Yet another additivity conjecture

Yet anther equivalent additivity conjecture

It is known that the additivity conjecture of Holevo capacity, output minimum entoropy, and the entanglement of formation (EoF), are equivalent with each other. Among them, the output minimum entropy is simplest, and hence many researchers are focusing on this quantity. Here, we suggest yet another entanglement measure, whose strong superadditivity and additivity are equivalent to the additivit...

On Shor ’ s channel extension and constrained channels

Several equivalent formulations of the additivity conjecture for constrained channels, which formally is substantially stronger than the unconstrained additivity, are given. To this end a characteristic property of the optimal ensemble for such a channel is derived, generalizing the maximal distance property. It is shown that the additivity conjecture for constrained channels holds true for cer...

Remark on the additivity conjecture for a quantum depolarizing channel

We consider bistochastic quantum channels generated by unitary representations of the discret group. The proof of the additivity conjecture for the quantum depolarizing channel Φ based on the decreasing property of the relative entropy is given. We show that the ad-ditivity conjecture holds for the channel Ξ = Ψ • Φ, where Ψ is the phase damping.

On the Closed-Form Solution of a Nonlinear Difference Equation and Another Proof to Sroysang’s Conjecture

The purpose of this paper is twofold. First we derive theoretically, using appropriate transformation on x(n), the closed-form solution of the nonlinear difference equation x(n+1) = 1/(±1 + x(n)), n ∈ N_0. The form of solution of this equation, however, was first obtained in [10] but through induction principle. Then, with the solution of the above equation at hand, we prove a case ...

On the Additivity Conjecture for Channels with Arbitrary Constraints