Abstract We show that pulsed finite-strength nonselective measurements can generate exceptional points in the spectrum of a non-unitary Floquet channel. A resonantly driven qubit evolves between equally spaced measurement operations and is repeatedly subjected to an unsharp dephasing map in the σ z basis. The resulting stroboscopic CPTP map is exactly solvable and exhibits a transition from a complex-conjugate pair of multipliers to two real modes, with the small-pulse-area branch reducing to the usual overdamped Zeno-like limit. At the exceptional point, the measured population contains a Jordan-block contribution, giving a direct dynamical signature of channel defectiveness. We also derive the continuous-measurement limit and show how finite-pulse corrections, relaxation, and background dephasing modify the transition without changing the channel-level mechanism. This minimal construction shows how a periodic measurement protocol can engineer channel-level exceptional points without structured reservoirs, engineered loss, selective measurement records, or no-jump postselection.
Abstract We show that pulsed finite-strength nonselective measurements can generate exceptional points in the spectrum of a non-unitary Floquet channel. A resonantly driven qubit evolves between equally spaced measurement operations and is repeatedly subjected to an unsharp dephasing map in the σ z basis. The resulting stroboscopic CPTP map is exactly solvable and exhibits a transition from a complex-conjugate pair of multipliers to two real modes, with the small-pulse-area branch reducing to the usual overdamped Zeno-like limit. At the exceptional point, the measured population contains a Jordan-block contribution, giving a direct dynamical signature of channel defectiveness. We also derive the continuous-measurement limit and show how finite-pulse corrections, relaxation, and background dephasing modify the transition without changing the channel-level mechanism. This minimal construction shows how a periodic measurement protocol can engineer channel-level exceptional points without structured reservoirs, engineered loss, selective measurement records, or no-jump postselection.
The dynamics of an isolated quantum system is coherent and unitary. Weak coupling to the environment leads to decoherence, which is traditionally modeled with a Lindblad equation for the system's density matrix. Starting from a pure state, such a system approaches a steady state (mixed or otherwise) in an underdamped or overdamped manner. This transition occurs at an eigenvalue degeneracy of a Lindblad superoperator, called an exceptional point (EP), where corresponding eigenvectors coalesce. Recent years have seen an explosion of interest in creating exceptional points in a truly quantum domain, driven by the enhanced sensitivity and topological features EPs have shown in their classical realizations. Here, we present Floquet analysis of a prototypical qubit whose drive or dissipator strengths are varied periodically. We consider models with a single dissipator that generate global loss (phase damping) or mode-selective loss (spontaneous emission). In all cases, we find that periodic modulations lead to EP lines at small dissipator strengths and a rich EP structure in the parameter space. Our analytical and numerical results show that extending Lindblad Liouvillians to the Floquet domain is a potentially preferred route to accessing exceptional points in the transient dynamics towards the Lindblad steady state.
Exceptional points (EPs) are usually introduced as defective degeneracies of non-Hermitian Hamiltonians and, in fully open quantum dynamics, of Liouvillian generators. Here we formulate an operational theory of exceptional points that does not invoke a Hamiltonian or a master equation. The primitive dynamical object is a completely positive trace-preserving (CPTP) quantum channel Φ, applied an integer number n of times, while physical data are probabilities pnA(x∣ρ) associated with states ρ and observables A having measurements results x. We define exceptional channels through nontrivial Jordan chains of Φ and show that a Jordan block of order m generates discrete polynomial-exponential terms with maximal degree m−1. This places the physics of exceptional points in contact with what can be directly measured in experiments.
We investigate the spectral structure of reset-driven Floquet quantum channels generated by the Hamiltonian evolution of a many-body system followed by periodic resetting of a bath. By tuning a perturbation parameter in the interacting Aubry-André-Harper(AAH) model, we find that exceptional points could emerge in the spectral transition from a symmetry-constrained ergodic regime to a fully chaotic regime. Across this transition, increasing the perturbation causes the real eigenvalues of the channel to drift, coalesce at exceptional points, and bifurcate into complex-conjugate pairs, reflecting the progressive breaking of symmetry constraints in operator space. We further show that the channel spectrum sharply distinguishes chaotic, ergodic, many-body localized, and scarred dynamical regimes. Finally, we connect the leading channel eigenvalues to experimentally accessible probes based on quantum mutual information, establishing a link between the spectral organization of reset-driven quantum channels and observable relaxation dynamics. We implement the protocol on the IBM Quantum Platform and verify that the dynamical differences are reflected in the decay of mutual information.
This paper develops the measurement and reset layer of sigma-time quantum dynamics. The first paper treats unitary BV-clock evolutions with gates and pulses; the second treats bounded open-system channel products with CPTP atom maps and random-clock averages. Here we add finite-outcome measurement and reset events. A measurement event is modeled as a quantum instrument placed at a locally finite atom of a BV sigma clock. Selective outcomes are completely positive trace-nonincreasing branch maps; their traces are joint outcome probabilities. Positive-probability branches normalize to density matrices, while the nonselective sum over all outcomes is a completely positive trace-preserving channel. Reset atoms and measurement-thenreset chains are included by finite Kraus certificates. We also give a finite adaptive scaffolding theorem: when the next event instrument is chosen from a finite recorded outcome history, the same branch and nonselective closure follow by induction on the event tree. The paper includes event ledger schemas, examples, refusal walls, and a reproducible qubit benchmark for projective measurement, weak POVM measurement, reset, measurement-reset, and a two-stage adaptive event tree. Zeno accumulation, continuous outcomes, unbounded measurement domains, and hardware fidelity are explicitly outside the Scope of the results.
Dynamical decoupling suppresses decoherence by averaging selected interactions between a quantum system and its environment. Here, we extend this notion through a general Floquet formalism that maps periodic control onto relaxation and dephasing channels. Environmental fluctuations are decomposed into Floquet components that sample the noise spectrum at distinct frequencies, with coupling strengths determined by control-induced Floquet coefficients. We experimentally investigate this approach using a single nitrogen-vacancy center in diamond under multi-pulse control. By tuning the drive and detuning, we reshape the coupling to environmental fluctuations and create isolated operating points where the dominant decoherence channel vanishes, strongly suppressing Floquet dephasing. The resulting coherence enhancement follows the predicted Floquet coupling coefficients and can be shifted by modifying the control sequence. These results establish Floquet driving as a general framework for engineering transverse and longitudinal relaxation through the design of quantum control protocols.
Abstract Exceptional points (EPs) occur in non-Hermitian systems where eigenvalues and eigenvectors coalesce. In open quantum systems, EPs are typically studied via non-Hermitian effective Hamiltonians or Liouvillians, but these omit the full generality of quantum dynamics, which requires description using quantum channels. Here, we introduce a general strategy for generating quantum-channel EPs in the single-qubit setting. We show that quantum channels naturally fall into two distinct phases, purely real or complex-conjugate eigenvalues, without the need of enforcing additional symmetries, and interpolating between different phases induces a phase transition where EPs can emerge. We experimentally simulate such channels on a nuclear magnetic resonance quantum computer, observing second-order quantum-channel EPs with 93% fidelity, and extend the approach to three channels to uncover exceptional lines and a third-order quantum-channel EP. Our results promise potential applications from enhanced quantum sensing to quantum control, such as Jordan-chain mediated asymmetric conversion.