On estimating the output entropy of the tensor product of a phase-damping channel and an arbitrary channel

Abstract

We obtained the estimation from below for the output entropy of a tensor product of the quantum phase-damping channel with an arbitrary channel. It is shown that from this estimation immediately follows that the strong superadditivity of the output entropy holds for this channel as well as for the quantum depolarizing channel.

On classical capacity of Weyl channels

“…Here we use the techniques introduced in [14,15] and developed in [16][17][18][19]. Fix an orthonormal basis (e j , j ∈ Z n ) in a Hilbert space H with dimension dimH = n, and consider two unitary operators in H defined by the formula Ue j = e 2πi n j e j , V e j = e j+1 , j ∈ Z n .…”

Estimating the output entropy of a tensor product of two quantum channels

“…for some complex numbers (λ n ) N −1 n=0 which are the discrete Fourier transform of a probability distribution (π n ) N −1 n=0 [2]. In [2] the inequality (8) was obtained for a phase-damping channel Φ in the case dimH < +∞.…”

“…Suppose that a state ρ ∈ S(H ⊗ K) has the form (20). Following [2] let us define the orthogonal projection P by the formula P = n |e n >< e n | ⊗ |h n >< h n |.…”

“…Now let dimH = +∞. Fix the orthonormal basis (e n ) and consider a quantum phase damping channel Φ defined by (2).…”

On the Entropy Gain Under the Action of the Amplitude Damping Channel on Qutrit

“…In particular, this method allows to estimate the von Neumann entropy S(ρ) = −T rρ log ρ of a qutrit state ρ by means of the entropies of its qubit portraits [2]. On the other hand, for bipartite systems there is a possibility to estimate the entropy gain under the action of quantum channels having a special form [3]. Suppose that a state ρ ∈ S(H ⊗ K) has the form…”