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We show that for the tensor product of an entanglement-breaking quantum channel with an arbitrary quantum channel, both the minimum entropy of an output of the channel and the Holevo-Schumacher-Westmoreland capacity are additive. In…

Quantum Physics · Physics 2015-06-26 Peter W. Shor

We study quantum channels with respect to their image, i.e., the image of the set of density operators under the action of the channel. We first characterize the set of quantum channels having polytopic images and show that additivity of…

Quantum Physics · Physics 2015-10-15 Motohisa Fukuda , Ion Nechita , Michael M. Wolf

It is known that the minimal output entropy is additive for any product of entanglement breaking (EB) channels. The same is true for the Renyi entropy, where additivity is equivalent to multiplicativity of the $1 \rightarrow q$ norm for all…

Quantum Physics · Physics 2013-10-23 Christopher King

Hastings recently reported a randomized construction of channels violating the minimum output entropy additivity conjecture. Here we revisit his argument, presenting a simplified proof. In particular, we do not resort to the exact…

Quantum Physics · Physics 2010-07-08 Fernando G. S. L. Brandao , Michal Horodecki

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

A random unitary channel is one that is given by a convex combination of unitary channels. It is shown that the conjectures on the additivity of the minimum output entropy and the multiplicativity of the maximum output $p$-norm can be…

Quantum Physics · Physics 2008-10-15 Bill Rosgen

In this paper, we consider the minimal entropy of qubit states transmitted through two uses of a noisy quantum channel, which is modeled by the action of a completely positive trace-preserving (or stochastic) map. We provide strong support…

Quantum Physics · Physics 2007-05-23 C. King , M. B. Ruskai

Determining capacities of quantum channels is a fundamental question in quantum information theory. Despite having rigorous coding theorems quantifying the flow of information across quantum channels, their capacities are poorly understood…

Quantum Physics · Physics 2023-06-14 Felix Leditzky , Debbie Leung , Vikesh Siddhu , Graeme Smith , John A. Smolin

We consider bistochastic quantum channels generated by unitary representations of the discret group. The proof of the additivity conjecture for the quantum depolarizing channel $\Phi$ based on the decreasing property of the relative entropy…

Quantum Physics · Physics 2007-05-23 G. G. Amosov

We generalize recent results of Collins and Youn (2022), presenting new classes of quantum channels violating the additivity of the regularized minimum output entropy in the commuting-operator setup.

Operator Algebras · Mathematics 2025-01-28 Mehrdad Kalantar , Homayoon Shobeiri

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…

Quantum Physics · Physics 2007-07-05 A. S. Holevo

A conjecture arising naturally in the investigation of additivity of classical information capacity of quantum channels states that the maximal purity of outputs from a quantum channel, as measured by the p-norm, should be multiplicative…

Quantum Physics · Physics 2015-06-26 R. F. Werner , A. S. Holevo

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

We prove additivity of the minimum output entropy and the Holevo capacity for rotationally invariant quantum channels acting on spin-1/2 and spin-1 systems. The physical significance of these channels and their relations to other known…

Quantum Physics · Physics 2007-05-23 Nilanjana Datta

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

We give a simple and conceptual proof of the fact that random unitary channels yield violation of the Minimum Output Entropy additivity. The proof relies on strong convergence of random unitary matrices and Haagerup's inequality.

Operator Algebras · Mathematics 2019-02-27 Benoit Collins

We show that the minimum output entropy for all single-mode Gaussian channels is additive and is attained for Gaussian inputs. This allows the derivation of the channel capacity for a number of Gaussian channels, including that of the…

Quantum Physics · Physics 2010-01-21 S. Lloyd , V. Giovannetti , L. Maccone , S. Pirandola , R. Garcia-Patron

It is now well-known that, with high probability, the additivity of minimum output entropy does not hold for a pair of a random quantum channel and its complex conjugate. We investigate asymptotic behavior of output states of $r$-tensor…

Mathematical Physics · Physics 2015-02-12 Motohisa Fukuda , Ion Nechita

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 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