Entanglement and magic on the light-front

TL;DR

This paper investigates how entanglement and quantum magic are utilized in light-front versus instant-form formulations of quantum field theory, revealing that light-front states are simpler and require fewer quantum resources.

Contribution

It derives the light-front energy operator for the transverse-field Ising model and compares quantum resources needed in light-front and instant-form formulations.

Findings

LF ground state is separable in LF momentum-space

LF ground state requires less magic to prepare

At criticality, LF and IF ground states differ in entanglement structure

Abstract

In the light-front (LF) formulation of quantum field theory (QFT), physics is formulated from the perspective of a massless observer necessarily traveling at the speed of light. The LF formulation provides an alternative computational approach to lattice gauge theory, and has recently been investigated as a future application of quantum computers. A natural question is how quantum resources such as entanglement and contextuality amongst physical qubits in the laboratory are utilized in LF simulations of QFTs. We use the (1+1)D transverse-field Ising model to explore this question. We derive the LF energy operator that generates the LF dynamics of the system, which is distinct from the instant-form (IF) Hamiltonian. We find that while the eigenstates of the IF Hamiltonian exhibit pairwise entanglement between positive and negative momenta in IF momentum-space, the eigenstates of the LF Hamiltonian are separable in LF momentum-space. We then calculate the momentum-space magic of the IF-momentum-space ground state and show that it always requires more magic to prepare than the LF-momentum-space ground state. At the quantum critical point, corresponding to a massless free fermion, both LF and IF ground states are stabilizers, but the LF ground state is separable in LF momentum-space while the IF ground state is a product of maximally entangled pairs in IF momentum-space. These results show that quantum resources such as entanglement and magic are utilized differently by quantum simulations formulated in LF and IF, and that the simplicity of the LF ground state results in fewer required quantum resources.