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Search Results (2)

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Keywords = pseudo-Hermitian symmetric space

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13 pages, 256 KB  
Article
Contact Metric Spaces and pseudo-Hermitian Symmetry
by Jong Taek Cho
Mathematics 2020, 8(9), 1583; https://doi.org/10.3390/math8091583 - 14 Sep 2020
Viewed by 3384
Abstract
We prove that a contact strongly pseudo-convex CR (Cauchy–Riemann) manifold M2n+1, n≥2, is locally pseudo-Hermitian symmetric and satisfies ∇ξh=μhϕ, μ∈R, if and only if M [...] Read more.
We prove that a contact strongly pseudo-convex CR (Cauchy–Riemann) manifold M2n+1, n≥2, is locally pseudo-Hermitian symmetric and satisfies ∇ξh=μhϕ, μ∈R, if and only if M is either a Sasakian locally ϕ-symmetric space or a non-Sasakian (k,μ)-space. When n=1, we prove a classification theorem of contact strongly pseudo-convex CR manifolds with pseudo-Hermitian symmetry. Full article
(This article belongs to the Special Issue Complex and Contact Manifolds)
17 pages, 967 KB  
Article
Efficient Quantum Simulation of an Anti-P-Pseudo-Hermitian Two-Level System
by Chao Zheng, Jin Tian, Daili Li, Jingwei Wen, Shijie Wei and Yansong Li
Entropy 2020, 22(8), 812; https://doi.org/10.3390/e22080812 - 24 Jul 2020
Cited by 12 | Viewed by 4114
Abstract
Besides Hermitian systems, quantum simulation has become a strong tool to investigate non-Hermitian systems, such as PT-symmetric, anti-PT-symmetric, and pseudo-Hermitian systems. In this work, we theoretically investigate quantum simulation of an anti-P-pseudo-Hermitian two-level system in different dimensional Hilbert spaces. In an [...] Read more.
Besides Hermitian systems, quantum simulation has become a strong tool to investigate non-Hermitian systems, such as PT-symmetric, anti-PT-symmetric, and pseudo-Hermitian systems. In this work, we theoretically investigate quantum simulation of an anti-P-pseudo-Hermitian two-level system in different dimensional Hilbert spaces. In an arbitrary phase, we find that six dimensions are the minimum to construct the anti-P-pseudo-Hermitian two-level subsystem, and it has a higher success probability than using eight dimensions. We find that the dimensions can be reduced further to four or two when the system is in the anti-PT-symmetric or Hermitian phase, respectively. Both qubit-qudit hybrid and pure-qubit systems are able to realize the simulation, enabling experimental implementations in the near future. Full article
(This article belongs to the Special Issue Quantum Information Processing)
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