Entropic partial orderings of quantum measurements
Fuente:
arXiv
Enregistré dans:
| Auteurs principaux: | , , |
|---|---|
| Format: | Preprint |
| Publié: |
2023
|
| Sujets: | |
| Accès en ligne: | |
| Tags: |
Ajouter un tag
Pas de tags, Soyez le premier à ajouter un tag!
|
| _version_ | 1866917960266809344 |
|---|---|
| author | Teixidó-Bonfill, Adam Schindler, Joseph Šafránek, Dominik |
| author_facet | Teixidó-Bonfill, Adam Schindler, Joseph Šafránek, Dominik |
| contents | We investigate four partial orderings on the space of quantum measurements (i.e on POVMs or positive operator valued measures), describing four notions of coarse/fine-ness of measurement. These are the partial orderings induced by: (1) classical post-processing, (2) measured relative entropy, (3) observational entropy, and (4) linear relation of POVMs. The orderings form a hierarchy of implication, where e.g. post-processing relation implies all the others. We show that this hierarchy is strict for general POVMs, with examples showing that all four orderings are strictly inequivalent. Restricted to projective measurements, all are equivalent. Finally we show that observational entropy equality $S_M = S_N$ (for all $ρ$) holds if and only if $M \equiv N$ are post-processing equivalent, which shows that the first three orderings induce identical equivalence classes. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2310_14086 |
| institution | arXiv |
| publishDate | 2023 |
| record_format | arxiv |
| spellingShingle | Entropic partial orderings of quantum measurements Teixidó-Bonfill, Adam Schindler, Joseph Šafránek, Dominik Quantum Physics Mathematical Physics We investigate four partial orderings on the space of quantum measurements (i.e on POVMs or positive operator valued measures), describing four notions of coarse/fine-ness of measurement. These are the partial orderings induced by: (1) classical post-processing, (2) measured relative entropy, (3) observational entropy, and (4) linear relation of POVMs. The orderings form a hierarchy of implication, where e.g. post-processing relation implies all the others. We show that this hierarchy is strict for general POVMs, with examples showing that all four orderings are strictly inequivalent. Restricted to projective measurements, all are equivalent. Finally we show that observational entropy equality $S_M = S_N$ (for all $ρ$) holds if and only if $M \equiv N$ are post-processing equivalent, which shows that the first three orderings induce identical equivalence classes. |
| title | Entropic partial orderings of quantum measurements |
| topic | Quantum Physics Mathematical Physics |
| url | https://arxiv.org/abs/2310.14086 |