Simulating broken PT-symmetric Hamiltonian systems by weak measurement
Minyi Huang, Ray-Kuang Lee, Lijian Zhang, Shao-Ming Fei, and Junde Wu
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Submission date: 21. Aug. 2019
published in: Physical review letters, 123 (2019) 8, art-no. 080404
DOI number (of the published article): 10.1103/PhysRevLett.123.080404
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By embedding a 𝒫𝒯 -symmetric (pseudo-Hermitian) system into a large Hermitian one, we disclose the relations between 𝒫𝒯 -symmetric quantum theory and weak measurement theory. We show that the weak measurement can give rise to the inner product structure of 𝒫𝒯 -symmetric systems, with the pre-selected state and its post-selected state resident in the dilated conventional system. Typically in quantum information theory, by projecting out the irrelevant degrees and projecting onto the subspace, even local broken 𝒫𝒯 -symmetric Hamiltonian systems can be eﬀectively simulated by this weak measurement paradigm.