Distance-based resource quantification for sets of quantum measurements
The advantage that quantum systems provide for certain quantum information processing tasks over their classical counterparts can be quantified within the general framework of resource theories. Certain distance functions between quantum states have successfully been used to quantify resources like...
| Main Authors: | , , , |
|---|---|
| Format: | Article |
| Language: | English |
| Published: |
Verein zur Förderung des Open Access Publizierens in den Quantenwissenschaften
2023-05-01
|
| Series: | Quantum |
| Online Access: | https://quantum-journal.org/papers/q-2023-05-15-1003/pdf/ |
| _version_ | 1797826733734363136 |
|---|---|
| author | Lucas Tendick Martin Kliesch Hermann Kampermann Dagmar Bruß |
| author_facet | Lucas Tendick Martin Kliesch Hermann Kampermann Dagmar Bruß |
| author_sort | Lucas Tendick |
| collection | DOAJ |
| description | The advantage that quantum systems provide for certain quantum information processing tasks over their classical counterparts can be quantified within the general framework of resource theories. Certain distance functions between quantum states have successfully been used to quantify resources like entanglement and coherence. Perhaps surprisingly, such a distance-based approach has not been adopted to study resources of quantum measurements, where other geometric quantifiers are used instead. Here, we define distance functions between sets of quantum measurements and show that they naturally induce resource monotones for convex resource theories of measurements. By focusing on a distance based on the diamond norm, we establish a hierarchy of measurement resources and derive analytical bounds on the incompatibility of any set of measurements. We show that these bounds are tight for certain projective measurements based on mutually unbiased bases and identify scenarios where different measurement resources attain the same value when quantified by our resource monotone. Our results provide a general framework to compare distance-based resources for sets of measurements and allow us to obtain limitations on Bell-type experiments. |
| first_indexed | 2024-04-09T12:37:00Z |
| format | Article |
| id | doaj.art-e6bd6aca4374405185e6320167d9d769 |
| institution | Directory Open Access Journal |
| issn | 2521-327X |
| language | English |
| last_indexed | 2024-04-09T12:37:00Z |
| publishDate | 2023-05-01 |
| publisher | Verein zur Förderung des Open Access Publizierens in den Quantenwissenschaften |
| record_format | Article |
| series | Quantum |
| spelling | doaj.art-e6bd6aca4374405185e6320167d9d7692023-05-15T12:03:44ZengVerein zur Förderung des Open Access Publizierens in den QuantenwissenschaftenQuantum2521-327X2023-05-017100310.22331/q-2023-05-15-100310.22331/q-2023-05-15-1003Distance-based resource quantification for sets of quantum measurementsLucas TendickMartin KlieschHermann KampermannDagmar BrußThe advantage that quantum systems provide for certain quantum information processing tasks over their classical counterparts can be quantified within the general framework of resource theories. Certain distance functions between quantum states have successfully been used to quantify resources like entanglement and coherence. Perhaps surprisingly, such a distance-based approach has not been adopted to study resources of quantum measurements, where other geometric quantifiers are used instead. Here, we define distance functions between sets of quantum measurements and show that they naturally induce resource monotones for convex resource theories of measurements. By focusing on a distance based on the diamond norm, we establish a hierarchy of measurement resources and derive analytical bounds on the incompatibility of any set of measurements. We show that these bounds are tight for certain projective measurements based on mutually unbiased bases and identify scenarios where different measurement resources attain the same value when quantified by our resource monotone. Our results provide a general framework to compare distance-based resources for sets of measurements and allow us to obtain limitations on Bell-type experiments.https://quantum-journal.org/papers/q-2023-05-15-1003/pdf/ |
| spellingShingle | Lucas Tendick Martin Kliesch Hermann Kampermann Dagmar Bruß Distance-based resource quantification for sets of quantum measurements Quantum |
| title | Distance-based resource quantification for sets of quantum measurements |
| title_full | Distance-based resource quantification for sets of quantum measurements |
| title_fullStr | Distance-based resource quantification for sets of quantum measurements |
| title_full_unstemmed | Distance-based resource quantification for sets of quantum measurements |
| title_short | Distance-based resource quantification for sets of quantum measurements |
| title_sort | distance based resource quantification for sets of quantum measurements |
| url | https://quantum-journal.org/papers/q-2023-05-15-1003/pdf/ |
| work_keys_str_mv | AT lucastendick distancebasedresourcequantificationforsetsofquantummeasurements AT martinkliesch distancebasedresourcequantificationforsetsofquantummeasurements AT hermannkampermann distancebasedresourcequantificationforsetsofquantummeasurements AT dagmarbruß distancebasedresourcequantificationforsetsofquantummeasurements |