$\mathcal{P}\mathcal{T}$ symmetric evolution, coherence and violation of Leggett-Garg inequalities

Abstract

We report an unusual buildup of the quantum coherence in a qubit subjected to non-Hermitian evolution generated by a Parity-Time ($\mathcal{P}\mathcal{T}$) symmetric Hamiltonian, which is reinterpreted as a Hermitian system in a higher dimensional space using Naimark dilation. The coherence is found to be maximum about the exceptional points (EPs), i.e., the points of coalescence of the eigenvalues as well as the eigenvectors. The nontrivial physics about EPs has been observed in various systems, particularly in photonic systems. As a consequence of enhancement in coherence, the various formulations of Leggett-Garg inequality tests show maximal violation about the EPs.

References in corpus (7)

• PT-Symmetric Phonon Laser
• Reversing the Pump-Dependence of a Laser at an Exceptional Point
• Electromagnetically induced transparency controlled by a microwave field
• Maximally coherent mixed states: Complementarity between maximal coherence and mixedness
• Distinguishing quantum and classical transport through nanostructures
• Wigner's form of the Leggett-Garg inequality, No-Signalling in Time, and Unsharp Measurements
• Krein-Space Formulation of PT-Symmetry, CPT-Inner Products, and Pseudo-Hermiticity

Cited by in corpus (9)

• Essential role of quantum speed limit in violation of Leggett-Garg inequality across a PT-transition
• Experimental demonstration of the dynamics of quantum coherence evolving under a PT-symmetric Hamiltonian on an NMR quantum processor
• Non-Hermitian quantum walks and non-Markovianity: the coin-position interaction
• Extracting the internal nonlocality from the dilated Hermiticity
• Witnessing criticality in non-Hermitian systems via entropic uncertainty relation
• Lüders bounds of Leggett-Garg inequalities, $\mathcal{P}\mathcal{T}$- symmetric evolution and arrow-of-time
• Quantum violations of Lüders bound Leggett-Garg inequalities for quantum channel
• Fractional Conformal Map, Qubit Dynamics and the Leggett-Garg Inequality
• $\mathcal{P}\mathcal{T}-$Symmetric Two-Level Open Quantum Systems: Information Theoretic Facets