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Register a new userAdditivity of the Renyi entropy of order 2 for positive-partial-transpose-inducing channels
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We prove that the minimal Renyi entropy of order 2 (RE2) output of a positive-partial-transpose(PPT)-inducing channel joint to an arbitrary other channel is equal to the sum of the minimal RE2 output of the individual channels. PPT-inducing channels are channels with a Choi matrix which is bound entangled or separable. The techniques used can be easily recycled to prove additivity for some non-PPT-inducing channels such as the depolarizing and transpose depolarizing channels, though not all known additive channels. We explicitly make the calculations for generalized Werner-Holevo channels as an example of both the scope and limitations of our techniques.
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We study the distinguishability of a particular type of maximally entangled states -- the lattice states using a new approach of semidefinite program. With this, we successfully construct all sets of four ququad-ququad orthogonal maximally entangled states that are locally indistinguishable and find some curious sets of six states having interesting property of distinguishability. Also, some of the problems arose from cite{CosentinoR14} about the PPT-distinguishability of lattice maximally entangled states can be answered.
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 $-2/(d^2-2)le t le 1/(d+1)$.
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