Related papers: Emulation of Self-Consistent Non-Hermitian Quantum Formalisms

Emulation of Self-Consistent Non-Hermitian Quantum Formalisms

URL: http://arxiv.org/abs/2507.13078v1
Date: Thu, 17 Jul 2025 12:47:55 GMT
Title: Emulation of Self-Consistent Non-Hermitian Quantum Formalisms
Authors: Mario Gonzalez, Karin Sim, R. Chitra,
Abstract summary: Biorthogonal quantum mechanics provides a rigorous formulation of non-Hermitian quantum mechanics.<n>We show that the self-consistent non-Hermitian quantum mechanics can be accessed in physical platforms via an embedding in closed Hermitian systems.<n>Using digital quantum simulators, we present a proof of principle and the first experimental evidence for the dynamical metric engendered by non-Hermiticity in a qubit.
Score: 1.2289361708127877
License: http://arxiv.org/licenses/nonexclusive-distrib/1.0/
Abstract: Standard quantum mechanics predicts the non-conservation of state norms and probability when the fundamental requirement of the Hermiticity of the Hamiltonian is relaxed. Biorthogonal quantum mechanics, or the more general metric formalism, provides a rigorous formulation of non-Hermitian quantum mechanics wherein norms and probabilities are conserved. The key feature is that the Hilbert space is endowed with a non-trivial dynamical metric. Beyond theoretical considerations, the physical implementation of the metric formalism remains unaddressed. In this work, we propose novel operator dilation schemes, which show that the self-consistent non-Hermitian quantum mechanics can be accessed in physical platforms via an embedding in closed Hermitian systems. Using digital quantum simulators, we present a proof of principle and the first experimental evidence for the dynamical metric engendered by non-Hermiticity in a qubit. Our work ushers in a new paradigm in the quantum simulation of non-Hermitian systems.

Related papers

Operationally classical simulation of quantum states [41.94295877935867]
A classical state-preparation device cannot generate superpositions and hence its emitted states must commute.<n>We show that no such simulation exists, thereby certifying quantum coherence.<n>Our approach is a possible avenue to understand how and to what extent quantum states defy generic models based on classical devices.
arXiv Detail & Related papers (2025-02-03T15:25:03Z)
Speed limits and thermodynamic uncertainty relations for quantum systems governed by non-Hermitian Hamiltonian [1.6574413179773757]
Non-Hermitian Hamiltonians play a crucial role in describing open quantum systems and nonequilibrium dynamics. We derive trade-off relations for systems governed by non-Hermitian Hamiltonians, focusing on the Margolus-Levitin-type and Mandelstam-Tamm-type bounds.
arXiv Detail & Related papers (2024-04-25T08:00:12Z)
A Theory of Quantum Jumps [44.99833362998488]
We study fluorescence and the phenomenon of quantum jumps'' in idealized models of atoms coupled to the quantized electromagnetic field. Our results amount to a derivation of the fundamental randomness in the quantum-mechanical description of microscopic systems.
arXiv Detail & Related papers (2024-04-16T11:00:46Z)
Correspondence Between the Energy Equipartition Theorem in Classical Mechanics and its Phase-Space Formulation in Quantum Mechanics [62.997667081978825]
In quantum mechanics, the energy per degree of freedom is not equally distributed. We show that in the high-temperature regime, the classical result is recovered.
arXiv Detail & Related papers (2022-05-24T20:51:03Z)
A mathematical formalism of non-Hermitian quantum mechanics and observable-geometric phases [0.0]
We present a formalism of non-Hermitian quantum mechanics, following the Dirac-von Neumann formalism of quantum mechanics. Our formalism is nether Hamiltonian-dependent nor basis-dependent, but can recover both PT-symmetric and biorthogonal quantum mechanics.
arXiv Detail & Related papers (2021-11-25T02:56:54Z)
Quantum realism: axiomatization and quantification [77.34726150561087]
We build an axiomatization for quantum realism -- a notion of realism compatible with quantum theory. We explicitly construct some classes of entropic quantifiers that are shown to satisfy almost all of the proposed axioms.
arXiv Detail & Related papers (2021-10-10T18:08:42Z)
Flattening the Curve with Einstein's Quantum Elevator: Hermitization of Non-Hermitian Hamiltonians via a Generalized Vielbein Formalism [0.0]
We present a systematic study of the vielbein-like formalism which transforms the Hilbert space bundles of non-Hermitian systems into the conventional ones. In other words, any non-Hermitian Hamiltonian can be "transformed" into a Hermitian one without altering the physics.
arXiv Detail & Related papers (2021-07-25T23:23:47Z)
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)
Self-adjointness in Quantum Mechanics: a pedagogical path [77.34726150561087]
This paper aims to make quantum observables emerge as necessarily self-adjoint, and not merely hermitian operators. Next to the central core of our line of reasoning, the necessity of a non-trivial declaration of a domain to associate with the formal action of an observable.
arXiv Detail & Related papers (2020-12-28T21:19:33Z)
The Non-Hermitian quantum mechanics and its canonical structure [7.784991832712813]
The non-Hermitian Schr"odinger equation is re-expressed generally in the form of Hamilton's canonical equation without any approximation. The conventional difficulties in non-Hermitian quantum mechanics are totally overcome by the reformulation.
arXiv Detail & Related papers (2020-05-21T05:52:53Z)

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