Ideal Projective Measurements Have Infinite Resource Costs
We show that it is impossible to perform ideal projective measurements on quantum systems using finite resources. We identify three fundamental features of ideal projective measurements and show that when limited by finite resources only one of these features can be salvaged. Our framework is genera...
| Main Authors: | , , |
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| Format: | Article |
| Language: | English |
| Published: |
Verein zur Förderung des Open Access Publizierens in den Quantenwissenschaften
2020-01-01
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| Series: | Quantum |
| Online Access: | https://quantum-journal.org/papers/q-2020-01-13-222/pdf/ |
| _version_ | 1818014459998765056 |
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| author | Yelena Guryanova Nicolai Friis Marcus Huber |
| author_facet | Yelena Guryanova Nicolai Friis Marcus Huber |
| author_sort | Yelena Guryanova |
| collection | DOAJ |
| description | We show that it is impossible to perform ideal projective measurements on quantum systems using finite resources. We identify three fundamental features of ideal projective measurements and show that when limited by finite resources only one of these features can be salvaged. Our framework is general enough to accommodate any system and measuring device (pointer) models, but for illustration we use an explicit model of an $N$-particle pointer. For a pointer that perfectly reproduces the statistics of the system, we provide tight analytic expressions for the energy cost of performing the measurement. This cost may be broken down into two parts. First, the cost of preparing the pointer in a suitable state, and second, the cost of a global interaction between the system and pointer in order to correlate them. Our results show that, even under the assumption that the interaction can be controlled perfectly, achieving perfect correlation is infinitely expensive. We provide protocols for achieving optimal correlation given finite resources for the most general system and pointer Hamiltonians, phrasing our results as fundamental bounds in terms of the dimensions of these systems. |
| first_indexed | 2024-04-14T06:44:53Z |
| format | Article |
| id | doaj.art-87a00b4a8d8547f6be551b14f7e08b4d |
| institution | Directory Open Access Journal |
| issn | 2521-327X |
| language | English |
| last_indexed | 2024-04-14T06:44:53Z |
| publishDate | 2020-01-01 |
| publisher | Verein zur Förderung des Open Access Publizierens in den Quantenwissenschaften |
| record_format | Article |
| series | Quantum |
| spelling | doaj.art-87a00b4a8d8547f6be551b14f7e08b4d2022-12-22T02:07:12ZengVerein zur Förderung des Open Access Publizierens in den QuantenwissenschaftenQuantum2521-327X2020-01-01422210.22331/q-2020-01-13-22210.22331/q-2020-01-13-222Ideal Projective Measurements Have Infinite Resource CostsYelena GuryanovaNicolai FriisMarcus HuberWe show that it is impossible to perform ideal projective measurements on quantum systems using finite resources. We identify three fundamental features of ideal projective measurements and show that when limited by finite resources only one of these features can be salvaged. Our framework is general enough to accommodate any system and measuring device (pointer) models, but for illustration we use an explicit model of an $N$-particle pointer. For a pointer that perfectly reproduces the statistics of the system, we provide tight analytic expressions for the energy cost of performing the measurement. This cost may be broken down into two parts. First, the cost of preparing the pointer in a suitable state, and second, the cost of a global interaction between the system and pointer in order to correlate them. Our results show that, even under the assumption that the interaction can be controlled perfectly, achieving perfect correlation is infinitely expensive. We provide protocols for achieving optimal correlation given finite resources for the most general system and pointer Hamiltonians, phrasing our results as fundamental bounds in terms of the dimensions of these systems.https://quantum-journal.org/papers/q-2020-01-13-222/pdf/ |
| spellingShingle | Yelena Guryanova Nicolai Friis Marcus Huber Ideal Projective Measurements Have Infinite Resource Costs Quantum |
| title | Ideal Projective Measurements Have Infinite Resource Costs |
| title_full | Ideal Projective Measurements Have Infinite Resource Costs |
| title_fullStr | Ideal Projective Measurements Have Infinite Resource Costs |
| title_full_unstemmed | Ideal Projective Measurements Have Infinite Resource Costs |
| title_short | Ideal Projective Measurements Have Infinite Resource Costs |
| title_sort | ideal projective measurements have infinite resource costs |
| url | https://quantum-journal.org/papers/q-2020-01-13-222/pdf/ |
| work_keys_str_mv | AT yelenaguryanova idealprojectivemeasurementshaveinfiniteresourcecosts AT nicolaifriis idealprojectivemeasurementshaveinfiniteresourcecosts AT marcushuber idealprojectivemeasurementshaveinfiniteresourcecosts |