Simulating broken $\mathcal{P}\mathcal{T}$-symmetric Hamiltonian systems by weak measurement

Abstract

By embedding a $\mathcal{P}\mathcal{T}$-symmetric (pseudo-Hermitian) system into a large Hermitian one, we disclose the relations between $\mathcal{P}\mathcal{T}$-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 $\mathcal{P}\mathcal{T}$-symmetric Hamiltonian system, with the pre-selected state in the $\mathcal{P}\mathcal{T}$-symmetric Hamiltonian system and its post-selected state resident in the dilated Hamiltonian system.

4 pages; with Supplemental Material

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• Faster than Hermitian Quantum Mechanics
• The ODE/IM Correspondence
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• Precision frequency measurements with interferometric weak values
• The Naimark dilated PT-symmetric brachistochrone
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• Stable States with Non-Zero Entropy under Broken $\mathcal{P}\mathcal{T}$-Symmetry
• Direct Characterization of Quantum Measurements using Weak Values
• Two-qubit entanglement generation through non-Hermitian Hamiltonians induced by repeated measurements on an ancilla
• Quantum parameter estimation of non-Hermitian systems with optimal measurements
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• Algebraic maximum violation of the Leggett-Garg inequality in a two-level system under PT symmetric dynamics
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• Extracting the internal nonlocality from the dilated Hermiticity
• Markovian to non-Markovian phase transition in the operator dynamics of a mobile impurity
• Necessary condition for information transfer under simulated parity-time-symmetric evolution
• Quantifying Algebraic Asymmetry of Hamiltonian Systems