Comment on "Strong Quantum Darwinism and Strong Independence are Equivalent to Spectrum Broadcast Structure"

Abstract

In a recent Letter [Phys. Rev. Lett. 122, 010403 (2019)], an equivalence is proposed between the so-called Spectrum Broadcast Structure for a system-multienvironment quantum state, and the conjunction of two information-theory notions: (a) Strong Quantum Darwinism; and (b) Strong Independence. Here, we show that the mathematical formulation of condition (b) by the authors (namely, the pairwise independence of the fragments of the environment, conditioned on the system), is necessary but not sufficient to ensure the equivalence. We propose a simple counter-example, together with a strengthened formulation of condition (b), ensuring the equivalence proposed by the authors.

arXiv comment2 pages, no figure

References in corpus (2)

• Squashed entanglement for multipartite states and entanglement measures based on the mixed convex roof
• Strong Quantum Darwinism and Strong Independence is equivalent to Spectrum Broadcast Structure

Cited by in corpus (5)

• Roads to objectivity: Quantum Darwinism, Spectrum Broadcast Structures, and Strong quantum Darwinism -- a review
• A thermodynamically consistent approach to the energy costs of quantum measurements
• The meaning of redundancy and consensus in quantum objectivity
• Non-perfect propagation of information to noisy environment with self-evolution
• Thermodynamic Constraints on the Emergence of Intersubjectivity in Quantum Systems