Related papers: Additivity rates and PPT property for random quant…
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…
The super-additivity of quantum channel capacity is an important feature of quantum information theory different from classical theory, which has been attracting attention. Recently a special channel called ``platypus channel'' exhibits…
Spectral properties of an arbitrary matrix can be characterized by the entropy of its rescaled singular values. Any quantum operation can be described by the associated dynamical matrix or by the corresponding superoperator. The entropy of…
The purpose of this work is to extend the result of previous papers quant-ph/9611023, quant-ph/9703013 to quantum channels with additive constraints onto the input signal, by showing that the capacity of such channel is equal to the…
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 channels represent a broad spectrum of operations crucial to quantum information theory, encompassing everything from the transmission of quantum information to the manipulation of various resources. In the domain of states, the…
In this paper, we compute the exact values of the minimum output entropy and the completely bounded minimal entropy of very large classes of quantum channels acting on matrix algebras $\mathrm{M}_n$. Our new and simple approach relies on…
Tradeoffs between the information rate and fidelity of quantum error-correcting codes are discussed. Quantum channels to be considered are those subject to independent errors and modeled as tensor products of copies of a general completely…
We study the additivity problems for the classical capacity of quantum channels, the minimal output entropy and its convex closure. We show for each of them that additivity for arbitrary pairs of channels holds iff it holds for arbitrary…
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…
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…
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…
The measured relative entropies of quantum states and channels find operational significance in quantum information theory as achievable error rates in hypothesis testing tasks. They are of interest in the near term, as they correspond to…
Quantum channels can represent dynamic resources, which are indispensable elements in many physical scenarios. To describe certain facets of nonclassicality of the channels, it is necessary to quantify their properties. In the framework of…
For a partially degradable (PD) channel, the channel output state can be used to simulate the degraded environment state. The quantum capacity of a PD channel has been proven to be additive. Here, we show that the private classical capacity…
The highest fidelity of quantum error-correcting codes of length n and rate R is proven to be lower bounded by 1 - exp [-n E(R)+ o(n)] for some function E(R) on noisy quantum channels that are subject to not necessarily independent errors.…
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…
Entropy rate is a real valued functional on the space of discrete random sources which lacks a closed formula even for subclasses of sources which have intuitive parameterizations. A good way to overcome this problem is to examine its…
We investigate the Weyl channels being covariant with respect to the maximum commutative group of unitary operators. This class includes the quantum depolarizing channel and the "two-Pauli" channel as well. Then, we show that our estimation…
We consider discrete memoryless channels with input alphabet size $n$ and output alphabet size $m$, where $m=$ceil$(\gamma n)$ for some constant $\gamma>0$. The channel transition matrix consists of entries that, before being normalised,…