Challenges
Datasets
Workspaces
Papers
Discussions
Leaderboard
Log inSign up
Challenges
Datasets
Workspaces
Papers
Discussions
Leaderboard
Blog
Job Board
Q3AS

© 2026 Aqora Quantum S.A.S.

TermsPrivacyLegal Notice

arXiv:1706.03782 · Physical Review Letters

Infrared Quantum Information

Daniel Carney, Laurent Chaurette, Dominik Neuenfeld, Gordon Walter Semenoff

Published Oct 30, 2017• 71 citations
arXivHTMLPDF

Abstract

We discuss information-theoretic properties of low-energy photons and gravitons in the S matrix. Given an incoming n-particle momentum eigenstate, we demonstrate that unobserved soft photons decohere nearly all outgoing momentum superpositions of charged particles, while the universality of gravity implies that soft gravitons decohere nearly all outgoing momentum superpositions of all the hard particles. Using this decoherence, we compute the entanglement entropy of the soft bosons and show that it is infrared-finite when the leading divergences are resummed in the manner of Bloch and Nordsieck.

DOI
10.1103/physrevlett.119.180502

Related papers

IR dynamics and entanglement entropy

Theodore N. Tomaras, Nicolaos Toumbas

We consider scattering of Faddeev-Kulish electrons in QED and study the entanglement between the hard and soft particles in the final state at the perturbative level. The soft photon spectrum naturally splits into two parts: (i) soft photons with energies less than a characteristic infrared scale ${E}_{d}$ present in the clouds accompanying the asymptotic charged particles, and (ii) sufficiently low energy photons with energies greater than ${E}_{d}$, comprising the soft part of the emitted radiation. We construct the density matrix associated with tracing over the radiative soft photons and calculate the entanglement entropy perturbatively. We find that the entanglement entropy is free of any infrared divergences order by order in perturbation theory. On the other hand, infrared divergences in the perturbative expansion for the entanglement entropy appear upon tracing over the entire spectrum of soft photons, including those in the clouds. To leading order the entanglement entropy is set by the square of the Fock basis amplitude for real single soft photon emission, which leads to a logarithmic infrared divergence when integrated over the photon momentum. We argue that the infrared divergences in the entanglement entropy (per particle flux per unit time) in this latter case persist to all orders in perturbation theory in the infinite volume limit.

arXiv:1910.07847•Physical review. D/Physical review. D.•Mar 16, 2020•20 citations

Aspects of quantum information in quantum field theory and quantum gravity

Dominik Neuenfeld

In this thesis we discuss applications of quantum information theoretic concepts to quantum gravity and the low-energy regime of quantum field theories. The first part of this thesis is concerned with how quantum information spreads in four-dimensional scattering experiments for theories coupled to quantum electrodynamics or perturbative quantum gravity. In these cases, every scattering process is accompanied by the emission of an infinite number of soft photons or gravitons, which cause infrared divergences in the calculation of scattering probabilities. There are two methods to deal with IR divergences: the inclusive and dressed formalisms. We demonstrate that in the late-time limit, independent of the method, the hard outgoing particles are entangled with soft particles in such a way that the reduced density matrix of the hard particles is essentially completely decohered. Furthermore, we show that the inclusive formalism is ill-suited to describe scattering of wavepackets, requiring the use of the dressed formalism. We construct the Hilbert space for QED in the dressed formalism as a representation of the canonical commutation relations of the photon creation/annihilation algebra, and argue that it splits into superselection sectors which correspond to eigenspaces of the generators of large gauge transformations. In the second part of this thesis, we turn to applications of quantum information theoretic concepts in the AdS/CFT correspondence. In pure AdS, we find an explicit formula for the Ryu-Takayanagi (RT) surface for special subregions in the dual conformal field theory, whose entangling surface lie on a light cone. The explicit form of the RT surface is used to give a holographic proof of Markovicity of the CFT vacuum on a light cone. Relative entropy of a state on such special subregions is dual to a novel measure of energy associated with a timelike vector flow between the causal and entanglement wedge. Positivity and monotonicity of relative entropy imply positivity and monotonicity of this energy, which yields a consistency conditions for solutions to quantum gravity.

•Jan 1, 2019•0 citations

Gravitational decoherence from soft-graviton SSS-matrix

Hiroki Matsui

We revisit gravitational decoherence of matter superpositions using the leading soft sector of the graviton $S$-matrix. Starting from Weinberg's soft theorem and the overlap of coherent radiation states, we derive, for branch configurations with the same total four-momentum, a gauge-invariant, nonnegative leading-soft decoherence exponent and evaluate the polarization sum and angular integrals exactly at this order. In the vacuum, coherence between branches with distinguishable soft radiation vanishes as the infrared cutoff is removed. The leading nonrelativistic term is purely quadrupolar as a consequence of energy--momentum conservation. We extend the analysis to single- and two-mode squeezed graviton states, including the two-mode case motivated by inflation. Squeezing can enhance or suppress decoherence depending on the relative phase, while phase averaging gives an enhancement governed by the graviton occupation. For a phase-averaged relic background with an approximately flat energy-density spectrum over the relevant soft frequency band, the sharp-cutoff identification of the infrared scale with the inverse observation time gives a contribution that grows with the gravitational-wave energy density and with the fourth power of the observation time. These results connect soft-graviton scattering, infrared quantum information, and decoherence in nonvacuum gravitational backgrounds.

hep-thCross-listedarXiv:2609.08584•Sep 9, 2026•0 citations

Decoherence of a 2-Path System by Infrared Photons

Colby DeLisle, Philip C. E. Stamp

We calculate the decoherence caused by photon emission for a charged particle travelling through an interferometer; the decoherence rate gives a quantitative measure of how much "which-path" quantum information is gained by the electromagnetic field. We isolate the quantum information content of both leading and sub-leading soft photons, and show that it can be extracted entirely from information about the endpoints of the particle's paths. When infrared dressing is used to cure the infrared divergences in the theory, the leading order soft photons then give no contribution to decoherence, and carry no quantum information. The sub-leading soft photons in contrast may carry finite which-path information, and the sub-leading contribution to decoherence takes an extremely simple, time-independent form depending only on the size of the interferometer. An interesting open question is whether or not dressing should also be applied at sub-leading order; we discuss the possibility of answering this question experimentally.

arXiv:2211.05813•Nov 10, 2022•0 citations

Soft QED as Open Quantum System: Infrared Cancellation and Soft-Shell Coarse Graining

Soo-Jong Rey

I formulate unresolved soft-photon sector of QED as open quantum system. Resolved charged particles and hard photons form the system, unresolved soft photons form the environment, and basic object is the reduced density matrix. A resolved outcome $f$ of multiple hard particles and photons has probability $P_{f}(i) =\sum_n|\langle f,n|S|i,0\rangle|^2=\langle i|F_f|i\rangle$, with Kraus operators $K_n= {}_{\rm soft} \langle n|S|0 \rangle_{\rm soft}$ and effect $F_f=\sum_nK_n^\daggerΠ_fK_n$. The SK formulation places unresolved virtual and real terms in one doubled-contour expansion. At one loop they carry the same on-shell eikonal kernel with opposite signs. This elegantly organizes the QED probability: for the same observable, perturbative order, diagrams, and phase space, the OQS gives the same infrared-finite terms as the full-QED. The soft-photon evolution is a unitary coherent-state displacement driven by the scattering current. The equal-history identity of influence functional exactly normalizes this soft evolution; together with the soft-photon theorem it removes the IR divergent leading-soft factor from inclusive probability. I also derive explicit leading-soft QED realization of scale-parametrized Lindblad evolution on a fixed hard-branch space. Tracing an infinitesimal soft-photon shell produces diagonal jump operators whose entries are fixed by the corresponding eikonal emission amplitudes. The finite-shell map is a completely positive unital Schur channel and, in the sharp scale-invariant leading-soft regime, a dephasing semigroup of a completely-positive-divisible scale flow. The resulting logarithmic visibility slope and monotonic purity loss are off-diagonal predictions of the reduced-state description. The same controlled-displacement dilation gives the Sudakov probability, Poisson soft-photon multiplicities, and the bremsstrahlung number spectrum.

hep-thCross-listedarXiv:2606.27498•Jun 29, 2026

Decoherence of a two-path system by infrared photons

Colby DeLisle, Philip C. E. Stamp

We calculate the decoherence caused by photon emission for a charged particle traveling through an interferometer; the decoherence rate gives a quantitative measure of how much ``which-path'' quantum information is gained by the electromagnetic field. We isolate the quantum information content of both leading and subleading soft photons, and show that it can be extracted entirely from information about the end points of the particle's paths. When infrared dressing is used to cure the infrared divergences in the theory, the leading-order soft photons then give no contribution to decoherence, and carry no quantum information. The subleading soft photons in contrast may carry finite which-path information, and the subleading contribution to decoherence takes an extremely simple, time-independent form depending only on the size of the interferometer. An interesting open question is whether or not dressing should also be applied at subleading order; we discuss the possibility of answering this question experimentally.

Physical Review A•Aug 26, 2024•1 citation
We discuss information-theoretic properties of low-energy photons and gravitons in the S matrix. Given an incoming n-particle momentum eigenstate, we demonstrate that unobserved soft photons decohere nearly all outgoing momentum superpositions of charged particles, while the universality of gravity implies that soft gravitons decohere nearly all outgoing momentum superpositions of all the hard particles. Using this decoherence, we compute the entanglement entropy of the soft bosons and show that it is infrared-finite when the leading divergences are resummed in the manner of Bloch and Nordsieck.
We consider scattering of Faddeev-Kulish electrons in QED and study the entanglement between the hard and soft particles in the final state at the perturbative level. The soft photon spectrum naturally splits into two parts: (i) soft photons with energies less than a characteristic infrared scale Ed{E}_{d}Ed​ present in the clouds accompanying the asymptotic charged particles, and (ii) sufficiently low energy photons with energies greater than Ed{E}_{d}Ed​, comprising the soft part of the emitted radiation. We construct the density matrix associated with tracing over the radiative soft photons and calculate the entanglement entropy perturbatively. We find that the entanglement entropy is free of any infrared divergences order by order in perturbation theory. On the other hand, infrared divergences in the perturbative expansion for the entanglement entropy appear upon tracing over the entire spectrum of soft photons, including those in the clouds. To leading order the entanglement entropy is set by the square of the Fock basis amplitude for real single soft photon emission, which leads to a logarithmic infrared divergence when integrated over the photon momentum. We argue that the infrared divergences in the entanglement entropy (per particle flux per unit time) in this latter case persist to all orders in perturbation theory in the infinite volume limit.
In this thesis we discuss applications of quantum information theoretic concepts to quantum gravity and the low-energy regime of quantum field theories. The first part of this thesis is concerned with how quantum information spreads in four-dimensional scattering experiments for theories coupled to quantum electrodynamics or perturbative quantum gravity. In these cases, every scattering process is accompanied by the emission of an infinite number of soft photons or gravitons, which cause infrared divergences in the calculation of scattering probabilities. There are two methods to deal with IR divergences: the inclusive and dressed formalisms. We demonstrate that in the late-time limit, independent of the method, the hard outgoing particles are entangled with soft particles in such a way that the reduced density matrix of the hard particles is essentially completely decohered. Furthermore, we show that the inclusive formalism is ill-suited to describe scattering of wavepackets, requiring the use of the dressed formalism. We construct the Hilbert space for QED in the dressed formalism as a representation of the canonical commutation relations of the photon creation/annihilation algebra, and argue that it splits into superselection sectors which correspond to eigenspaces of the generators of large gauge transformations. In the second part of this thesis, we turn to applications of quantum information theoretic concepts in the AdS/CFT correspondence. In pure AdS, we find an explicit formula for the Ryu-Takayanagi (RT) surface for special subregions in the dual conformal field theory, whose entangling surface lie on a light cone. The explicit form of the RT surface is used to give a holographic proof of Markovicity of the CFT vacuum on a light cone. Relative entropy of a state on such special subregions is dual to a novel measure of energy associated with a timelike vector flow between the causal and entanglement wedge. Positivity and monotonicity of relative entropy imply positivity and monotonicity of this energy, which yields a consistency conditions for solutions to quantum gravity.
We revisit gravitational decoherence of matter superpositions using the leading soft sector of the graviton SSS-matrix. Starting from Weinberg's soft theorem and the overlap of coherent radiation states, we derive, for branch configurations with the same total four-momentum, a gauge-invariant, nonnegative leading-soft decoherence exponent and evaluate the polarization sum and angular integrals exactly at this order. In the vacuum, coherence between branches with distinguishable soft radiation vanishes as the infrared cutoff is removed. The leading nonrelativistic term is purely quadrupolar as a consequence of energy--momentum conservation. We extend the analysis to single- and two-mode squeezed graviton states, including the two-mode case motivated by inflation. Squeezing can enhance or suppress decoherence depending on the relative phase, while phase averaging gives an enhancement governed by the graviton occupation. For a phase-averaged relic background with an approximately flat energy-density spectrum over the relevant soft frequency band, the sharp-cutoff identification of the infrared scale with the inverse observation time gives a contribution that grows with the gravitational-wave energy density and with the fourth power of the observation time. These results connect soft-graviton scattering, infrared quantum information, and decoherence in nonvacuum gravitational backgrounds.
We calculate the decoherence caused by photon emission for a charged particle travelling through an interferometer; the decoherence rate gives a quantitative measure of how much "which-path" quantum information is gained by the electromagnetic field. We isolate the quantum information content of both leading and sub-leading soft photons, and show that it can be extracted entirely from information about the endpoints of the particle's paths. When infrared dressing is used to cure the infrared divergences in the theory, the leading order soft photons then give no contribution to decoherence, and carry no quantum information. The sub-leading soft photons in contrast may carry finite which-path information, and the sub-leading contribution to decoherence takes an extremely simple, time-independent form depending only on the size of the interferometer. An interesting open question is whether or not dressing should also be applied at sub-leading order; we discuss the possibility of answering this question experimentally.
I formulate unresolved soft-photon sector of QED as open quantum system. Resolved charged particles and hard photons form the system, unresolved soft photons form the environment, and basic object is the reduced density matrix. A resolved outcome fff of multiple hard particles and photons has probability Pf(i)=∑n∣⟨f,n∣S∣i,0⟩∣2=⟨i∣Ff∣i⟩P_{f}(i) =\sum_n|\langle f,n|S|i,0\rangle|^2=\langle i|F_f|i\ranglePf​(i)=∑n​∣⟨f,n∣S∣i,0⟩∣2=⟨i∣Ff​∣i⟩, with Kraus operators Kn=soft⟨n∣S∣0⟩softK_n= {}_{\rm soft} \langle n|S|0 \rangle_{\rm soft}Kn​=soft​⟨n∣S∣0⟩soft​ and effect Ff=∑nKn†ΠfKnF_f=\sum_nK_n^\daggerΠ_fK_nFf​=∑n​Kn†​Πf​Kn​. The SK formulation places unresolved virtual and real terms in one doubled-contour expansion. At one loop they carry the same on-shell eikonal kernel with opposite signs. This elegantly organizes the QED probability: for the same observable, perturbative order, diagrams, and phase space, the OQS gives the same infrared-finite terms as the full-QED. The soft-photon evolution is a unitary coherent-state displacement driven by the scattering current. The equal-history identity of influence functional exactly normalizes this soft evolution; together with the soft-photon theorem it removes the IR divergent leading-soft factor from inclusive probability. I also derive explicit leading-soft QED realization of scale-parametrized Lindblad evolution on a fixed hard-branch space. Tracing an infinitesimal soft-photon shell produces diagonal jump operators whose entries are fixed by the corresponding eikonal emission amplitudes. The finite-shell map is a completely positive unital Schur channel and, in the sharp scale-invariant leading-soft regime, a dephasing semigroup of a completely-positive-divisible scale flow. The resulting logarithmic visibility slope and monotonic purity loss are off-diagonal predictions of the reduced-state description. The same controlled-displacement dilation gives the Sudakov probability, Poisson soft-photon multiplicities, and the bremsstrahlung number spectrum.
We calculate the decoherence caused by photon emission for a charged particle traveling through an interferometer; the decoherence rate gives a quantitative measure of how much ``which-path'' quantum information is gained by the electromagnetic field. We isolate the quantum information content of both leading and subleading soft photons, and show that it can be extracted entirely from information about the end points of the particle's paths. When infrared dressing is used to cure the infrared divergences in the theory, the leading-order soft photons then give no contribution to decoherence, and carry no quantum information. The subleading soft photons in contrast may carry finite which-path information, and the subleading contribution to decoherence takes an extremely simple, time-independent form depending only on the size of the interferometer. An interesting open question is whether or not dressing should also be applied at subleading order; we discuss the possibility of answering this question experimentally.