Entanglement of random hypergraph states
Random quantum states and operations are of fundamental and practical interests. In this work, we investigate the entanglement properties of random hypergraph states, which generalize the notion of graph states by applying generalized controlled-phase gates on an initial reference product state....
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| Main Authors: | , |
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| Other Authors: | |
| Format: | Article |
| Language: | English |
| Published: |
2023
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| Subjects: | |
| Online Access: | https://hdl.handle.net/10356/164310 |
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| Institution: | Nanyang Technological University |
| Language: | English |
| Summary: | Random quantum states and operations are of fundamental and practical
interests. In this work, we investigate the entanglement properties of random
hypergraph states, which generalize the notion of graph states by applying
generalized controlled-phase gates on an initial reference product state. In
particular, we study the two ensembles generated by random Controlled-Z(CZ) and
Controlled-Controlled-Z(CCZ) gates, respectively. By applying tensor network
representation and combinational counting, we analytically show that the
average subsystem purity and entanglement entropy for the two ensembles feature
the same volume law, but greatly differ in typicality, namely the purity
fluctuation is small and universal for the CCZ ensemble while it is large for
the CZ ensemble. We discuss the implications of these results for the onset of
entanglement complexity and quantum chaos. |
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