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Some new examples of quantum channels for which the infimum of the output entropy is additive under taking a tensor product of channels are given.

Quantum Physics · Physics 2007-05-23 Grigori Amosov

We consider the additivity of the minimal output entropy and the classical information capacity of a class of quantum channels. For this class of channels the norm of the output is maximized for the output being a normalized projection. We…

Quantum Physics · Physics 2009-11-10 M. M. Wolf , J. Eisert

We present explicit quantum channels with strictly sub-additive minimum output R\'enyi entropy for all $p>1$, improving upon prior constructions which handled $p>2$. Our example is provided by explicit constructions of linear subspaces with…

Quantum Physics · Physics 2026-01-27 Harm Derksen , Benjamin Lovitz

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

Recently, King and Ruskai [1] conjectured that the maximal p-norm of the Werner--Holevo channel is multiplicative for all $1\le p \le 2$. In this paper we prove this conjecture. Our proof relies on certain convexity and monotonicity…

Quantum Physics · Physics 2007-05-23 Nilanjana Datta

We introduce a condition for memoryless quantum channels which, when satisfied guarantees the multiplicativity of the maximal l_p-norm with p a fixed integer. By applying the condition to qubit channels, it can be shown that it is not a…

Quantum Physics · Physics 2009-11-10 Vittorio Giovannetti , Seth Lloyd , Mary Beth Ruskai

We introduce two additive invariants of output quantum channels. If the value of one these invariants is less than 1 then the logarithm of the inverse of its value is a positive lower bound for the regularized minimum entropy of an output…

Quantum Physics · Physics 2009-02-12 Shmuel Friedland

Inspired by Montanaro's work, we introduce the concept of additivity rates of a quantum channel $L$, which give the first order (linear) term of the minimum output $p$-R\'enyi entropies of $L^{\otimes r}$ as functions of $r$. We lower bound…

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

The von Neumann entropy of a quantum state is a central concept in physics and information theory, having a number of compelling physical interpretations. There is a certain perspective that the most fundamental notion in quantum mechanics…

Quantum Physics · Physics 2021-05-12 Gilad Gour , Mark M. Wilde

The primary entropic measures for quantum states are additive under the tensor product. In the analysis of quantum information processing tasks, the minimum entropy of a set of states, e.g., the minimum output entropy of a channel, often…

Quantum Physics · Physics 2026-03-13 Omar Fawzi , Jan Kochanowski , Cambyse Rouzé , Thomas Van Himbeeck

Additivity violation of minimum output entropy, which shows non-classical properties in quantum communication, had been proved in most cases for random quantum channels defined by Haar-distributed unitary matrices. In this paper, we…

Mathematical Physics · Physics 2021-05-03 Motohisa Fukuda , Takahiro Hasebe , Shinya Sato

In this Letter, two counterexamples show that the superadditivity inequality of relative entropy is not true even for the full-ranked quantum states. Thus, an inequality of quantum channels and complementary channels is not also true.…

Quantum Physics · Physics 2013-06-10 Lin Zhang , Junde Wu , Shao-Ming Fei

A problem in quantum information theory that has received considerable attention in recent years is the question of multiplicativity of the so-called maximal output purity (MOP) of a quantum channel. This quantity is defined as the maximum…

Quantum Physics · Physics 2009-11-13 Koenraad M. R. Audenaert

We introduce an quantum entropy for bimodule quantum channels on finite von Neumann algebras, generalizing the remarkable Pimsner-Popa entropy. The relative entropy for Fourier multipliers of bimodule quantum channels establishes an upper…

Operator Algebras · Mathematics 2024-01-01 Zishuo Zhao

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

We prove additivity of the minimal conditional entropy associated with a quantum channel Phi, represented by a completely positive (CP), trace-preserving map, when the infimum of S(gamma_{12}) - S(gamma_1) is restricted to states of the…

Quantum Physics · Physics 2009-11-11 Igor Devetak , Marius Junge , Christopher King , Mary Beth Ruskai

We prove a lemma which allows one to extend results about the additivity of the minimal output entropy from highly symmetric channels to a much larger class. A similar result holds for the maximal output $p$-norm. Examples are given showing…

Quantum Physics · Physics 2009-11-11 Motohisa Fukuda

The minimum entropy output is computed for rotationally invariant quantum channels acting on spin-1/2 and spin-1 systems. For the case of two parallel such channels and initial entangled (singlet) state the entropy of the output is higher…

Quantum Physics · Physics 2007-05-23 Robert Alicki

When can noiseless quantum information be sent across noisy quantum devices? And at what maximum rate? These questions lie at the heart of quantum technology, but remain unanswered because of non-additivity -- a fundamental synergy which…

Quantum Physics · Physics 2021-10-04 Vikesh Siddhu

It is shown that for real finite dimensional Hilbert spaces the additivity property of the minimum output entropy for quantum channels is always true.

Mathematical Physics · Physics 2013-04-01 Norbert Riedel