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| Main Authors: | , |
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| Format: | Preprint |
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2024
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| Online Access: | https://arxiv.org/abs/2401.17537 |
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| _version_ | 1866929480069545984 |
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| author | Steiner, Michael Rendell, Ronald |
| author_facet | Steiner, Michael Rendell, Ronald |
| contents | Complementary relationships exist regarding interference properties of particles such as pattern visibility, predictability and distinguishability. Additionally, relationships are known between information gain $G$ and measurement disturbance $F$ for entangled spin pairs. The question of whether a similar complementary relationship between entanglement and measurement occurs is examined herein. For qubit systems, both measurement on a single system and measurements on a bipartite system are considered in regards to the entanglement. It is proven that $\overline{E}+D\le 1$ holds where $\overline{E}$ is the average entanglement after a measurement is made and for which $D$ is a measure of the measurement disturbance of a single measurement. For measurements on a bipartite system shared by Alice and Bob ,it is shown that $\overline{E}+\overline{G}\le 1$ where $\overline{G}$ is the maximum average information gain regarding Alice's result that can be obtained by Bob. These results are generalized for arbitrary initial mixed states and as well to non-Hermitian operators. In the case of maximally entangled initial states, it is found that $D\le E_{L}$ and $\overline{G}\le E_{L}$ where $E_{L}$ is the entanglement loss due to measurement by Alice. We conclude that the amount of disturbance and information gain that one can gain are strictly limited by entanglement. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2401_17537 |
| institution | arXiv |
| publishDate | 2024 |
| record_format | arxiv |
| spellingShingle | Complementary Relationships between Entanglement and Measurement Steiner, Michael Rendell, Ronald Quantum Physics Complementary relationships exist regarding interference properties of particles such as pattern visibility, predictability and distinguishability. Additionally, relationships are known between information gain $G$ and measurement disturbance $F$ for entangled spin pairs. The question of whether a similar complementary relationship between entanglement and measurement occurs is examined herein. For qubit systems, both measurement on a single system and measurements on a bipartite system are considered in regards to the entanglement. It is proven that $\overline{E}+D\le 1$ holds where $\overline{E}$ is the average entanglement after a measurement is made and for which $D$ is a measure of the measurement disturbance of a single measurement. For measurements on a bipartite system shared by Alice and Bob ,it is shown that $\overline{E}+\overline{G}\le 1$ where $\overline{G}$ is the maximum average information gain regarding Alice's result that can be obtained by Bob. These results are generalized for arbitrary initial mixed states and as well to non-Hermitian operators. In the case of maximally entangled initial states, it is found that $D\le E_{L}$ and $\overline{G}\le E_{L}$ where $E_{L}$ is the entanglement loss due to measurement by Alice. We conclude that the amount of disturbance and information gain that one can gain are strictly limited by entanglement. |
| title | Complementary Relationships between Entanglement and Measurement |
| topic | Quantum Physics |
| url | https://arxiv.org/abs/2401.17537 |