Existence of Approximately Macroscopically Unique States
Fuente:
arXiv
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| Format: | Preprint |
| Publié: |
2024
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| _version_ | 1866911780137074688 |
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| author | Lin, Huaxin |
| author_facet | Lin, Huaxin |
| contents | Let $H$ be an infinite dimensional separable Hilbert space and $B(H)$ the C*-algebra of bounded operators on $H.$ Suppose that $T_1,T_2,..., T_n$ are self-adjoint operators in $B(H).$ We show that, if commutators $[T_i, T_j]$ are sufficiently small in norm, then ``Approximately Macroscopically Unique" states always exist for any values in a synthetic spectrum of the $n$-tuple of self-adjoint operators. This is achieved under the circumstance for which the $n$-tuple may not be approximated by commuting ones. This answers a question proposed by David Mumford for measurements in quantum theory. If commutators are not small in norm but small modulo compact operators, then ``Approximate Macroscopic Uniqueness" states also exist. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2402_12609 |
| institution | arXiv |
| publishDate | 2024 |
| record_format | arxiv |
| spellingShingle | Existence of Approximately Macroscopically Unique States Lin, Huaxin Operator Algebras Let $H$ be an infinite dimensional separable Hilbert space and $B(H)$ the C*-algebra of bounded operators on $H.$ Suppose that $T_1,T_2,..., T_n$ are self-adjoint operators in $B(H).$ We show that, if commutators $[T_i, T_j]$ are sufficiently small in norm, then ``Approximately Macroscopically Unique" states always exist for any values in a synthetic spectrum of the $n$-tuple of self-adjoint operators. This is achieved under the circumstance for which the $n$-tuple may not be approximated by commuting ones. This answers a question proposed by David Mumford for measurements in quantum theory. If commutators are not small in norm but small modulo compact operators, then ``Approximate Macroscopic Uniqueness" states also exist. |
| title | Existence of Approximately Macroscopically Unique States |
| topic | Operator Algebras |
| url | https://arxiv.org/abs/2402.12609 |