Environment-Assisted Invariance Does Not Necessitate Born’s Rule for Quantum Measurement
The argument of environment-assisted invariance (known as envariance) implying Born’s rule is widely used in models for quantum measurement to reason that they must yield the correct statistics, specifically for linear models. However, it has recently been shown that linear collapse models can never...
| Main Authors: | , |
|---|---|
| Format: | Article |
| Language: | English |
| Published: |
MDPI AG
2023-03-01
|
| Series: | Entropy |
| Subjects: | |
| Online Access: | https://www.mdpi.com/1099-4300/25/3/435 |
| _version_ | 1797611969152286720 |
|---|---|
| author | Lotte Mertens Jasper van Wezel |
| author_facet | Lotte Mertens Jasper van Wezel |
| author_sort | Lotte Mertens |
| collection | DOAJ |
| description | The argument of environment-assisted invariance (known as envariance) implying Born’s rule is widely used in models for quantum measurement to reason that they must yield the correct statistics, specifically for linear models. However, it has recently been shown that linear collapse models can never give rise to Born’s rule. Here, we address this apparent contradiction and point out an inconsistency in the assumptions underlying the arguments based on envariance. We use a construction in which the role of the measurement machine is made explicit and shows that the presence of envariance does <i>not</i> imply that every measurement will behave according to Born’s rule. Rather, it implies that every quantum state allows a measurement machine to be constructed, which yields Born’s rule when measuring that particular state. This resolves the paradox and is in agreement with the recent result of objective collapse models necessarily being nonlinear. |
| first_indexed | 2024-03-11T06:34:53Z |
| format | Article |
| id | doaj.art-52d0bc6b2c4c461f954c9813aabc6a22 |
| institution | Directory Open Access Journal |
| issn | 1099-4300 |
| language | English |
| last_indexed | 2024-03-11T06:34:53Z |
| publishDate | 2023-03-01 |
| publisher | MDPI AG |
| record_format | Article |
| series | Entropy |
| spelling | doaj.art-52d0bc6b2c4c461f954c9813aabc6a222023-11-17T10:56:10ZengMDPI AGEntropy1099-43002023-03-0125343510.3390/e25030435Environment-Assisted Invariance Does Not Necessitate Born’s Rule for Quantum MeasurementLotte Mertens0Jasper van Wezel1Institute for Theoretical Physics Amsterdam, University of Amsterdam, Science Park 904, 1098XH Amsterdam, The NetherlandsInstitute for Theoretical Physics Amsterdam, University of Amsterdam, Science Park 904, 1098XH Amsterdam, The NetherlandsThe argument of environment-assisted invariance (known as envariance) implying Born’s rule is widely used in models for quantum measurement to reason that they must yield the correct statistics, specifically for linear models. However, it has recently been shown that linear collapse models can never give rise to Born’s rule. Here, we address this apparent contradiction and point out an inconsistency in the assumptions underlying the arguments based on envariance. We use a construction in which the role of the measurement machine is made explicit and shows that the presence of envariance does <i>not</i> imply that every measurement will behave according to Born’s rule. Rather, it implies that every quantum state allows a measurement machine to be constructed, which yields Born’s rule when measuring that particular state. This resolves the paradox and is in agreement with the recent result of objective collapse models necessarily being nonlinear.https://www.mdpi.com/1099-4300/25/3/435quantum foundationsBorn’s ruleenvariance |
| spellingShingle | Lotte Mertens Jasper van Wezel Environment-Assisted Invariance Does Not Necessitate Born’s Rule for Quantum Measurement Entropy quantum foundations Born’s rule envariance |
| title | Environment-Assisted Invariance Does Not Necessitate Born’s Rule for Quantum Measurement |
| title_full | Environment-Assisted Invariance Does Not Necessitate Born’s Rule for Quantum Measurement |
| title_fullStr | Environment-Assisted Invariance Does Not Necessitate Born’s Rule for Quantum Measurement |
| title_full_unstemmed | Environment-Assisted Invariance Does Not Necessitate Born’s Rule for Quantum Measurement |
| title_short | Environment-Assisted Invariance Does Not Necessitate Born’s Rule for Quantum Measurement |
| title_sort | environment assisted invariance does not necessitate born s rule for quantum measurement |
| topic | quantum foundations Born’s rule envariance |
| url | https://www.mdpi.com/1099-4300/25/3/435 |
| work_keys_str_mv | AT lottemertens environmentassistedinvariancedoesnotnecessitatebornsruleforquantummeasurement AT jaspervanwezel environmentassistedinvariancedoesnotnecessitatebornsruleforquantummeasurement |