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 (100)

• Double-slit photoelectron interference in strong-field ionization of the neon dimer
• Experimental loophole-free violation of a Bell inequality using entangled electron spins separated by 1.3 km
• Nonreciprocal light transmission in parity-time-symmetric whispering-gallery microcavities
• Unidirectional Invisibility induced by PT-Symmetric Periodic Structures
• Complex Extension of Quantum Mechanics
• Significant-loophole-free test of Bell's theorem with entangled photons
• Measure for the Degree of Non-Markovian Behavior of Quantum Processes in Open Systems
• The physics of exceptional points
• Non-Markovian dynamics in open quantum systems
• A strong loophole-free test of local realism
• Dynamically encircling exceptional points in a waveguide: asymmetric mode switching from the breakdown of adiabaticity
• Shortcuts to adiabaticity: concepts, methods, and applications
• Entanglement and non-Markovianity of quantum evolutions
• Quantum Non-Markovianity: Characterization, Quantification and Detection
• Topological energy transfer in an optomechanical system with exceptional points
• Quantum trajectories and open many-body quantum systems
• Experimental Study of Active LRC Circuits with PT-Symmetries
• Spawning rings of exceptional points out of Dirac cones
• Non-Markovian effects on the dynamics of entanglement
• Quantum Fisher information matrix and multiparameter estimation
• PT-Symmetric Phonon Laser
• Observation of non-Hermitian degeneracies in a chaotic exciton-polariton billiard
• Observation of parity-time symmetry breaking transitions in a dissipative Floquet system of ultracold atoms
• Quantum Fisher Information Flow in Non-Markovian Processes of Open Systems
• Measure for the Non-Markovianity of Quantum Processes
• Anti-Parity-Time Symmetric Optics via Flying Atoms
• Metrology with $\mathcal{P}\mathcal{T}$-symmetric cavities: Enhanced sensitivity near the $\mathcal{P}\mathcal{T}$-phase transition
• Observation of parity-time symmetry breaking in a single spin system
• Faster than Hermitian Quantum Mechanics
• Quantum state tomography across the exceptional point in a single dissipative qubit
• Must a Hamiltonian be Hermitian?
• General non-Markovian dynamics of open quantum systems
• Optomechanically-Induced Transparency in partiy-time-symmetric microresonators
• Quantum Noise Theory of Exceptional Point Sensors
• Dynamics of quantum correlations in two-qubit systems within non-Markovian environments
• A non-Hermitian $PT-$symmetric Bose-Hubbard model: eigenvalue rings from unfolding higher-order exceptional points
• Information Retrieval and Criticality in Parity-Time-Symmetric Systems
• Antisymmetric PT-photonic structures with balanced positive and negative index materials
• Shortcuts to Adiabaticity for the Quantum Rabi Model: Efficient Generation of Giant Entangled cat States via Parametric Amplification
• Observation of critical phenomena in parity-time-symmetric quantum dynamics
• Entanglement measures and the Hilbert-Schmidt distance
• Revival of quantum correlations without system-environment back-action
• Markovian and non-Markovian dynamics in quantum and classical systems
• Mixed-state evolution in the presence of gain and loss
• Breaking Anti-$\mathcal{P}\mathcal{T}$ Symmetry by Spinning a Resonator
• Local PT symmetry violates the no-signaling principle
• PT symmetric square well
• Witness for initial system-environment correlations in open system dynamics
• Experimental on-demand recovery of entanglement by local operations within non-Markovian dynamics
• Introduction to quantum Fisher information
• Effective spontaneous PT-symmetry breaking in hybridized metamaterials
• Giant nonlinearity via breaking parity-time symmetry: a route to low-threshold phonon diodes
• Non-Hermitian Hamiltonians and no-go theorems in quantum information
• Exceptional Points in Random-Defect Phonon Lasers
• Linear Optics Simulation of Non-Markovian Quantum Dynamics
• Recovering Entanglement by Local Operations
• Experimental observation of weak non-Markovianity
• Quantifying Non-Markovianity with Temporal Steering
• $\mathcal{P}\mathcal{T}$-symmetric circuit-QED
• Generalized trace distance measure connecting quantum and classical non-Markovianity
• Harnessing non-Markovian quantum memory by environmental coupling
• Distance between quantum states in presence of initial qubit-environment correlations: a comparative study
• Lecture Notes on the Theory of Open Quantum Systems
• Distributed correlations and information flows within a hybrid multipartite quantum-classical system
• Consistency of PT-symmetric quantum mechanics
• Shortcuts to Adiabaticity in Driven Open Quantum Systems: Balanced Gain and Loss and Non-Markovian Evolution
• 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
• Protecting entanglement by adjusting the velocities of moving qubits inside non-Markovian environments
• Statistical speed of quantum states: Generalized quantum Fisher information and Schatten speed
• Scully-Lamb quantum laser model for parity-time-symmetric whispering-gallery microcavities: Gain saturation effects and non-reciprocity
• High-order exceptional points in supersymmetric arrays
• Mean-field validity in a dissipative critical system: Liouvillian gap, $\mathbb{PT}$-symmetric antigap, and permutational symmetry in the $XYZ$ model
• 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
• Spin Squeezing under Non-Markovian Channels by Hierarchy Equation Method
• Experimental observation of information flow in the anti-$\mathcal{P}\mathcal{T}$-symmetric system
• Observing information backflow from controllable non-Markovian multi-channels in diamond
• Enabling quantum non-Markovian dynamics by injection of classical colored noise
• Facets of quantum information under non-Markovian evolution
• Shortcuts to Adiabatic Pumping in Classical Stochastic Systems
• Witnessing non-Markovian effects of quantum processes through Hilbert-Schmidt speed
• Revealing memory effects in phase-covariant quantum master equations
• Coherence and entanglement dynamics of vibrating qubits
• PT-symmetric quantum state discrimination
• Quantum information dynamics in a high-dimensional parity-time-symmetric system
• Dynamics of correlations due to a phase noisy laser
• Hidden entanglement in the presence of random telegraph dephasing noise
• Fast quantum control in dissipative systems using dissipationless solutions
• Quantumness and memory of one qubit in a dissipative cavity under classical control
• Transition Probabilities in the Two-Level Quantum System with PT-Symmetric Non-Hermitian Hamiltonians
• Detecting non-Markovian plasmonic band gaps in quantum dots using electron transport
• Scattering properties of anti-parity-time symmetric non-Hermitian system
• Multiparameter estimation, lower bound on quantum Fisher information and non-Markovianity witnesses of noisy two-qubit systems
• Trace distance from the viewpoint of quantum operation techniques
• Improving shortcuts to non-Hermitian adiabaticity for fast population transfer in open quantum systems
• Observation of exceptional point in a PT broken non-Hermitian system simulated using a quantum circuit
• Effects of partial measurements on quantum resources and quantum Fisher information of a teleported state in a relativistic scenario
• Simulating non-Hermitian dynamics of a multi-spin quantum system and an emergent central spin model
• Adiabatic Quantum Estimation: A Numerical Study of the Heisenberg XX Model with Antisymmetric Exchange
• Cramér-Rao bound and quantum parameter estimation with non-Hermitian systems

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• Memory effects in high-dimensional systems faithfully identified by Hilbert-Schmidt speed-based witness
• Witnessing global memory effects of multiqubit correlated noisy channels by Hilbert-Schmidt speed
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