Information-theoretic derivation of energy and speed bounds

• URL: http://arxiv.org/abs/2403.13223v2
• Date: Mon, 25 Mar 2024 10:02:39 GMT
• Title: Information-theoretic derivation of energy and speed bounds
• Authors: Lorenzo Giannelli, Giulio Chiribella,
• Abstract summary: We provide a model where the dynamics originates from a condition of informational non-equilibrium. We derive a notion of energy that captures the main features of energy in quantum theory. Our results provide an information-theoretic reconstruction of the Mandelstam-Tamm bound on the speed of quantum evolutions.
• Score: 0.2302001830524133
• License: http://arxiv.org/licenses/nonexclusive-distrib/1.0/
• Abstract: Information-theoretic insights have proven fruitful in many areas of quantum physics. But can the fundamental dynamics of quantum systems be derived from purely information-theoretic principles, without resorting to Hilbert space structures such as unitary evolution and self-adjoint observables? Here we provide a model where the dynamics originates from a condition of informational non-equilibrium, the deviation of the system's state from a reference state associated to a field of identically prepared systems. Combining this idea with three basic information-theoretic principles, we derive a notion of energy that captures the main features of energy in quantum theory: it is observable, bounded from below, invariant under time-evolution, in one-to-one correspondence with the generator of the dynamics, and quantitatively related to the speed of state changes. Our results provide an information-theoretic reconstruction of the Mandelstam-Tamm bound on the speed of quantum evolutions, establishing a bridge between dynamical and information-theoretic notions.

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