Related papers: Yet another additivity conjecture
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…
Recently Shor proved equivalence of several open (sub)additivity problems related to the Holevo capacity and the entanglement of formation [15]. In our previous note [6] equivalence of these to the additivity of the Holevo capacity for…
We employ a basic formalism from convex analysis to show a simple relation between the entanglement of formation $E_F$ and the conjugate function $E^*$ of the entanglement function $E(\rho)=S(\trace_A\rho)$. We then consider the conjectured…
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 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…
The additivity of both the entanglement of formation and the classical channel capacity is known to be a consequence of the strong superadditivity conjecture. We show that, conversely, the strong superadditivity conjecture follows from the…
We prove the strong super-additivity of the entanglement of formation for stabilizer pure states, and the set of mixed states which minimize their average entropy of entanglement as a mixture of stabilizer pure states sharing the same…
The purpose of these notes is to discuss the relation between the additivity questions regarding the quantities (Holevo) capacity of a quantum channel T and entanglement of formation of a given bipartite state. In particular, using the…
The proof of additivity of entanglement of formation for some special cases is given. The strong concavity of von Neumann entropy due to strong subadditivity of von Neumann entropy is presented. Some general relations concerning about 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 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…
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…
Various lower bounds are established for the entropy of sums, products and their combinations. First, we derive a prime-field analogue of a version of the entropy power inequality established by Tao over torsion-free groups. Next, we prove…
Additivity of the Holevo capacity is proved for product channels, under the condition that one of the channels is in a certain class of unital qubit channels, with the other completely arbitrary. This qubit class includes the depolarizing…
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…
We show how the fundamental entropic inequality proved recently in [arXiv:2408.15306] can be applied to obtain a useful relation for the Holevo quantity of discrete and continuous ensembles of quantum states. This relation gives a tight…
We prove that the relative entropy of entanglement is additive when \emph{at least one of the two states} belongs to some specific class. We show that these classes include bipartite pure, maximally correlated, GHZ, Bell diagonal,…
As two of the most important entanglement measures--the entanglement of formation and the entanglement of distillation--have so far been limited to bipartite settings, the study of other entanglement measures for multipartite systems…
The Amosov-Holevo-Werner conjecture implies the additivity of the minimum Re'nyi entropies at the output of a channel. The conjecture is proven true for all Re'nyi entropies of integer order greater than two in a class of Gaussian bosonic…
A short and elementary proof of the joint convexity of relative entropy is presented, using nothing beyond linear algebra. The key ingredients are an easily verified integral representation and the strategy used to prove the Cauchy-Schwarz…