Manifestation of Superposition and Coherence in $\mathcal{P}\mathcal{T}$-symmetry through the $\eta$-inner Product

Abstract

Through the $\eta$-inner product, we investigate $\mathcal{P}\mathcal{T}$-symmetric quantum mechanics from the viewpoint of superposition and coherence theory. It is argued that $\mathcal{P}\mathcal{T}$-symmetric quantum systems are endowed with stationary superposition or superposition-free properties. A physical interpretation of $\eta$-inner product in ${\mathbb{C}}^2$ is given through the Stokes parameters, showing the difference between broken and unbroken $\mathcal{P}\mathcal{T}$-symmetric quantum systems.

Add an author Ray-Kuang Lee

References in corpus (4)

• Making Sense of Non-Hermitian Hamiltonians
• The Naimark dilated PT-symmetric brachistochrone
• A resource theory of superposition
• Converting multilevel nonclassicality into genuine multipartite entanglement

Cited by in corpus (3)

• Simulating broken $\mathcal{P}\mathcal{T}$-symmetric Hamiltonian systems by weak measurement
• Minimal model of permutation symmetry in unsupervised learning
• Extracting the internal nonlocality from the dilated Hermiticity