Hasan Mermer | Searcharxiv

arXiv2025

Harnessing Floquet dynamics for selective metrology in few-qubit systems

Periodically driven quantum systems can function as highly selective parameter filters. We demonstrate this capability in a finite-size, three-qubit system described by the transverse-field Floquet Ising model. In this system, we identify a period-doubling (PD) dynamical phase that exhibits a stark asymmetry in metrological sensitivity to the magnetic field applied on the qubits and to the coupling strength between the qubits. The PD phase originates from $\pi$-pairing, where the initial state exhibits strong overlap with $\pi$-paired Floquet eigenstates, leading to robust period-doubled dynamics and enhanced metrological sensitivity. The analysis of quantum Fisher information reveals that the PD regime significantly enhances precision for estimating the Ising interaction strength while simultaneously suppressing sensitivity to the transverse magnetic field. Conversely, non-PD regimes are optimal for sensing the transverse field. This filtering effect is robust for larger system sizes and is quantifiable using experimentally accessible observables, such as magnetization and two-qubit correlations, via the classical Fisher information. Our work shows that distinct dynamical regimes in finite-size Floquet systems can be harnessed for targeted quantum sensing.

quant-ph↗

arXiv2025

Pseudo-Hermiticity, Anti-Pseudo-Hermiticity, and Generalized Parity-Time-Reversal Symmetry at Exceptional Points

For a diagonalizable linear operator $H:\mathscr{H}\to\mathscr{H}$ acting in a separable Hilbert space $\mathscr{H}$, i.e., an operator with a purely point spectrum, eigenvalues with finite algebraic multiplicities, and a set of eigenvectors that form a Reisz basis of $\mathscr{H}$, the pseudo-Hermiticity of $H$ is equivalent to its generalized parity-time-reversal ($PT$) symmetry, where the latter means the existence of an antilinear operator $X:\mathscr{H}\to\mathscr{H}$ satisfying $[X,H]=0$ and $X^2=1$. {The original proof of this result makes use of the anti-pesudo-Hermiticity of every diagonalizable operator $L:\mathscr{H}\to\mathscr{H}$, which means the existence of an antilinear Hermitian bijection $\tau:\mathscr{H}\to\mathscr{H}$ satisfying $L^\dagger=\tau L\,\tau^{-1}$. We establish the validity of this result for block-diagonalizable operators}, i.e., those which have a purely point spectrum, eigenvalues with finite algebraic multiplicities, and a set of generalized eigenvectors that form a Jordan Reisz basis of $\mathscr{H}$. {This allows us to generalize the original proof of the equivalence of pseudo-Hermiticity and generalized $PT$-symmetry for diagonalizable operators to block-diagonalizable operators. For a pair of pseudo-Hermitian operators acting respectively in two-dimensional and infinite-dimensional Hilbert spaces, we obtain explicit expressions for the antlinear operators $\tau$ and $X$ that realize their anti-pseudo-Hermiticity and generalized $PT$-symmetry at and away from the exceptional points.

math-ph↗