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arXiv:2610.04513

Symmetry resolved entanglement in Schwinger pair production

Wajid Joyia, S. M. Al-Marzoug, Amaria Javed

quant-phphysics.opticsSubmitted Oct 3, 2026• Announced Oct 6, 2026
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Abstract

We study the charge resolved structure of the pairwise mode entanglement produced by the Schwinger effect. Using the $U(1)$ electric charge of quantum electrodynamics, we decompose the entanglement of the reduced density matrices of momentum modes into individual charge sectors, applying the symmetry resolved entanglement entropy to the pure bipartition reductions and the charge imbalance resolved negativity to the mixed particle-antiparticle pair. For a constant electric field we obtain closed form results for every mode pairing, with all field dependence controlled by the single pair production probability $|β|^2=e^{-πμ}$. For the particle, particle and antiparticle antiparticle pairs the entanglement entropy within each charge sector is field independent, so that the field acts only by redistributing statistical weight among the sectors; for the mixed particle antiparticle pair the populated sector additionally carries a field dependent entropy. The vacuum created pair is the richest case: its resolved negativity is distributed over three imbalance sectors and is transported from one sector to the next as the field increases, the sectors contributing equally only at the critical field. The entanglement across a fixed momentum bipartition, by contrast, is frozen at its initial value because pair creation conserves the sector charge. Symmetry resolution thus refines the total entanglement measures into a sector resolved picture, exposing where in charge space the entanglement of the Schwinger mechanism resides and how the electric field moves it, information beyond that contained in the total measures or in particle number distributions.

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quant-pharXiv:2610.01394•Oct 2, 2026
We study the charge resolved structure of the pairwise mode entanglement produced by the Schwinger effect. Using the U(1)U(1)U(1) electric charge of quantum electrodynamics, we decompose the entanglement of the reduced density matrices of momentum modes into individual charge sectors, applying the symmetry resolved entanglement entropy to the pure bipartition reductions and the charge imbalance resolved negativity to the mixed particle-antiparticle pair. For a constant electric field we obtain closed form results for every mode pairing, with all field dependence controlled by the single pair production probability ∣β∣2=e−πμ|β|^2=e^{-πμ}∣β∣2=e−πμ. For the particle, particle and antiparticle antiparticle pairs the entanglement entropy within each charge sector is field independent, so that the field acts only by redistributing statistical weight among the sectors; for the mixed particle antiparticle pair the populated sector additionally carries a field dependent entropy. The vacuum created pair is the richest case: its resolved negativity is distributed over three imbalance sectors and is transported from one sector to the next as the field increases, the sectors contributing equally only at the critical field. The entanglement across a fixed momentum bipartition, by contrast, is frozen at its initial value because pair creation conserves the sector charge. Symmetry resolution thus refines the total entanglement measures into a sector resolved picture, exposing where in charge space the entanglement of the Schwinger mechanism resides and how the electric field moves it, information beyond that contained in the total measures or in particle number distributions.
We analyze entanglement generated by the Schwinger effect using a mode-by-mode formalism for scalar and spinor QED in constant backgrounds. Starting from thermal initial states, we derive compact, closed-form results for bipartite entanglement between particle-antiparticle partners in terms of the Bogoliubov coefficients. For bosons, thermal fluctuations enhance production but suppress quantum correlations: the logarithmic negativity is nonzero only below a (mode-dependent) critical temperature TcT_cTc​. At fixed TTT, entanglement appears only above a critical field EentangE_{\text{entang}}Eentang​. For fermions, we observe a qualitatively different pattern: the fermionic logarithmic negativity is non-vanishing at finite temperature, and is monotonically suppressed by thermal noise. As a function of the electric field, it is non-monotonic, featuring a temperature-independent optimal field strength E∗E_*E∗​ and decreasing on both sides of the maximum. We give quantitative estimates for analog experiments, where our entanglement criteria convert directly into concrete temperature and electric field constraints. These findings identify realistic regimes where the quantum character of Schwinger physics may be tested in the laboratory.
In the presence of symmetry, entanglement measures of quantum many-body states can be decomposed into contributions from distinct symmetry sectors. Here we investigate the decomposability of negativity, a measure of entanglement between two parts of a generally open system in a mixed state. While the entanglement entropy of a subsystem within a closed system can be resolved according to its total preserved charge, we find that negativity of two subsystems may be decomposed into contributions associated with their charge imbalance. We show that this charge-imbalance decomposition of the negativity may be measured by employing existing techniques based on creation and manipulation of many-body twin or triple states in cold atomic setups. Next, using a geometrical construction in terms of an Aharonov-Bohm-like flux inserted in a Riemann geometry, we compute this decomposed negativity in critical one-dimensional systems described by conformal field theory. We show that it shares the same distribution as the charge-imbalance between the two subsystems. We numerically confirm our field theory results via exact calculations for noninteracting particles based on a double-Gaussian representation of the partially transposed density matrix.
We use the concept of quantum entanglement to analyze the Schwinger effect on an entangled state of a qubit and a boson mode coupled with the electric field. As a consequence of the Schwinger production of particle-antiparticle pairs, the electric field decreases both the correlation and the entanglement between the qubit and the particle mode. This work exposes a profound difference between bosons and fermions. In the boson case, entanglement between the qubit and the antiparticle mode cannot be caused by the Schwinger effect on the preexisting entanglement between the qubit and the particle mode, though correlation can. In the fermion case, both can.
Quantum entanglement and its main quantitative measures, the entanglement entropy and entanglement negativity, play a central role in many-body physics. An interesting twist arises when the system considered has symmetries leading to conserved quantities: Recent studies introduced a way to define, represent in field theory, calculate for 1+1D1+1\mathrm{D}1+1D conformal systems, and measure, the contribution of individual charge sectors to the entanglement measures between different parts of a system in its ground state. In this paper, we apply these ideas to the time evolution of the charge-resolved contributions to the entanglement entropy and negativity after a local quantum quench. We employ conformal field-theory techniques and find that the known dependence of the total entanglement on time after a quench ${S}_{A}\ensuremath{\sim}ln(t)$, results from $\ensuremath{\sim}\sqrt{ln(t)}$ significant charge sectors, each of which contributes $\ensuremath{\sim}\sqrt{ln(t)}$ to the entropy. We compare our calculations to numerical results obtained by the time-dependent density matrix renormalization-group algorithm and exact solution in the noninteracting limit, finding good agreement between all these methods.
Quantum entanglement, a defining feature of quantum theory, is generated dynamically by the Schwinger effect—the production of particle-antiparticle pairs from a strong electric field. In this work, we go beyond traditional particle-number analyses to study the quantum entanglement gen- erated in this process. We partition the system into momentum modes and calculate entanglement entropy and logarithmic negativity as functions of time. For a single Sauter pulse, entanglement exhibits a monotonic growth that closely tracks the pair creation process. Strikingly, a train of alternating pulses induces coherent interference, leading to a cumulative enhancement of entan- glement and revealing a clear interplay between successive creation events. Most significantly, we show that the temporal delay (𝑇) between pulses acts as a tunable parameter, controlling the level of entanglement via constructive or destructive interference. This tunability provides a distinct sig- nature of vacuum memory, establishing pair production as a platform for entanglement-controlled strong-field physics.
We analyze the correlations of the vacuum state of a charged scalar field by constructing localized observables in two disjoint regions. We consider a time-dependent homogeneous electric field and examine the time evolution of correlations by relating it with the particle-antiparticle creation through the Schwinger effect. Our results show that the electric field increases the mixedness of the states and enhances total correlations, while the distillable entanglement among the regions decreases, vanishing at a finite time for sufficiently intense pulses within the non-perturbative pair-production regime. We also discuss the effect of anisotropy induced by the external background, showing that the distribution of correlations acquires a nontrivial directional dependence.