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2025
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| Online Access: | https://doi.org/10.5281/zenodo.17427004 |
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| _version_ | 1866901695086198784 |
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| author | Mosetti, Renzo |
| author_facet | Mosetti, Renzo |
| contents | <p>The measurement postulate of quantum mechanics can be reformulated in the</p> <p>language of linear system theory. In classical control theory, observability is defined</p> <p>by the injectivity of the operator mapping initial states to observed outputs. We</p> <p>show that the projection postulate structurally violates this condition: spectral</p> <p><span>projectors are non-injective, hence the pre-measurement state is non-observable in</span></p> <p>the precise system-theoretic sense. While algebraically elementary, this highlights</p> <p>that loss of information in measurement is a structural feature of the theory. We</p> <p>illustrate this with a qubit measured in the <span>σ</span><span>z </span>basis and discuss implications for</p> <p><span>quantum tomography, decoherence, and interpretations of quantum mechanics.</span></p> |
| format | Recurso digital |
| id | zenodo_https___doi_org_10_5281_zenodo_17427004 |
| institution | Zenodo |
| language | |
| publishDate | 2025 |
| publisher | Zenodo |
| record_format | zenodo |
| spellingShingle | IQuantum measurement and the structural non-observability of states in linear system theory Mosetti, Renzo <p>The measurement postulate of quantum mechanics can be reformulated in the</p> <p>language of linear system theory. In classical control theory, observability is defined</p> <p>by the injectivity of the operator mapping initial states to observed outputs. We</p> <p>show that the projection postulate structurally violates this condition: spectral</p> <p><span>projectors are non-injective, hence the pre-measurement state is non-observable in</span></p> <p>the precise system-theoretic sense. While algebraically elementary, this highlights</p> <p>that loss of information in measurement is a structural feature of the theory. We</p> <p>illustrate this with a qubit measured in the <span>σ</span><span>z </span>basis and discuss implications for</p> <p><span>quantum tomography, decoherence, and interpretations of quantum mechanics.</span></p> |
| title | IQuantum measurement and the structural non-observability of states in linear system theory |
| url | https://doi.org/10.5281/zenodo.17427004 |