Conditional work statistics of quantum measurements
In this paper we introduce a definition for conditional energy changes due to general quantum measurements, as the change in the conditional energy evaluated before, and after, the measurement process. By imposing minimal physical requirements on these conditional energies, we show that the most gen...
| Main Authors: | , |
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| Format: | Article |
| Language: | English |
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Verein zur Förderung des Open Access Publizierens in den Quantenwissenschaften
2019-08-01
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| Series: | Quantum |
| Online Access: | https://quantum-journal.org/papers/q-2019-08-19-175/pdf/ |
| _version_ | 1818147621693292544 |
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| author | M. Hamed Mohammady Alessandro Romito |
| author_facet | M. Hamed Mohammady Alessandro Romito |
| author_sort | M. Hamed Mohammady |
| collection | DOAJ |
| description | In this paper we introduce a definition for conditional energy changes due to general quantum measurements, as the change in the conditional energy evaluated before, and after, the measurement process. By imposing minimal physical requirements on these conditional energies, we show that the most general expression for the conditional energy after the measurement is simply the expected value of the Hamiltonian given the post-measurement state. Conversely, the conditional energy before the measurement process is shown to be given by the real component of the weak value of the Hamiltonian. Our definition generalises well-known notions of distributions of internal energy change, such as that given by stochastic thermodynamics. By determining the conditional energy change of both system and measurement apparatus, we obtain the full conditional work statistics of quantum measurements, and show that this vanishes for all measurement outcomes if the measurement process conserves the total energy. Additionally, by incorporating the measurement process within a cyclic heat engine, we quantify the non-recoverable work due to measurements. This is shown to always be non-negative, thus satisfying the second law, and will be independent of the apparatus specifics for two classes of projective measurements. |
| first_indexed | 2024-12-11T12:38:10Z |
| format | Article |
| id | doaj.art-5dbf40d2069944778fde16d20e892e55 |
| institution | Directory Open Access Journal |
| issn | 2521-327X |
| language | English |
| last_indexed | 2024-12-11T12:38:10Z |
| publishDate | 2019-08-01 |
| publisher | Verein zur Förderung des Open Access Publizierens in den Quantenwissenschaften |
| record_format | Article |
| series | Quantum |
| spelling | doaj.art-5dbf40d2069944778fde16d20e892e552022-12-22T01:07:04ZengVerein zur Förderung des Open Access Publizierens in den QuantenwissenschaftenQuantum2521-327X2019-08-01317510.22331/q-2019-08-19-17510.22331/q-2019-08-19-175Conditional work statistics of quantum measurementsM. Hamed MohammadyAlessandro RomitoIn this paper we introduce a definition for conditional energy changes due to general quantum measurements, as the change in the conditional energy evaluated before, and after, the measurement process. By imposing minimal physical requirements on these conditional energies, we show that the most general expression for the conditional energy after the measurement is simply the expected value of the Hamiltonian given the post-measurement state. Conversely, the conditional energy before the measurement process is shown to be given by the real component of the weak value of the Hamiltonian. Our definition generalises well-known notions of distributions of internal energy change, such as that given by stochastic thermodynamics. By determining the conditional energy change of both system and measurement apparatus, we obtain the full conditional work statistics of quantum measurements, and show that this vanishes for all measurement outcomes if the measurement process conserves the total energy. Additionally, by incorporating the measurement process within a cyclic heat engine, we quantify the non-recoverable work due to measurements. This is shown to always be non-negative, thus satisfying the second law, and will be independent of the apparatus specifics for two classes of projective measurements.https://quantum-journal.org/papers/q-2019-08-19-175/pdf/ |
| spellingShingle | M. Hamed Mohammady Alessandro Romito Conditional work statistics of quantum measurements Quantum |
| title | Conditional work statistics of quantum measurements |
| title_full | Conditional work statistics of quantum measurements |
| title_fullStr | Conditional work statistics of quantum measurements |
| title_full_unstemmed | Conditional work statistics of quantum measurements |
| title_short | Conditional work statistics of quantum measurements |
| title_sort | conditional work statistics of quantum measurements |
| url | https://quantum-journal.org/papers/q-2019-08-19-175/pdf/ |
| work_keys_str_mv | AT mhamedmohammady conditionalworkstatisticsofquantummeasurements AT alessandroromito conditionalworkstatisticsofquantummeasurements |