Simulating broken $\cal PT$-symmetric Hamiltonian systems by weak measurement

TL;DR

This paper demonstrates how weak measurement techniques can simulate broken $ ext{PT}$-symmetric Hamiltonian systems by embedding them into larger Hermitian systems, revealing new links between $ ext{PT}$ symmetry and quantum measurement.

Contribution

It introduces a method to simulate broken $ ext{PT}$-symmetric systems using weak measurement amplification within a Hermitian embedding, connecting $ ext{PT}$ symmetry with measurement theory.

Findings

Weak measurement can effectively simulate broken $ ext{PT}$-symmetric Hamiltonians.

Embedding $ ext{PT}$-symmetric systems into Hermitian systems reveals their relation to weak measurement.

The approach enables experimental simulation of non-Hermitian quantum systems.

Abstract

By embedding a $\cal PT$-symmetric (pseudo-Hermitian) system into a large Hermitian one, we disclose the relations between $\cal{PT}$-symmetric Hamiltonians and weak measurement theory. We show that the amplification effect in weak measurement on a conventional quantum system can be used to effectively simulate a local broken $\cal PT$-symmetric Hamiltonian system, with the pre-selected state in the $\cal PT$-symmetric Hamiltonian system and its post-selected state resident in the dilated Hamiltonian system.