25 Jun 2024 | Thomas Colas, Julien Grain, Greg Kaplanek, Vincent Vennin
This paper presents a systematic perturbative approach to compute the purity and entanglement entropy of quantum fields in curved spacetimes using the in-in formalism, extended to non-unitary dynamics and quantum information measures. The method reduces the problem to standard correlation functions, allowing a diagrammatic expansion with corresponding Feynman rules. It is applied to a cosmological model inspired by inflationary effective field theory. The results show that non-linear loop corrections at late times behave similarly to linear contributions, only slightly affecting the purity. When the environment is heavy compared to the Hubble scale, recoherence is robust against non-linear extensions. This bridges perturbative quantum field theory with open quantum systems, enabling better understanding of renormalization and resummation in open effective field theories. It also allows a more systematic study of quantum information properties in field theories.
The paper addresses two main challenges: the in-in formalism is developed for unitary theories, while purity loss is non-unitary; and purity is not an observable, requiring extension of the formalism. The reduced density matrix is obtained by tracing out the environment, leading to a statistical mixture when the system becomes entangled. Purity, defined as the trace of the square of the reduced density matrix, measures decoherence. In a unitary evolution, purity is conserved, but deviations from unity indicate non-unitary effects.
The paper presents a systematic expansion of purity in powers of the interaction Hamiltonian, showing that the second-order term involves unequal-time two-point functions. For linear system operators, this reduces to a determinant of the covariance matrix. The results provide a framework for computing quantum information measures in open quantum field theories, with applications to cosmology and inflationary models.This paper presents a systematic perturbative approach to compute the purity and entanglement entropy of quantum fields in curved spacetimes using the in-in formalism, extended to non-unitary dynamics and quantum information measures. The method reduces the problem to standard correlation functions, allowing a diagrammatic expansion with corresponding Feynman rules. It is applied to a cosmological model inspired by inflationary effective field theory. The results show that non-linear loop corrections at late times behave similarly to linear contributions, only slightly affecting the purity. When the environment is heavy compared to the Hubble scale, recoherence is robust against non-linear extensions. This bridges perturbative quantum field theory with open quantum systems, enabling better understanding of renormalization and resummation in open effective field theories. It also allows a more systematic study of quantum information properties in field theories.
The paper addresses two main challenges: the in-in formalism is developed for unitary theories, while purity loss is non-unitary; and purity is not an observable, requiring extension of the formalism. The reduced density matrix is obtained by tracing out the environment, leading to a statistical mixture when the system becomes entangled. Purity, defined as the trace of the square of the reduced density matrix, measures decoherence. In a unitary evolution, purity is conserved, but deviations from unity indicate non-unitary effects.
The paper presents a systematic expansion of purity in powers of the interaction Hamiltonian, showing that the second-order term involves unequal-time two-point functions. For linear system operators, this reduces to a determinant of the covariance matrix. The results provide a framework for computing quantum information measures in open quantum field theories, with applications to cosmology and inflationary models.