Embedding of a non-Hermitian Hamiltonian to emulate the von Neumann measurement scheme

• URL: http://arxiv.org/abs/2308.15411v2
• Date: Tue, 12 Dec 2023 01:12:19 GMT
• Title: Embedding of a non-Hermitian Hamiltonian to emulate the von Neumann measurement scheme
• Authors: Gurpahul Singh, Ritesh K. Singh and Soumitro Banerjee
• Abstract summary: We propose a non-Hermitian formalism to emulate the first part of the von Neumann measurement scheme. We have used the embedding protocol to dilate a non-Hermitian Hamiltonian that governs the dynamics in the system subspace. This work lends a new perspective to the measurement problem by employing non-Hermitian Hamiltonians.
• Score: 0.05261718469769446
• License: http://arxiv.org/licenses/nonexclusive-distrib/1.0/
• Abstract: The problem of how measurement in quantum mechanics takes place has existed since its formulation. Von Neumann proposed a scheme where he treated measurement as a two-part process -- a unitary evolution in the full system-ancilla space and then a projection onto one of the pointer states of the ancilla (representing the "collapse" of the wavefunction). The Lindblad master equation, which has been extensively used to explain dissipative quantum phenomena in the presence of an environment, can effectively describe the first part of the von Neumann measurement scheme when the jump operators in the master equation are Hermitian. We have proposed a non-Hermitian Hamiltonian formalism to emulate the first part of the von Neumann measurement scheme. We have used the embedding protocol to dilate a non-Hermitian Hamiltonian that governs the dynamics in the system subspace into a higher-dimensional Hermitian Hamiltonian that evolves the full space unitarily. We have obtained the various constraints and the required dimensionality of the ancilla Hilbert space in order to achieve the required embedding. Using this particular embedding and a specific projection operator, one obtains non-Hermitian dynamics in the system subspace that closely follow the Lindblad master equation. This work lends a new perspective to the measurement problem by employing non-Hermitian Hamiltonians.

Related papers

• Integral quantization based on the Heisenberg-Weyl group [39.58317527488534]
  We develop a framework of integral quantization applied to the motion of spinless particles in the four-dimensional Minkowski spacetime. The proposed scheme is based on coherent states generated by the action of the Heisenberg-Weyl group. A direct application of our model, including a computation of transition amplitudes between states characterized by fixed positions and momenta, is postponed to a forthcoming article.
  arXiv  Detail & Related papers  (2024-10-31T14:36:38Z)
• On the Liouville-von Neumann equation for unbounded Hamiltonians [44.99833362998488]
  We present and discuss a characterization of the domain of the Liouville superoperator originally due to M. Courbage. We also provide, with explicit proofs, some domains of essential self-adjointness (cores) of the Liouvillian.
  arXiv  Detail & Related papers  (2024-08-09T10:13:35Z)
• A non-Hermitian loop for a quantum measurement [0.0]
  We establish a framework for a mechanism steering state vector collapse through time evolution. For two-level systems, we put forward the phenomenon of chiral state conversion as a mechanism effectively eliminating superpositions.
  arXiv  Detail & Related papers  (2024-08-08T17:59:10Z)
• Non-Hermitian Parent Hamiltonian from Generalized Quantum Covariance Matrix [0.0]
  We provide a systematical and efficient way to construct non-Hermitian Hamiltonian from a single pair of biorthogonal eigenstates. Our work sheds light on future exploration on non-Hermitian physics.
  arXiv  Detail & Related papers  (2023-07-06T16:27:22Z)
• Evolution of many-body systems under ancilla quantum measurements [58.720142291102135]
  We study the concept of implementing quantum measurements by coupling a many-body lattice system to an ancillary degree of freedom. We find evidence of a disentangling-entangling measurement-induced transition as was previously observed in more abstract models.
  arXiv  Detail & Related papers  (2023-03-13T13:06:40Z)
• Emulating the measurement postulates of quantum mechanics via non-Hermitian Hamiltonian [0.0]
  We show that a non-Hermitian Hamiltonian operates during the process of measurement, which evolves any state to an attracting equilibrium state, thus, mimicking a "collapse" For a 2-level system, we also demonstrate that the dynamics generated by the Lindblad master equation can be replicated as an incoherent sum of the evolution by two separate non-Hermitian Hamiltonians.
  arXiv  Detail & Related papers  (2023-02-03T18:22:10Z)
• Construction of Non-Hermitian Parent Hamiltonian from Matrix Product States [23.215516392012184]
  We propose a new method to construct non-Hermitian many-body systems by generalizing the parent Hamiltonian method into non-Hermitian regimes. We demonstrate this method by constructing a non-Hermitian spin-$1$ model from the asymmetric Affleck-Kennedy-Lieb-Tasaki state.
  arXiv  Detail & Related papers  (2023-01-29T14:13:55Z)
• Entanglement timescale and mixedness in non-Hermitian quantum systems [0.0]
  We discuss the short-time perturbative expansion of the linear entropy for finite-dimensional quantum systems. We find that the non-Hermitian Hamiltonian enhances the short-time dynamics of the linear entropy for the considered input states. Our results find applications to non-Hermitian quantum sensing, quantum thermodynamics of non-Hermitian systems, and $mathcalPT$-symmetric quantum field theory.
  arXiv  Detail & Related papers  (2022-09-23T15:53:07Z)
• From geometry to coherent dissipative dynamics in quantum mechanics [68.8204255655161]
  We work out the case of finite-level systems, for which it is shown by means of the corresponding contact master equation. We describe quantum decays in a 2-level system as coherent and continuous processes.
  arXiv  Detail & Related papers  (2021-07-29T18:27:38Z)
• 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)
• Two-qubit entanglement generation through non-Hermitian Hamiltonians induced by repeated measurements on an ancilla [0.0]
  We present a scheme for engineering non-Hermitian Hamiltonians as a result of repetitive measurements on an anicillary qubit. We show that the effective non-Hermitian Hamiltonian drives the system to a maximally entangled stationary state. In addition, we report a new recipe to construct a physical scenario where the quantum dynamics of a physical system represented by a given non-Hermitian Hamiltonian model may be simulated.
  arXiv  Detail & Related papers  (2020-09-21T16:30:18Z)

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.