Abstract: The speed of light c sets a strict upper bound on the speed of information transfer in both classical and quantum systems. In nonrelativistic systems, the Lieb-Robinson Theorem imposes an emergent speed limit v << c, establishing locality under unitary quantum dynamics and constraining the time needed to perform useful quantum tasks. We extend the Lieb-Robinson Theorem to quantum dynamics with measurements. In contrast to the general expectation that measurements can arbitrarily violate spatial locality, we find at most an (M+1)-fold enhancement to the speed of quantum information (v), provided the outcomes of M local measurements are known, and holds even when classical communication is instantaneous. Our bound is asymptotically optimal, and saturated by existing measurement-based protocols. We tightly constrain the resource requirements for quantum computation, error correction, teleportation, and generating entangled resource states (long-range Bell pairs, GHZ, W, and spin-squeezed states) from short-range entangled states. Our results impose limits on the extent to which measurements and active feedback can speed up quantum information processing, resolve fundamental questions about the nature of measurement in quantum dynamics, and constrain the scalability of a wide range of proposed quantum technologies.
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Theory Colloquia (formerly CTQM Seminars) will be held in-person on Fridays at 11 am in Duane G126.