Searching for exceptional points and inspecting non-contractivity of trace distance in (anti-)$\mathcal{P}\mathcal{T}-$symmetric systems

Abstract

Non-Hermitian systems with parity-time ($\mathcal{P}\mathcal{T}$) symmetry and anti-$\mathcal{P}\mathcal{T}$ symmetry give rise to exceptional points (EPs) with intriguing properties related to, e.g., chiral transport and enhanced sensitivity, due to the coalescence of eigenvectors. In this paper, we propose a powerful and easily computable tool, based on the Hilbert-Schmidt speed (HSS), which does not require the diagonalization of the evolved density matrix, to detect exactly the EPs and hence the critical behavior of the (anti-)$\mathcal{P}\mathcal{T}-$symmetric systems, especially high-dimensional ones. Our theoretical predictions, made without the need for modification of the Hilbert space, which is performed by diagonalizing one of the observables, are completely consistent with results extracted from recent experiments studying the criticality in (anti-)$\mathcal{P}\mathcal{T}-$symmetric systems. Nevertheless, not modifying the Hilbert space of the non-Hermitian system, we find that the trace distance, a measure of distinguishability of two arbitrary quantum states, whose dynamics is known as a faithful witness of non-Markovianity in Hermitian systems, may be non-contractive under the non-Hermitian evolution of the system. Therefore, it lacks one of the most important characteristics which must be met by any standard witness of non-Markovianity.

References in corpus (25)

• The physics of exceptional points
• Quantum Non-Markovianity: Characterization, Quantification and Detection
• Quantum trajectories and open many-body quantum systems
• Non-Markovian effects on the dynamics of entanglement
• PT-Symmetric Phonon Laser
• Observation of parity-time symmetry breaking in a single spin system
• Faster than Hermitian Quantum Mechanics
• Optomechanically-Induced Transparency in partiy-time-symmetric microresonators
• A non-Hermitian $PT-$symmetric Bose-Hubbard model: eigenvalue rings from unfolding higher-order exceptional points
• Shortcuts to Adiabaticity for the Quantum Rabi Model: Efficient Generation of Giant Entangled cat States via Parametric Amplification
• Mixed-state evolution in the presence of gain and loss
• Experimental on-demand recovery of entanglement by local operations within non-Markovian dynamics
• Witness for initial system-environment correlations in open system dynamics
• Harnessing non-Markovian quantum memory by environmental coupling
• Liouvillian exceptional points of any order in dissipative linear bosonic systems: Coherence functions and switching between $\mathcal{P}\mathcal{T}$ and anti-$\mathcal{P}\mathcal{T}$ symmetries
• Scully-Lamb quantum laser model for parity-time-symmetric whispering-gallery microcavities: Gain saturation effects and non-reciprocity
• Exceptional points of any order in a single, lossy, waveguide beamsplitter by photon-number-resolved detection
• Quantum simulation of parity-time symmetry breaking with a superconducting quantum processor
• Facets of quantum information under non-Markovian evolution
• Quantum information dynamics in a high-dimensional parity-time-symmetric system
• Hidden entanglement in the presence of random telegraph dephasing noise
• Trace distance from the viewpoint of quantum operation techniques
• Improving shortcuts to non-Hermitian adiabaticity for fast population transfer in open quantum systems
• Simulating non-Hermitian dynamics of a multi-spin quantum system and an emergent central spin model
• Cramér-Rao bound and quantum parameter estimation with non-Hermitian systems

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• Witnessing global memory effects of multiqubit correlated noisy channels by Hilbert-Schmidt speed
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