Zero discord implies classicality
Michel Boyer

TL;DR
This paper provides a straightforward proof that zero quantum discord in bipartite states is equivalent to the state being classical on one subsystem, linking it to Petz's theorem on relative entropy preservation.
Contribution
It offers a simple, direct proof connecting zero discord to classical-quantum states using Petz's theorem, simplifying previous complex proofs.
Findings
Zero discord states are exactly classical-quantum states.
The proof uses Petz's theorem on channels preserving relative entropy.
Clarifies the relationship between discord and classicality in quantum states.
Abstract
The "classical-quantum" () discord of a bipartite state is the smallest difference between the mutual information of and that of after a measurement channel is applied on the system. Relating zero discord to the strong subadditivity of the Von Neumann entropy, Datta proved that a state has zero discord iff and only if it can be written in the form for a probability distribution, a basis of the system and states of the system. We provide a simple proof of that same result using directly a theorem of Petz on channels that leave unchanged the relative entropy of two given states.
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Taxonomy
TopicsQuantum Computing Algorithms and Architecture · Quantum Mechanics and Applications · Quantum Information and Cryptography
