ABSTRACT

The concept of causality, stating that physical actions cannot propagate in space at an arbitrary speed, can be captured for qudit systems by the notion of Quantum Cellular Automata (QCA), defined as unitary maps preserving locality of observables. In this talk, I will show that QCA can be identified, in any dimension and geometry, with special tensor network operators, yielding a general connection between causality and bounds on entanglement production in the form of area laws. I will stress the importance of unitarity, by discussing generalizations of our results for different classes of non-unitary quantum channels. Finally, I will show how the set of QCA can be extended to a larger class of deterministic maps via LOCC (local operations and classical communication) and illustrate implications on state-preparation protocols and classification of phases of matter.

_{Talk based on:
[1] LP and J. I. Cirac, Quantum Cellular Automata, Tensor Networks, and Area Laws,
PRL 125, 190402 (2020).
[2] LP, G. Styliaris, and J. I. Cirac, Quantum Circuits Assisted by LOCC: Transformations and Phases of Matter, PRL 127, 220503 (2021).}