Speaker
Description
Hamiltonian simulations offer a promising path for computing the nonperturbative real-time dynamics of gauge theories. In this setting, entanglement entropy is both a diagnostic of many-body correlations and, together with other resources, relevant to the cost of representing, preparing, and evolving quantum states. Quantum simulations often employ distinct formulations of the same lattice gauge theory, with different tradeoffs between locality and constraint complexity. Although these formulations encode the same gauge-invariant physics, they use different elementary degrees of freedom and hence different tensor-product structures. Consequently, physically equivalent formulations need not assign the same entanglement entropy to the same state. We introduce the encoding entropy, defined by bipartitioning the native tensor factors of a chosen Hamiltonian formulation. This quantity characterizes the correlation structure intrinsic to that encoding, but need not measure spatial correlations when the formulation is spatially nonlocal. To probe the latter, we adopt the Kogut-Susskind extended-Hilbert-space entropy as a fixed reference definition of spatial entanglement. We compute both quantities for several formulations of SU(2) lattice gauge theory in (1+1)D and (2+1)D. In spatially local formulations, the reference spatial entropy can be related to the native variables through local transformations at the boundary of a region. In spatially nonlocal formulations, it is instead recovered through a nonlocal reconstruction of the Kogut-Susskind spatial algebra. Our results distinguish formulation-dependent encoding correlations from spatial correlations and clarify how the latter can be extracted across different Hamiltonian encodings.