Observing geometry of quantum states in a three-level system
| Autor: | Nung-Sing Sze, Yiu-Tung Poon, Bei Zeng, Jie Xie, Lijian Zhang, Huichao Xu, Kaimin Zheng, Ping Xu, Aonan Zhang, Ningping Cao |
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| Rok vydání: | 2019 |
| Předmět: |
Physics
Bloch sphere Quantum Physics Euclidean space General Physics and Astronomy FOS: Physical sciences Geometry Observable Quantum phases 01 natural sciences symbols.namesake Quantum state Qubit 0103 physical sciences symbols 010306 general physics Hamiltonian (quantum mechanics) Quantum Physics (quant-ph) Quantum |
| DOI: | 10.48550/arxiv.1909.05463 |
| Popis: | In quantum mechanics, geometry has been demonstrated as a useful tool for inferring non-classical behaviors and exotic properties of quantum systems. One standard approach to illustrate the geometry of quantum systems is to project the quantum state space to the Euclidean space via measurements of observables on the system. Despite the great success of this method in studying two-level quantum systems (qubits) with the celebrated Bloch sphere representation, there is always the difficulty to reveal the geometry of multi-dimensional quantum systems. Here we report the first experiment measuring the geometry of such projections beyond the qubit. Specifically, we observe the joint numerical ranges (JNRs) of a triple of observables in a three-level photonic system, providing complete classification of the JNRs. We further show that the geometry of different classes reveal ground-state degeneracies of a Hamiltonian as a linear combination of the observables, which is related to quantum phases in the thermodynamic limit. Our results offer a versatile geometric approach for exploring the properties of higher-dimensional quantum systems. Comment: 14 pages, 7 figures |
| Databáze: | OpenAIRE |
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