Related papers: On Hastings' counterexamples to the minimum output…
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…
We prove the claim made in the title by showing that approximately randomising maps of large dimension are counterexamples to the multiplicativity conjecture.
In this paper we give several equivalent formulations of the additivity conjecture for constrained channels, which formally is substantially stronger than the unconstrained additivity. To this end a characteristic property of the optimal…
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…
It is well-known that the action of a quantum channel on a state can be represented, using an auxiliary space, as the partial trace of an associated bipartite state. Recently, it was observed that for the bipartite state associated with the…
A formulation of the generalized minimal output entropy conjecture for Gaussian channels is presented. It asserts that, for states with fixed input entropy, the minimal value of the output entropy of the channel (i.e. the minimal output…
We study mixed unitary channels generated by finite subgroups of the group of all unitary operators in a Hilbert space. Based on the majorization theory we introduce techniques allowing to calculate different characteristics of output…
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…
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…
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…
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…
Entropy comparison inequalities are obtained for the differential entropy $h(X+Y)$ of the sum of two independent random vectors $X,Y$, when one is replaced by a Gaussian. For identically distributed random vectors $X,Y$, these are closely…
The continuity properties of the convex closure of the output entropy of infinite dimensional channels and their applications to the additivity problem are considered. The main result of this paper is the statement that the superadditivity…
We consider the image of some classes of bipartite quantum states under a tensor product of random quantum channels. Depending on natural assumptions that we make on the states, the eigenvalues of their outputs have new properties which we…
The minimum mean square error of the estimation of a non Gaussian signal where observed from an additive white Gaussian noise channel's output, is analyzed. First, a quite general time-continuous channel model is assumed for which the…
We simplify some conjectures in quantum information theory; the additivity of minimal output entropy, the multiplicativity of maximal output p-norm and the superadditivity of convex closure of output entropy. We construct a unital channel…
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…
For a given quantum channel we consider two optimal sets of states, related to the Holevo capacity and to the minimal output entropy of this channel. Some properties of these sets as well as the necessary and sufficient condition for their…
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.
The von Neumann entropy at the output of a bosonic channel with thermal noise is analyzed. Coherent-state inputs are conjectured to minimize this output entropy. Physical and mathematical evidence in support of the conjecture is provided. A…