Upper Bound on Quantum Fisher Information in Pseudo-Hermitian Systems

• URL: http://arxiv.org/abs/2506.09763v2
• Date: Thu, 12 Jun 2025 05:40:05 GMT
• Title: Upper Bound on Quantum Fisher Information in Pseudo-Hermitian Systems
• Authors: Ievgen I. Arkhipov, Franco Nori, Şahin K. Özdemir,
• Abstract summary: We develop a covariant formulation of quantum Fisher information defined on the curved Hilbert space of pseudo-Hermitian Hamiltonians.<n>This framework ensures the preservation of the state norm and enables a consistent treatment of parameter sensitivity.<n>We identify the criteria under which quantum sensing in pseudo-Hermitian systems can exhibit supremacy over Hermitian ones.
• Score: 0.0
• License: http://arxiv.org/licenses/nonexclusive-distrib/1.0/
• Abstract: Non-Hermitian systems have attracted considerable interest over the last few decades due to their unique spectral and dynamical properties not encountered in Hermitian counterparts. An intensely debated question is whether non-Hermitian systems, described by pseudo-Hermitian Hamiltonians with real spectra, can offer enhanced sensitivity for parameter estimation when they are operated at or close to exceptional points. However, much of the current analysis and conclusions are based on mathematical formalism developed for Hermitian quantum systems, which is questionable when applied to pseudo-Hermitian Hamiltonians, whose Hilbert space is intrinsically curved. Here, we develop a covariant formulation of quantum Fisher information (QFI) defined on the curved Hilbert space of pseudo-Hermitian Hamiltonians. This covariant framework ensures the preservation of the state norm and enables a consistent treatment of parameter sensitivity. We further show that the covariant QFI of pseudo-Hermitian systems can be mapped to the ordinary QFI of corresponding Hermitian systems, and establish conditions when they become dual to each other, thus revealing a deeper geometric connection between the two. Importantly, this correspondence naturally imposes an upper bound on the covariant QFI and identifies the criteria under which quantum sensing in pseudo-Hermitian systems can exhibit supremacy over Hermitian ones.

Related papers

• Uncertainty Relation for Pseudo-Hermitian Quantum Systems [0.0]
  We extend the uncertainty relation for such systems, demonstrating its equivalence to the standard Hermitian case within a pseudo-Hermitian inner product.<n>We show that the uncertainty relation for position and momentum remains real and greater than 1/2, highlighting the significance of non-Hermitian systems in quantum mechanics.
  arXiv  Detail & Related papers  (2025-08-01T14:06:05Z)
• Generalised state space geometry in Hermitian and non-Hermitian quantum systems [0.0]
  We show that it is possible to construct a family of connections that are dual to each other in a generalised sense.<n>We also elucidate the role of the metric in a quantum natural gradient descent problem.
  arXiv  Detail & Related papers  (2025-07-24T15:01:04Z)
• Grassmann Variational Monte Carlo with neural wave functions [45.935798913942904]
  We formalize the framework introduced by Pfau et al.citepfau2024accurate in terms of Grassmann geometry of the Hilbert space.<n>We validate our approach on the Heisenberg quantum spin model on the square lattice, achieving highly accurate energies and physical observables for a large number of excited states.
  arXiv  Detail & Related papers  (2025-07-14T13:53:13Z)
• Non-Hermitian effects on the quantum parameter estimation in pseudo-Hermitian systems [0.0]
  We investigate Quantum Fisher Information (QFI) in quantum states in non-Hermitian systems.<n>Our findings offer a new perspective for analyzing and enhancing QFI in non-Hermitian systems.
  arXiv  Detail & Related papers  (2025-05-25T10:23:57Z)
• Theory of the correlated quantum Zeno effect in a monitored qubit dimer [41.94295877935867]
  We show how the competition between two measurement processes give rise to two distinct Quantum Zeno (QZ) regimes.<n>We develop a theory based on a Gutzwiller ansatz for the wavefunction that is able to capture the structure of the Hilbert phase diagram.<n>We show how the two QZ regimes are intimately connected to the topology of the flow of the underlying non-Hermitian Hamiltonian governing the no-click evolution.
  arXiv  Detail & Related papers  (2025-03-28T19:44:48Z)
• Hilbert space geometry and quantum chaos [39.58317527488534]
  We consider the symmetric part of the QGT for various multi-parametric random matrix Hamiltonians. We find for a two-dimensional parameter space that, while the ergodic phase corresponds to the smooth manifold, the integrable limit marks itself as a singular geometry with a conical defect.
  arXiv  Detail & Related papers  (2024-11-18T19:00:17Z)
• Topological Order in the Spectral Riemann Surfaces of Non-Hermitian Systems [44.99833362998488]
  We show topologically ordered states in the complex-valued spectra of non-Hermitian systems.<n>These arise when the distinctive exceptional points in the energy surfaces of such models are annihilated.<n>We illustrate the characteristics of the topologically protected states in a non-Hermitian two-band model.
  arXiv  Detail & Related papers  (2024-10-24T10:16:47Z)
• Emergent non-Hermitian conservation laws at exceptional points [9.397121474087331]
  Non-Hermitian systems can manifest rich static and dynamical properties at their exceptional points (EPs)<n>We identify yet another class of distinct phenomena that is hinged on EPs, namely, the emergence of a series of non-Hermitian conservation laws.
  arXiv  Detail & Related papers  (2024-08-02T08:11:41Z)
• Quantum State Transfer in Interacting, Multiple-Excitation Systems [41.94295877935867]
  Quantum state transfer (QST) describes the coherent passage of quantum information from one node to another. We describe Monte Carlo techniques which enable the discovery of a Hamiltonian that gives high-fidelity QST. The resulting Jaynes-Cummings-Hubbard and periodic Anderson models can, in principle, be engineered in appropriate hardware to give efficient QST.
  arXiv  Detail & Related papers  (2024-05-10T23:46:35Z)
• Identifying non-Hermitian critical points with quantum metric [2.465888830794301]
  The geometric properties of quantum states are encoded by the quantum geometric tensor. For conventional Hermitian quantum systems, the quantum metric corresponds to the fidelity susceptibility. We extend this wisdom to the non-Hermitian systems for revealing non-Hermitian critical points.
  arXiv  Detail & Related papers  (2024-04-24T03:36:10Z)
• Composite Quantum Phases in Non-Hermitian Systems [18.53834485319812]
  We present a precise definition of quantum phases for non-Hermitian systems. We propose a new family of phases referred to as composite quantum phases. Our work establishes a new framework for studying and constructing quantum phases in non-Hermitian interacting systems.
  arXiv  Detail & Related papers  (2023-04-10T13:47:05Z)
• Continuous phase transition induced by non-Hermiticity in the quantum contact process model [44.58985907089892]
  How the property of quantum many-body system especially the phase transition will be affected by the non-hermiticity remains unclear. We show that there is a continuous phase transition induced by the non-hermiticity in QCP. We observe that the order parameter and susceptibility display infinitely even for finite size system, since non-hermiticity endows universality many-body system with different singular behaviour from classical phase transition.
  arXiv  Detail & Related papers  (2022-09-22T01:11:28Z)
• Non-equilibrium stationary states of quantum non-Hermitian lattice models [68.8204255655161]
  We show how generic non-Hermitian tight-binding lattice models can be realized in an unconditional, quantum-mechanically consistent manner. We focus on the quantum steady states of such models for both fermionic and bosonic systems.
  arXiv  Detail & Related papers  (2021-03-02T18:56:44Z)

This list is automatically generated from the titles and abstracts of the papers in this site.

This site does not guarantee the quality of this site (including all information) and is not responsible for any consequences.