Wave–Particle–Entanglement–Ignorance Complementarity for General Bipartite Systems
Wave–particle duality as the defining characteristic of quantum objects is a typical example of the principle of complementarity. The wave–particle–entanglement (WPE) complementarity, initially developed for two-qubit systems, is an extended form of complementarity that combines wave–particle dualit...
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MDPI AG
2020-07-01
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| author | Wei Wu Jin Wang |
| author_facet | Wei Wu Jin Wang |
| author_sort | Wei Wu |
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| description | Wave–particle duality as the defining characteristic of quantum objects is a typical example of the principle of complementarity. The wave–particle–entanglement (WPE) complementarity, initially developed for two-qubit systems, is an extended form of complementarity that combines wave–particle duality with a previously missing ingredient, quantum entanglement. For two-qubit systems in mixed states, the WPE complementarity was further completed by adding yet another piece that characterizes ignorance, forming the wave–particle–entanglement–ignorance (WPEI) complementarity. A general formulation of the WPEI complementarity can not only shed new light on fundamental problems in quantum mechanics, but can also have a wide range of experimental and practical applications in quantum-mechanical settings. The purpose of this study is to establish the WPEI complementarity for general multi-dimensional bipartite systems in pure or mixed states, and extend its range of applications to incorporate hierarchical and infinite-dimensional bipartite systems. The general formulation is facilitated by well-motivated generalizations of the relevant quantities. When faced with different directions of extensions to take, our guiding principle is that the formulated complementarity should be as simple and powerful as possible. We find that the generalized form of the WPEI complementarity contains unequal-weight averages reflecting the difference in the subsystem dimensions, and that the tangle, instead of the squared concurrence, serves as a more suitable entanglement measure in the general scenario. Two examples, a finite-dimensional bipartite system in mixed states and an infinite-dimensional bipartite system in pure states, are studied in detail to illustrate the general formalism. We also discuss our results in connection with some previous work. The WPEI complementarity for general finite-dimensional bipartite systems may be tested in multi-beam interference experiments, while the second example we studied may facilitate future experimental investigations on complementarity in infinite-dimensional bipartite systems. |
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| language | English |
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| spelling | doaj.art-b412967528f8439c91a1ff4a772f0ad12023-11-20T07:48:54ZengMDPI AGEntropy1099-43002020-07-0122881310.3390/e22080813Wave–Particle–Entanglement–Ignorance Complementarity for General Bipartite SystemsWei Wu0Jin Wang1State Key Laboratory of Electroanalytical Chemistry, Changchun Institute of Applied Chemistry, Chinese Academy of Sciences, Changchun 130022, ChinaDepartment of Chemistry, State University of New York at Stony Brook, Stony Brook, NY 11794, USAWave–particle duality as the defining characteristic of quantum objects is a typical example of the principle of complementarity. The wave–particle–entanglement (WPE) complementarity, initially developed for two-qubit systems, is an extended form of complementarity that combines wave–particle duality with a previously missing ingredient, quantum entanglement. For two-qubit systems in mixed states, the WPE complementarity was further completed by adding yet another piece that characterizes ignorance, forming the wave–particle–entanglement–ignorance (WPEI) complementarity. A general formulation of the WPEI complementarity can not only shed new light on fundamental problems in quantum mechanics, but can also have a wide range of experimental and practical applications in quantum-mechanical settings. The purpose of this study is to establish the WPEI complementarity for general multi-dimensional bipartite systems in pure or mixed states, and extend its range of applications to incorporate hierarchical and infinite-dimensional bipartite systems. The general formulation is facilitated by well-motivated generalizations of the relevant quantities. When faced with different directions of extensions to take, our guiding principle is that the formulated complementarity should be as simple and powerful as possible. We find that the generalized form of the WPEI complementarity contains unequal-weight averages reflecting the difference in the subsystem dimensions, and that the tangle, instead of the squared concurrence, serves as a more suitable entanglement measure in the general scenario. Two examples, a finite-dimensional bipartite system in mixed states and an infinite-dimensional bipartite system in pure states, are studied in detail to illustrate the general formalism. We also discuss our results in connection with some previous work. The WPEI complementarity for general finite-dimensional bipartite systems may be tested in multi-beam interference experiments, while the second example we studied may facilitate future experimental investigations on complementarity in infinite-dimensional bipartite systems.https://www.mdpi.com/1099-4300/22/8/813complementaritywave–particle dualityentanglementpredictabilityvisibility |
| spellingShingle | Wei Wu Jin Wang Wave–Particle–Entanglement–Ignorance Complementarity for General Bipartite Systems Entropy complementarity wave–particle duality entanglement predictability visibility |
| title | Wave–Particle–Entanglement–Ignorance Complementarity for General Bipartite Systems |
| title_full | Wave–Particle–Entanglement–Ignorance Complementarity for General Bipartite Systems |
| title_fullStr | Wave–Particle–Entanglement–Ignorance Complementarity for General Bipartite Systems |
| title_full_unstemmed | Wave–Particle–Entanglement–Ignorance Complementarity for General Bipartite Systems |
| title_short | Wave–Particle–Entanglement–Ignorance Complementarity for General Bipartite Systems |
| title_sort | wave particle entanglement ignorance complementarity for general bipartite systems |
| topic | complementarity wave–particle duality entanglement predictability visibility |
| url | https://www.mdpi.com/1099-4300/22/8/813 |
| work_keys_str_mv | AT weiwu waveparticleentanglementignorancecomplementarityforgeneralbipartitesystems AT jinwang waveparticleentanglementignorancecomplementarityforgeneralbipartitesystems |