Tensorization of the strong data processing inequality for quantum chi-square divergences

Published online

Journal Article

It is well-known that any quantum channel E satisfies the data processing inequality (DPI), with respect to various divergences, e.g., quantum χκ2 divergences and quantum relative entropy. More specifically, the data processing inequality states that the divergence between two arbitrary quantum states ρ and σ does not increase under the action of any quantum channel E. For a fixed channel E and a state σ, the divergence between output states E(ρ) and E(σ) might be strictly smaller than the divergence between input states ρ and σ, which is characterized by the strong data processing inequality (SDPI). Among various input states ρ, the largest value of the rate of contraction is known as the SDPI constant. An important and widely studied property for classical channels is that SDPI constants tensorize. In this paper, we extend the tensorization property to the quantum regime: we establish the tensorization of SDPIs for the quantum χκ1/22 divergence for arbitrary quantum channels and also for a family of χκ2 divergences (with κ≥κ1/2) for arbitrary quantum-classical channels.

Full Text

Duke Authors

Cited Authors

  • Cao, Y; Lu, J

Published In

Volume / Issue

  • 3 /

Chapter

  • 199

Start / End Page

  • 199 - 199

Published By

Electronic International Standard Serial Number (EISSN)

  • 2521-327X

Digital Object Identifier (DOI)

  • 10.22331/q-2019-10-28-199

Language

  • en