Quantum measurement as a continuous unitary evolution

Paul Jarvis

We construct a minimal discrete model in which a quantum probe on a lattice is coupled to a single auxiliary two-level qubit representing local geometry, implemented three ways: continuous unitary evolution, unitary evolution interrupted by measurement on a fixed schedule, and unitary evolution interrupted by measurement triggered adaptively by the qubit's own entanglement entropy. We show continuous unitary evolution is bit-for-bit reproducible across runs, while both measurement-based implementations are reproducible only up to the first ambiguous measurement outcome, and the adaptive schedule introduces a further failure mode: runs can diverge in when subsequent measurements occur, not just their outcome. Using GPU-batched Monte Carlo ensembles of 200,000 trajectories, we confirm both effects are structural, not artifacts of particular seed choices (77.5% and 73% convergence rates respectively), and give an analytic argument for both, checked directly against exact simulation at every measurement window. The work does not resolve which class of backreaction describes any real physical system, but provides a concrete, checkable diagnostic for backreaction models.

M. D. Srinivas

Михаил Борисович Менский

Erol Karazincir

This paper argues that unitary time evolution — the continuous, deterministic, reversible evolution of the wave function via the Schrodinger equation — is not a fundamental feature of quantum reality but a continuous approximation of an underlying discrete process, structurally parallel to how Newtonian mechanics approximates discrete molecular dynamics. The measurement problem is identified not as a feature of quantum reality but as an artifact of imposing continuous formalism on discrete physics. A continuous equation cannot produce discrete events; this is mathematical, not mysterious. Caldirola's finite-difference quantum mechanics is cited as the formal precedent. Companion paper to DOI: 10.5281/zenodo.19540088.

E.G. Eberle

Le Hu, Andrew N. Jordan

Abstract Quantum mechanics admits two distinct evolutions: deterministic unitary dynamics governed by the Schrödinger equation and the probabilistic collapse of the wave function. We show that the continuous collapse of a quantum state under measurement can, on a trajectory-by-trajectory basis, be equivalently described as unitary evolution generated by a time- and state-dependent Hermitian Hamiltonian with stochastic parameters. While the ensemble dynamics remains non-unitary, each individual trajectory thus admits a unitary representation. We derive explicit forms of such Hamiltonians for projective measurements on arbitrary n -level systems and for continuous position measurements of a harmonic oscillator, and we propose experimental schemes to test these predictions. Our framework provides a new approach to modeling and controlling continuously monitored quantum systems using only state-dependent unitary resources.