We study relativistic scattering when one only has access to a subset of the particles, using the language of quantum measurement theory. We give an exact, non-perturbative formula for the von Neumann entanglement entropy of an apparatus particle scattered off an arbitrary set of system particles, in either the elastic or inelastic regime, and show how to evaluate it perturbatively. We give general formulas for the late-time expectation values of apparatus observables. Some simple example applications are included: in particular, a protocol to verify preparation of coherent superpositions of spatially localized system states using position-space information in the outgoing apparatus state, at lowest order in perturbation theory in a weak apparatus-system coupling.
We are interested in the entanglement entropy of the final state of two particles in an elastic scattering. One can expect that the entanglement is yielded by the interaction between the particles. Within an S-matrix theory, by using the partial wave expansion of the S-matrix elements for two-particle states, we calculate a density matrix in a high energy elastic scattering, and obtain the entanglement entropy formula, which is described by physical observables. In the derivation of this formula, there appear divergences due to the infinite volume of two-particle Hilbert space. In order to avoid such divergences, we suggest a volume-regularization. Then we concretely evaluate the entanglement entropy for proton-proton scattering by using experimental data.
We consider a general quantum field relativistic scattering involving two half-spin fermions,
A and
B, which are initially entangled with another fermion
C that does not participate in the scattering dynamics. We construct general expressions for the reduced spin matrices for the out-state considering a general tripartite spin-entangled state. In particular we study an inelastic QED process at tree-level, namely ${e}^{\ensuremath{-}}{e}^{+}\ensuremath{\rightarrow}{\ensuremath{\mu}}^{\ensuremath{-}}{\ensuremath{\mu}}^{+}$ and a half-spin fermion
C as a spectator particle which can be entangled to the
AB system in the following ways: W state, GHZ state, $|{\mathrm{A}}^{\ensuremath{\alpha}}⟩\ensuremath{\bigotimes}|{\mathrm{\ensuremath{\Psi}}}^{\ifmmode\pm\else\textpm\fi{}}{⟩}_{\mathrm{BC}}$, and $|{\mathrm{A}}^{\ensuremath{\alpha}}⟩\ensuremath{\bigotimes}|{\mathrm{\ensuremath{\Phi}}}^{\ifmmode\pm\else\textpm\fi{}}{⟩}_{\mathrm{BC}}$, where ${|{\mathrm{\ensuremath{\Psi}}}^{\ifmmode\pm\else\textpm\fi{}}⟩,|{\mathrm{\ensuremath{\Phi}}}^{\ifmmode\pm\else\textpm\fi{}}⟩}$ are the Bell basis states and $|{\mathrm{A}}^{\ensuremath{\alpha}}⟩$ is a spin superposition state of system
A. We calculate the von Neumann entropy variation before and after the scattering for the particle
C and show that spin measurements in
C contain numerical information about the total cross section of the process. We compare the initial states W and GHZ as well as study the role played by the parameter $\ensuremath{\alpha}$ in the evaluation of the entropy variations and the cross section encoded in the spectator particle.
Unitarity provides mathematical and physical constraints on quantum information systems. e.g., in entanglement swapping, unitarity requires the same von Neumann entanglement entropy generation for either a particle interaction or an act of measurement. For the first time, the language of non-relativistic quantum mechanics is presented to derive the density matrix for hard scattering. We show that unitarity allows for finding the latter's cross section without using the scattering amplitude or the Lippmann-Schwinger equation plus Green's function. We also show the language of relativistic quantum mechanics can be used to derive the momentum entropy or Sackur-Tetrode equation for the inelastic scattering of an electron from a proton. The latter entropy derives from a Shannon entropy and an additional entropy that evokes the uncertainty principle. This article's presentation allows particle physicists to readily begin calculating quantum information metrics such as correlations and mutual information for any particle interaction.
We study the entanglement entropy between the two outgoing particles in an elastic scattering process. It is formulated within an S-matrix formalism using the partial wave expansion of two-body states, which plays a significant role in our computation. As a result, we obtain a novel formula that expresses the entanglement entropy in a high energy scattering by the use of physical observables, namely the elastic and total cross sections and a physical bound on the impact parameter range, related to the elastic differential cross-section.
A scattering event in a quantum field theory is a coherent superposition of all processes consistent with its symmetries and kinematics. While real-time simulations have progressed toward resolving individual channels, existing approaches rely on knowledge of the asymptotic particle wavefunctions. This work introduces an experimentally inspired method to isolate scattering channels in Matrix Product State simulations based on the entanglement structure of the late-time wavefunction. Schmidt decompositions at spatial bipartitions of the post-scattering state identify elastic and inelastic contributions, enabling deterministic detection of outgoing particles of specific species. This method may be used in settings beyond scattering and is applied to detect heavy particles produced in a collision in the one-dimensional Ising field theory. Natural extensions to quantum simulations of other systems and higher-order processes are discussed.
The aim of this work is to compute the entanglement entropy of real and virtual particles by rewriting the generating functional of ${\ensuremath{\phi}}^{4}$ theory as a mean value between states and observables defined through the correlation functions. Then the von Neumann definition of entropy can be applied to these quantum states and in particular, for the partial traces taken over the internal or external degrees of freedom. This procedure can be done for each order in the perturbation expansion showing that the entanglement entropy for real and virtual particles behaves as
ln(m0). In particular, entanglement entropy is computed at first order for the correlation function of two external points showing that mutual information is identical to the external entropy and that conditional entropies are negative for all the domain of
m0. In turn, from the definition of the quantum states, it is possible to obtain general relations between total traces between different quantum states of a ${\ensuremath{\phi}}^{r}$ theory. Finally, discussion about the possibility of taking partial traces over external degrees of freedom is considered, which implies the introduction of some observables that measure space-time points where an interaction occurs.