TY - JOUR
T1 - Bridging the gap between classical and quantum many-body information dynamics
AU - Pizzi, Andrea
AU - Malz, Daniel
AU - Nunnenkamp, Andreas
AU - Knolle, Johannes
N1 - Funding Information:
We thank C. Castelnovo, S. Choi, P. Claeys, A. G. Green, M. Hofstetter, I. Kaminer, A. Lamacraft, L. Pacchiardi, and N. Y. Yao for insightful discussions related to this work. We acknowledge support from the Imperial-TUM flagship partnership. A.P. acknowledges support from the Royal Society and hospitality at TUM. D.M. acknowledges funding from ERC Advanced Grant QUENOCOBA under the EU Horizon 2020 program (Grant Agreement No. 742102). This research is part of the Munich Quantum Valley, which is supported by the Bavarian state government with funds from the Hightech Agenda Bayern Plus.
Publisher Copyright:
© 2022 American Physical Society.
PY - 2022/12/1
Y1 - 2022/12/1
N2 - The fundamental question of how information spreads in closed quantum many-body systems is often addressed through the lens of the bipartite entanglement entropy, a quantity that describes correlations in a comprehensive (nonlocal) way. Among the most striking features of the entanglement entropy are its unbounded linear growth in the thermodynamic limit, its asymptotic extensivity in finite-size systems, and the possibility of measurement-induced phase transitions, all of which have no obvious classical counterpart. Here, we show how these key qualitative features emerge naturally also in classical information spreading, as long as one treats the classical many-body problem on par with the quantum one, that is, by explicitly accounting for the exponentially large classical probability distribution. Our analysis is supported by extensive numerics on prototypical cellular automata and Hamiltonian systems, for which we focus on the classical mutual information and also introduce a "classical entanglement entropy."Our study sheds light on the nature of information spreading in classical and quantum systems, and opens avenues for quantum-inspired classical approaches across physics, information theory, and statistics.
AB - The fundamental question of how information spreads in closed quantum many-body systems is often addressed through the lens of the bipartite entanglement entropy, a quantity that describes correlations in a comprehensive (nonlocal) way. Among the most striking features of the entanglement entropy are its unbounded linear growth in the thermodynamic limit, its asymptotic extensivity in finite-size systems, and the possibility of measurement-induced phase transitions, all of which have no obvious classical counterpart. Here, we show how these key qualitative features emerge naturally also in classical information spreading, as long as one treats the classical many-body problem on par with the quantum one, that is, by explicitly accounting for the exponentially large classical probability distribution. Our analysis is supported by extensive numerics on prototypical cellular automata and Hamiltonian systems, for which we focus on the classical mutual information and also introduce a "classical entanglement entropy."Our study sheds light on the nature of information spreading in classical and quantum systems, and opens avenues for quantum-inspired classical approaches across physics, information theory, and statistics.
UR - http://www.scopus.com/inward/record.url?scp=85143714343&partnerID=8YFLogxK
U2 - 10.1103/PhysRevB.106.214303
DO - 10.1103/PhysRevB.106.214303
M3 - Journal article
AN - SCOPUS:85143714343
VL - 106
JO - Physical Review B
JF - Physical Review B
SN - 2469-9950
IS - 21
M1 - 214303
ER -