Abstract

We introduce a new method permitting the analytical determination of entanglement entropy (and related quantities) between configurations of a quantum field, which is either free or in interaction with a classical source, at two distinct spatial locations. We show how such a setup can be described by a bipartite, continuous Gaussian system. This allows us to derive explicit and exact formulas for the entanglement entropy, the mutual information and the quantum discord, solely in terms of the Fourier-space power spectra of the field. This contrasts with previous studies, which mostly rely on numerical considerations. As an illustration, we apply our formalism to massless fields in flat space, where exact expressions are derived that only involve the ratio between the size of the regions over which the field is coarse-grained, and the distance between these regions. In particular, we recover the well-known fact that mutual information decays as the fourth power of this ratio at large distances, as previously observed in numerical works. Our method leads to the first analytical derivation of this result, and to an exact formula that also applies to arbitrary distances. Finally, we determine the quantum discord and find that it identically vanishes (unless coarse-graining is performed over smeared spheres, in which case it obeys the same suppression at large distance as mutual information).

Highlights

  • Quantum systems differ from classical systems because of the way they are correlated

  • We have proposed a new technique to compute the entanglement entropy and all related quantities, such as the mutual information and the quantum discord

  • Our approach relies on describing the field coarse-grained within several disjoint regions in real space as a multipartite Gaussian system, for which all the relevant tools have been developed over the past few years

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Summary

INTRODUCTION

Quantum systems differ from classical systems because of the way they are correlated. This leads us to explicit, analytical formulas solely in terms of the power spectra of the field This new method represents a significant improvement given that previous approaches were essentially based on numerical simulations. III, we discuss how the von Neumann entropy, the mutual information and the quantum discord of such systems can be calculated explicitly from the knowledge of the two-point correlation functions of the field We apply this generic framework to the case of a massless scalar field living in the Minkowski background in Sec. IV, where we show that the quantum discord identically vanishes.

BIPARTITE SYSTEMS FOR TWO-POINT CONFIGURATIONS OF A QUANTUM FIELD
VDF ðδÞ
ENTANGLEMENT ENTROPY OF GAUSSIAN STATES
D RD1 GðδÞ
APPLICATION
CONCLUSION
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