Quantum speed limit theorems

Quantum speed limit theorems bound how quickly a quantum system can evolve between states under specified constraints on energy or dynamics.

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Mandelstam–Tamm bound: A quantum speed limit that bounds evolution time using the energy uncertainty of a system. It links the minimum time to the system’s energy spread.
Schrödinger equation: The equation governing how a quantum state changes over time under a Hamiltonian. Its dynamics are the starting point for standard time-independent speed limits.
Quantum control: The design of external operations that steer quantum systems toward desired states or dynamics. Speed limits constrain the time available for steering a system to a target.
Quantum brachistochrone: The problem of finding the fastest evolution between quantum states under specified dynamical constraints. It turns a speed limit into an optimization problem for a chosen system.
Margolus–Levitin theorem: A quantum speed limit that bounds evolution time using the mean energy above the ground state. It supplies an energy-based bound distinct from the uncertainty-based limit.
Quantum state: A mathematical description of a quantum system’s physical state. Speed limits compare an initial state with a later state.
Quantum gate: A reversible operation that transforms the state of one or more quantum bits. Gate implementations face lower bounds on the time needed to enact state changes.
Quantum speed limit for open systems: A bound on evolution time for quantum systems interacting with an environment. Environmental effects require speed-limit formulations beyond closed-system bounds.
Fubini–Study metric: A geometric metric that measures distances between pure quantum states. Its state-space distance helps express how far a system must evolve.
Hamiltonian: An operator representing a quantum system’s total energy and generating its time evolution. Its spectrum and time dependence constrain the system’s possible speed.