Related papers: New constructive counterexamples to additivity of …

We present a constructive example of violation of additivity of minimum output R\'enyi entropy for each p>2. The example is provided by antisymmetric subspace of a suitable dimension. We discuss possibility of extension of the result to go…

Complementing recent progress on the additivity conjecture of quantum information theory, showing that the minimum output p-Renyi entropies of channels are not generally additive for p>1, we demonstrate here by a careful random selection…

For all p > 1, we demonstrate the existence of quantum channels with non-multiplicative maximal output p-norms. Equivalently, for all p >1, the minimum output Renyi entropy of order p of a quantum channel is not additive. The violations…

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…

We show that the minimum Renyi entropy output of a quantum channel is locally additive for Renyi parameter alpha>1. While our work extends the results of [10] (in which local additivity was proven for alpha=1), it is based on several new…

For all 1 < p < 2, we demonstrate the existence of quantum channels with non-multiplicative maximal p-norms. Equivalently, the minimum output Renyi entropy of order p of a quantum channel is not additive for all 1 < p < 2. The violations…

We give a direct proof of the additivity of the minimum output entropy of a particular quantum channel which breaks the multiplicativity conjecture. This yields additivity of the classical capacity of this channel, a result obtained by a…

The goal of this note is to show that the analysis of the minimum output p-Renyi entropy of a typical quantum channel essentially amounts to applying Milman's version of Dvoretzky's Theorem about almost Euclidean sections of…

In this paper we obtain new bounds for the minimum output entropies of random quantum channels. These bounds rely on random matrix techniques arising from free probability theory. We then revisit the counterexamples developed by Hayden and…

We show that the minimum von-Neumann entropy output of a quantum channel is locally additive. Hasting's counterexample for the additivity conjecture, makes this result quite surprising. In particular, it indicates that the non-additivity of…

We investigate minimum output (R\'enyi) entropy of qubit channels and unital quantum channels. We obtain an exact formula for the minimum output entropy of qubit channels, and bounds for unital quantum channels. Interestingly, our bounds…

We investigate decoherence induced by a quantum channel in terms of minimal output entropy and of map entropy. The latter is the von Neumann entropy of the Jamiolkowski state of the channel. Both quantities admit q-Renyi versions. We prove…

Hastings disproved additivity conjecture for minimum output entropy by using random unitary channels. In this note, we employ his approach to show that minimum output $p-$R\'{e}nyi entropy is non-additive for $p\in(0,p_0)\cup(1-p_0,1)$…

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.

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…

Additivity of minimal entropy output is proven for the class of quantum channels $\Lambda_t (A):=t A^{T}+(1-t)\tau (A)$ in the parameter range $-2/(d^2-2)\le t \le 1/(d+1)$.

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…

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

Hastings recently provided a proof of the existence of channels which violate the additivity conjecture for minimal output entropy. In this paper we present an expanded version of Hastings' proof. In addition to a careful elucidation of the…

In this paper, we study the minimal output entropy of EPOSIC channels. We determine the cases where their minimal output entropy is zero, and obtain some partial results on the fulfillment of their entanglement breaking property.Our results…