aiqbench takeQuantum Computing

This theoretical study establishes the precise mathematical conditions required to maintain unitary evolution in timeless quantum frameworks relative to a specific clock. The findings demonstrate that preserving standard dynamics depends on clock rates remaining constant over time and being independent of internal structural details, offering critical insights for foundational quantum gravity research.

Source coveringarXiv

What this isA model's reading of the article and related coverage, written for aiqbench. Not the publisher's words.

Conditions for Unitarity in Timeless Quantum Theory

arXivJune 16, 20261 min read

arXiv:2504.01579v3 Announce Type: replace Abstract: Quantum timeless approaches solve the problem of time by recovering the usual unitary evolution of quantum theory relative to a clock in a stationary quantum Universe. For some Hamiltonians of the Universe, such as those including an interaction term with the clock, the dynamics is substantially altered and can be non-unitary. This work derives necessary and sufficient conditions for the relative dynamics to be unitary and finds the general form of the unitary evolution operator. A physical interpretation of these conditions is given in terms of the clock's rate. Unitary dynamics is associated with rates that are constant in time and independent of the clock's internal structure.

Abstract:Quantum timeless approaches solve the problem of time by recovering the usual unitary evolution of quantum theory relative to a clock in a stationary quantum Universe. For some Hamiltonians of the Universe, such as those including an interaction term with the clock, the dynamics is substantially altered and can be non-unitary. This work derives necessary and sufficient conditions for the relative dynamics to be unitary and finds the general form of the unitary evolution operator. A physical interpretation of these conditions is given in terms of the clock's rate. Unitary dynamics is associated with rates that are constant in time and independent of the clock's internal structure.

arXiv:2504.01579 [quant-ph]

(or arXiv:2504.01579v3 [quant-ph] for this version)

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