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MiS Preprint
75/2019
Simulating broken $PT$-symmetric Hamiltonian systems by weak measurement
By embedding a $\cal PT$-symmetric (pseudo-Hermitian) system into a large Hermitian one, we disclose the relations between $\cal{PT}$-symmetric quantum theory and weak measurement theory. We show that the weak measurement can give rise to the inner product structure of $\cal PT$-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 $\cal PT$-symmetric Hamiltonian systems can be effectively simulated by this weak measurement paradigm.
