The decreasing property of relative entropy and the strong superadditivity of quantum channels

@article{Amosov2009TheDP,
  title={The decreasing property of relative entropy and the strong superadditivity of quantum channels},
  author={Grigori G. Amosov and Stefano Mancini},
  journal={Quantum Inf. Comput.},
  year={2009},
  volume={9},
  pages={594-609}
}
  • G. Amosov, S. Mancini
  • Published 4 March 2008
  • Physics, Computer Science, Mathematics
  • Quantum Inf. Comput.
We argue that a fundamental (conjectured) property of memoryless quantum channels, namely the strong superadditivity, is intimately related to the decreasing property of the quantum relative entropy. Using the latter we first give, for a wide class of input states, an estimation of the output entropy for phase damping channels and some Weyl quantum channels. Then we prove, without any input restriction, the strong superadditivity for several quantum channels, including depolarizing quantum… 
Estimating the output entropy of a tensor product of two quantum channels
For a class of bipartite quantum states, we find a nontrivial lower bound on the entropy gain resulting from the action of a tensor product of the identity channel with an arbitrary channel. We use
Capacity of trace decreasing quantum operations and superadditivity of coherent information for a generalized erasure channel
  • S. Filippov
  • Physics
    Journal of Physics A: Mathematical and Theoretical
  • 2021
Losses in quantum communication lines severely affect the rates of reliable information transmission and are usually considered to be state-independent. However, the loss probability does depend on
Generalizations of 2-Dimensional Diagonal Quantum Channels with Constant Frobenius Norm
  • I. Sergeev
  • Physics, Mathematics
    Reports on Mathematical Physics
  • 2019
We introduce the set of quantum channels with constant Frobenius norm, the set of diagonal channels and the notion of equivalence of one-parameter families of channels. First, we show that all
On estimating the output entropy of a tensor product of the quantum phase-damping channel with an arbitrary channel
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
Classical capacity of generalized Pauli channels
We calculate and analyze the bounds of the Holevo capacity and classical capacity for the generalized Pauli channels. In particular, we obtain the lower and upper bounds of the Holevo capacity and
On estimating the output entropy of the tensor product of a phase-damping channel and an arbitrary channel
  • G. Amosov
  • Mathematics, Computer Science
    Probl. Inf. Transm.
  • 2013
TLDR
A lower estimate for the output entropy of a tensor product of the quantum phase-damping channel and an arbitrary channel is obtained and it is shown that strong superadditivity of theoutput entropy holds for this channel as well as for the quantum depolarizing channel.
On the classical capacity of quantum Gaussian channels
The set of quantum Gaussian channels acting on one bosonic mode can be classified according to the action of the group of Gaussian unitaries. We look for bounds on the classical capacity for channels
Upper Bounds for the Holevo Information Quantity and Their Use
  • M. Shirokov
  • Computer Science, Mathematics
    Probl. Inf. Transm.
  • 2019
TLDR
It is shown that an appropriate choice of the reference state gives tight upper bounds for the Holevo quantity which in many cases improve the estimates existing in the literature.
On capacity of quantum channels generated by irreducible projective unitary representations of finite groups
We study mixed unitary quantum channels generated by irreducible projective unitary representations of finite groups. Under some assumptions on the probability distribution determining a mixture the
Classical capacities of quantum channels with environment assistance
TLDR
This work defines and study the classical capacity of a unitary interaction with helper, in two variants: one where the helper can only prepare separable states across many channel uses, and one without this restriction.
...
1
2
...

References

SHOWING 1-10 OF 39 REFERENCES
Additivity of the classical capacity of entanglement-breaking quantum channels
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
Remark on the additivity conjecture for a quantum depolarizing channel
  • G. Amosov
  • Mathematics, Physics
    Probl. Inf. Transm.
  • 2006
TLDR
A proof of the additivity conjecture for a quantum depolarizing channel Φ based on the decreasing property of the relative entropy is given and it is shown that theAdditivity conjecture holds for a channel Ξ = Ψ o Φ, where Ψ is a phase damping channel.
On Some Additivity Problems in Quantum Information Theory
A class of problems in quantum information theory, having an elementary formulation but still resisting solution, concerns the additivity properties of various quantities characterizing quantum
Capacities of Quantum Erasure Channels
The quantum analog of the classical erasure channel provides a simple example of a channel whose asymptotic capacity for faithful transmission of intact quantum states, with and without the
Equivalence of Additivity Questions in Quantum Information Theory
We reduce the number of open additivity problems in quantum information theory by showing that four of them are equivalent. Namely, we show that the conjectures of additivity of the minimum output
Equivalence of Additivity Questions in Quantum Information Theory
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
The proper formula for relative entropy and its asymptotics in quantum probability
Umegaki's relative entropyS(ω,ϕ)=TrDω(logDω−logDϕ) (of states ω and ϕ with density operatorsDω andDϕ, respectively) is shown to be an asymptotic exponent considered from the quantum hypothesis
A counterexample to additivity of minimum output entropy
We present a random construction of a pair of channels which gives, with non-zero probability for sufficiently large dimensions, a counterexample to the minimum output entropy conjecture. As shown by
The maximal p-norm multiplicativity conjecture is false
For all 1 < p < 2, we demonstrate the existence of quantum channels with non-multiplicative maximal p-norms. Equivalently, the minimum output Renyi entropy of order p of a quantum channel is not
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
...
1
2
3
4
...