Non-representable quantum measures
Fuente:
arXiv
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| Natura: | Preprint |
| Pubblicazione: |
2025
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| _version_ | 1866918127491612672 |
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| author | Chirvasitu, Alexandru |
| author_facet | Chirvasitu, Alexandru |
| contents | Grade-$d$ measures on a $σ$-algebra $\mathcal{A}\subseteq 2^X$ over a set $X$ are generalizations of measures satisfying one of a hierarchy of weak additivity-type conditions initially introduced as interference operators in quantum mechanics. Every signed polymeasure $λ$ on $(X,\mathcal{A})^d$ produces a grade-$d$ measure as its diagonal $\widetildeλ(A):=λ(A,\cdots,A)$, and we prove that as soon as $d\ge 2$ measures (as opposed to polymeasures) do not suffice: the separate $σ$-additivity of a $λ$ producing $μ=\widetildeλ$ cannot, generally, be amplified to global $σ$-additivity. This amends a result in the literature, asserting the contrary in case $d=2$. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2508_14326 |
| institution | arXiv |
| publishDate | 2025 |
| record_format | arxiv |
| spellingShingle | Non-representable quantum measures Chirvasitu, Alexandru Quantum Physics Functional Analysis Quantum Algebra 28A35, 28A60, 47A07, 81Q65 Grade-$d$ measures on a $σ$-algebra $\mathcal{A}\subseteq 2^X$ over a set $X$ are generalizations of measures satisfying one of a hierarchy of weak additivity-type conditions initially introduced as interference operators in quantum mechanics. Every signed polymeasure $λ$ on $(X,\mathcal{A})^d$ produces a grade-$d$ measure as its diagonal $\widetildeλ(A):=λ(A,\cdots,A)$, and we prove that as soon as $d\ge 2$ measures (as opposed to polymeasures) do not suffice: the separate $σ$-additivity of a $λ$ producing $μ=\widetildeλ$ cannot, generally, be amplified to global $σ$-additivity. This amends a result in the literature, asserting the contrary in case $d=2$. |
| title | Non-representable quantum measures |
| topic | Quantum Physics Functional Analysis Quantum Algebra 28A35, 28A60, 47A07, 81Q65 |
| url | https://arxiv.org/abs/2508.14326 |