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| Main Authors: | , |
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| Format: | Preprint |
| Published: |
2022
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| Subjects: | |
| Online Access: | https://arxiv.org/abs/2205.01262 |
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| _version_ | 1866909438671060992 |
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| author | Lancaster, Jarrett L. Palladino, Nicholas M. |
| author_facet | Lancaster, Jarrett L. Palladino, Nicholas M. |
| contents | A recent experiment testing the necessity of complex numbers in the standard formulation of quantum theory is recreated using IBM quantum computers. To motivate the experiment, we present a basic construction for real-valued quantum theory. The real-valued description is shown to predict correlations identical to those of complex-valued quantum mechanics for two types of Bell tests based on the Clauser-Horne-Shimony-Holt (CHSH) inequality. A slight modification to one test, however, results in different predictions for the real- and complex-valued constructions. While noisier devices are incapable of delivering convincing results, it is shown that certain devices possess sufficiently small error rates to falsify real-valued formulations of quantum theory for composite states. The results obtained with quantum computers are consistent with published experiments. This work demonstrates the feasibility of using freely-available quantum devices to explore foundational features of quantum mechanics with minimal technical expertise. Accordingly, this treatment could inspire novel projects for undergraduate students taking a course on quantum mechanics. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2205_01262 |
| institution | arXiv |
| publishDate | 2022 |
| record_format | arxiv |
| spellingShingle | Testing the necessity of complex numbers in traditional quantum theory with quantum computers Lancaster, Jarrett L. Palladino, Nicholas M. Quantum Physics A recent experiment testing the necessity of complex numbers in the standard formulation of quantum theory is recreated using IBM quantum computers. To motivate the experiment, we present a basic construction for real-valued quantum theory. The real-valued description is shown to predict correlations identical to those of complex-valued quantum mechanics for two types of Bell tests based on the Clauser-Horne-Shimony-Holt (CHSH) inequality. A slight modification to one test, however, results in different predictions for the real- and complex-valued constructions. While noisier devices are incapable of delivering convincing results, it is shown that certain devices possess sufficiently small error rates to falsify real-valued formulations of quantum theory for composite states. The results obtained with quantum computers are consistent with published experiments. This work demonstrates the feasibility of using freely-available quantum devices to explore foundational features of quantum mechanics with minimal technical expertise. Accordingly, this treatment could inspire novel projects for undergraduate students taking a course on quantum mechanics. |
| title | Testing the necessity of complex numbers in traditional quantum theory with quantum computers |
| topic | Quantum Physics |
| url | https://arxiv.org/abs/2205.01262 |