-c Weyl channel. The classical capacity of channel is calculated.

Quantum Physics · Physics 2021-01-06 Grigori Amosov

The problem of additivity of the Minimum Output Entropy is of fundamental importance in Quantum Information Theory (QIT). It was solved by Hastings in the one-shot case, by exhibiting a pair of random quantum channels. However, the initial…

Operator Algebras · Mathematics 2023-10-25 Benoît Collins , Sang-Gyun Youn

We study subadditivity of the minimum output entropy ($H_{min}$) of quantum multiple access channels (MACs). We provide an example of violation of the additivity theorem for $H_{min}$ known in classical information theory. Our result is…

Quantum Physics · Physics 2012-03-14 Lukasz Czekaj

We argue that a fundamental (conjectured) property of memoryless quantum channels, namely the strong superadditivity, is intimately related to the decreasing property of the quantum relative entropy. Using the latter we first give, for a…

Quantum Physics · Physics 2009-07-09 Grigori G. Amosov , Stefano Mancini

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…

Quantum Physics · Physics 2018-12-05 Giacomo De Palma , Stefan Huber

We study the asymptotic behavior of the output states of sequences of quantum channels. Under a natural assumption, we show that the output set converges to a compact convex set, clarifying and substantially generalizing results in [BCN13].…

Mathematical Physics · Physics 2015-10-15 Benoit Collins , Motohisa Fukuda , Ion Nechita

We reduce the number of open additivity problems in quantum information theory by showing that four of them are equivalent. We show that the conjectures of additivity of the minimum output entropy of a quantum channel, additivity of the…

Quantum Physics · Physics 2009-11-10 Peter W. Shor

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 Physics · Physics 2026-04-13 Chiranjib Mukhopadhyay , Arun Kumar Pati , Sk Sazim

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…

Quantum Physics · Physics 2009-11-11 Tohya Hiroshima

Quantum channels can be described via a unitary coupling of system and environment, followed by a trace over the environment state space. Taking the trace instead over the system state space produces a different mapping which we call the…

Quantum Physics · Physics 2009-01-14 Christopher King , Keiji Matsumoto , Michael Nathanson , Mary Beth Ruskai

We define the coherence non-generating channel as the completely positive trace-preserving map which does not generate quantum coherence from an incoherent state. The incoherent operations are the strict subset of the coherence…

Quantum Physics · Physics 2016-07-19 Xueyuan Hu

In the present paper we study the entropy gain $H(\Phi [\rho])-H(\rho)$ for infinite-dimensional channels $\Phi$. We show that unlike finite-dimensional case where the minimal entropy gain is always nonpositive \cite{al}, there is a plenty…

Mathematical Physics · Physics 2010-11-23 A. S. Holevo

Capacities of quantum channels are fundamental quantities in the theory of quantum information. A desirable property is the additivity for a capacity. However, this cannot be achieved for a few quantities that have been established as…

Quantum Physics · Physics 2025-05-20 D. -S. Wang

We introduce an infinite sequence of quantum channels for which the Holevo capacity is additive. The channel series is closely related to the quantum channels arising from universal quantum cloning machines. The additivity proof is…

Quantum Physics · Physics 2016-11-17 Kamil Bradler

We show that the uniform distribution minimizes entropy among all one-dimensional symmetric log-concave distributions with fixed variance, as well as various generalizations of this fact to R\'enyi entropies of orders less than 1 and with…

Information Theory · Computer Science 2021-10-20 Mokshay Madiman , Piotr Nayar , Tomasz Tkocz

An example is given of a qubit quantum channel which requires four inputs to maximize the Holevo capacity. The example is one of a family of channels which are related to 3-state channels. The capacity of the product channel is studied and…

Quantum Physics · Physics 2007-05-23 Masahito Hayashi , Hiroshi Imai , Keiji Matsumoto , Mary Beth Ruskai , Toshiyuki Shimono