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arXiv:2610.38387

Fermionic Unruh effect revisited: Entanglement and correlation dynamics under symmetric transformations

Omid Yahyayi Monem, Hosein Mohammadzadeh

quant-phgr-qcSubmitted Oct 28, 2026• Announced Oct 29, 2026• 0 citations
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Abstract

A uniformly accelerated observer perceives the Minkowski vacuum as a thermal bath, so acceleration acts as a noise channel on correlations shared with an inertial partner. For a Dirac field in the standard treatment, the resulting map is a one-sided amplitude-damping channel, and entanglement and quantum discord survive at infinite acceleration. We introduce a symmetric Unruh-like map in which the vacuum and the one-particle state both exchange amplitude with the inaccessible Rindler region; for a Bell state it yields a bit-flip channel whose flip probability is the Fermi-Dirac occupation at the Unruh temperature. Using negativity, mutual information, and all six pairwise quantum discords, we find that the entanglement and discord between the inertial observer and the accessible mode vanish together at infinite acceleration, leaving only one bit of classical correlation. These results show that the fate of quantum correlations in noninertial frames depends on the structure of the Minkowski-Rindler map.

AI Summary

The paper asks whether residual fermionic entanglement at infinite acceleration depends on the asymmetric structure of the standard Minkowski–Rindler transformation. Rather than rederiving that transformation, it introduces a phenomenological symmetric isometry: $|0\rangle\mapsto\cos r|00\rangle+\sin r|11\rangle$ and $|1\rangle\mapsto\cos r|10\rangle+\sin r|01\rangle$. Tracing out the inaccessible mode gives the bit-flip channel $\mathcal E(\rho)=(1-p)\rho+pX\rho X$, with $p=\sin^2r$ set equal to the Fermi–Dirac occupation at the Unruh temperature. For an initial Bell pair, explicit reduced density matrices, partial-transpose spectra, entropy calculations, and local projective-measurement optimization yield negativity $N=(1-2p)/2$, mutual information $I=2-h(p)$, and quantum discord $D=1-h(p)$ in either measurement direction, where $h$ is binary entropy. At infinite acceleration, $p=1/2$: entanglement and discord vanish, leaving one bit of classical correlation. The standard fermionic map instead retains negativity $1/4$. Both pairs involving the inaccessible mode are separable throughout; each has mutual information $h(p)$ and discord that vanishes identically in one measurement direction. The accessible and complementary Alice-pair mutual informations sum to two bits. The stated limitations are that the symmetric map is not derived from Dirac-field Bogoliubov transformations and uses a single-mode description. Whether it corresponds to a legitimate choice of Unruh modes or a physically distinct regime remains unresolved. The paper also notes that the effective bit-flip dynamics retain coherences absent from a purely incoherent thermal process.

Some signs of AI-generated textOverclaimsUnclear noveltyStrong assumptionsPossible error

Error found: The symmetric channel has excitation and de-excitation probabilities both equal to p(r), so the paper incorrectly identifies 1 − p(r), the no-flip probability, as the de-excitation probability. The conclusion reverses the measurement directions of the identically vanishing discords: they vanish for measurements on A or R, not generally for measurements on the inaccessible mode. The discord section incorrectly states that standard-Unruh entanglement has vanished at infinite acceleration, although the paper's own formula gives negativity 1/4 in that limit.

Written by gpt-6.1-sol from the paper's full text. Automated: it can be wrong.

Comments
5 figures, 12 pages

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A uniformly accelerated observer perceives the Minkowski vacuum as a thermal bath, so acceleration acts as a noise channel on correlations shared with an inertial partner. For a Dirac field in the standard treatment, the resulting map is a one-sided amplitude-damping channel, and entanglement and quantum discord survive at infinite acceleration. We introduce a symmetric Unruh-like map in which the vacuum and the one-particle state both exchange amplitude with the inaccessible Rindler region; for a Bell state it yields a bit-flip channel whose flip probability is the Fermi-Dirac occupation at the Unruh temperature. Using negativity, mutual information, and all six pairwise quantum discords, we find that the entanglement and discord between the inertial observer and the accessible mode vanish together at infinite acceleration, leaving only one bit of classical correlation. These results show that the fate of quantum correlations in noninertial frames depends on the structure of the Minkowski-Rindler map.
The paper asks whether residual fermionic entanglement at infinite acceleration depends on the asymmetric structure of the standard Minkowski–Rindler transformation. Rather than rederiving that transformation, it introduces a phenomenological symmetric isometry: ∣0⟩↦cos⁡r∣00⟩+sin⁡r∣11⟩|0\rangle\mapsto\cos r|00\rangle+\sin r|11\rangle∣0⟩↦cosr∣00⟩+sinr∣11⟩ and ∣1⟩↦cos⁡r∣10⟩+sin⁡r∣01⟩|1\rangle\mapsto\cos r|10\rangle+\sin r|01\rangle∣1⟩↦cosr∣10⟩+sinr∣01⟩. Tracing out the inaccessible mode gives the bit-flip channel E(ρ)=(1−p)ρ+pXρX\mathcal E(\rho)=(1-p)\rho+pX\rho XE(ρ)=(1−p)ρ+pXρX, with p=sin⁡2rp=\sin^2rp=sin2r set equal to the Fermi–Dirac occupation at the Unruh temperature.
For an initial Bell pair, explicit reduced density matrices, partial-transpose spectra, entropy calculations, and local projective-measurement optimization yield negativity N=(1−2p)/2N=(1-2p)/2N=(1−2p)/2, mutual information I=2−h(p)I=2-h(p)I=2−h(p), and quantum discord D=1−h(p)D=1-h(p)D=1−h(p) in either measurement direction, where hhh is binary entropy. At infinite acceleration, p=1/2p=1/2p=1/2: entanglement and discord vanish, leaving one bit of classical correlation. The standard fermionic map instead retains negativity 1/41/41/4. Both pairs involving the inaccessible mode are separable throughout; each has mutual information h(p)h(p)h(p) and discord that vanishes identically in one measurement direction. The accessible and complementary Alice-pair mutual informations sum to two bits.
The stated limitations are that the symmetric map is not derived from Dirac-field Bogoliubov transformations and uses a single-mode description. Whether it corresponds to a legitimate choice of Unruh modes or a physically distinct regime remains unresolved. The paper also notes that the effective bit-flip dynamics retain coherences absent from a purely incoherent thermal process.
Geometric quantum discord of fermionic systems in the relativistic regime, that is, beyond the single-mode approximation, is investigated. It is shown that geometric quantum discord for the fermionic systems in non-inertial frames converges at an infinite acceleration limit, which means that the fermionic systems become independent of the choice of Unruh modes (q R ) beyond single-mode approximation. The discord may vanish or be retained depending upon the level of mixedness of the fermionic system. The dynamics of geometric discord are investigated under amplitude damping, depolarizing, phase damping and flipping channels. The vanishing behavior of discord is seen for a higher level of decoherence in the infinite acceleration limit. The depolarizing channel dominantly affects the fermionic geometric discord as compared to the amplitude and phase damping channels. This implies that the depolarizing channel has most destructive influence on the discord of the fermionic systems. However, the flipping channels have a symmetrical effect on the discord. Moreover, the discord heavily depends on the mixedness parameter of the quantum state of the fermionic systems in accelerated frames beyond single-mode approximation.
We investigate the redistribution of continuous-variable Gaussian quantum discord under the Unruh effect for both one and two uniformly accelerated observers. The discord shared between the inertial mode and the accessible accelerated mode, as well as that between the two accessible accelerated modes, decays monotonically with acceleration and vanishes in the limit a→∞a\to\inftya→∞, while the Unruh effect generates discord in all causally disconnected Rindler mode pairs. The initial quantum correlation is therefore redistributed across Rindler partitions rather than destroyed. We further characterize how the squeezing parameter sss and field frequency ωωω control the discord in different mode-pair classes. For causally connected pairs, sss and ωωω exert comparable, interchangeable effects; for cross-region pairs, the squeezing parameter dominates; and for intra-observer cross-region pairs, the field frequency is more influential. In the two-observer case, the AIIA_{II}AII​-BIIB_{II}BII​ pair exhibits non-monotonic behavior with a peak whose position shifts to larger aaa as ωωω increases, and both parameters contribute only weakly except near an optimal ωs\fracω{s}sω​ ratio.
While the Unruh effect has traditionally been studied under the assumption of uniform acceleration, a simplification motivated by experimental considerations, it is not necessarily true for all non-inertial motions. We propose a novel approach for the indirect detection of the Unruh effect without relying on the former restriction. Previous studies have shown that probing the decoherence of an Unruh-DeWitt detector can significantly reduce the acceleration required for observing the effect by several orders of magnitude compared to earlier proposals. Building on this idea, we develop a theoretical framework describing a non-inertial observer equipped with a detector undergoing non-uniform, time-dependent acceleration. We show that, in a non-uniformly accelerated Rindler spacetime, the particle distribution perceived in the Minkowski vacuum acquires a time-dependent modification of the standard Unruh spectrum. Furthermore, we demonstrate that the inclusion of quantum entanglement leads to a deformation of the Minkowski vacuum into squeezed states.
We make use of the tools of quantum information theory to shed light on the Unruh effect. A modal qubit appears as if subjected to quantum noise that degrades quantum information, as observed in the accelerated reference frame. The Unruh effect experienced by a mode of a free Dirac field, as seen by a relativistically accelerated observer, is treated as a noise channel, which we term the Unruh channel. We characterize this channel by providing its operator-sum representation, and study various facets of quantum correlations, such as, Bell inequality violations, entanglement, teleportation and measurement-induced decoherence under the effect. We compare and contrast this channel from conventional noise due to environmental decoherence. We show that the Unruh effect produces an amplitude-damping-like channel, associated with zero temperature, even though the Unruh effect is associated with a non-zero temperature. Asymptotically, the Bloch sphere subjected to the channel does not converge to a point, as would be expected by fluctuation-dissipation arguments, but contracts by a finite factor. We construct for the Unruh effect the inverse channel, a non-completely-positive map, that formally reverses the effect, and offer some physical interpretation.
The entanglement between two modes of free scalar and Dirac fields as seen by two relatively accelerated observers has been investigated. It is found that the same initial entanglement for an initial state parameter $\ensuremath{\alpha}$ and its ``normalized partner'' $\sqrt{1\ensuremath{-}{\ensuremath{\alpha}}^{2}}$ will be degraded by the Unruh effect along two different trajectories except for the maximally entangled state, which just shows the inequivalence of the quantization for a free field in Minkowski and Rindler coordinates. In the infinite-acceleration limit, the state does not have distillable entanglement for any $\ensuremath{\alpha}$ for the scalar field, but always remains entangled to a degree that is dependent on $\ensuremath{\alpha}$ for the Dirac field. It is also interesting to note that in this limit the mutual information equals just half of the initial mutual information; this result is independent of $\ensuremath{\alpha}$ and the type of field.
Abstract The Minkowski vacuum ∣0⟩M|0\rangle _M∣0⟩M​ | 0 ⟩ M , which for an inertial observer is devoid of particles, is perceived as a thermal bath by Rindler observers living in a single Rindler wedge (Unruh in Phys Rev D 14:870, 1976) as a result of the discrepancy in the definition of positive frequency between the two classes of observers and a strong entanglement between degrees of freedom in the left and right Rindler wedges. We revisit the problem of quantification of the correlations in a two-mode state of a free neutral scalar field which is observed by an inertial observer Alice and left/right Rindler observers Rob/AntiRob, a problem that pertains to the field of relativistic quantum information and has been previously studied in Martin-Martinez et al. (Phys Rev D 82:064006, 2010) and Datta (Phys Rev A 80:052304, 2009). We focus on the analysis of informational quantities like the locally accessible and locally inaccessible information (Koashi and Winter in Phys Rev A 69:022309, 2004; Fanchini et al. in Phys Rev A 84:012313, 2011; Fanchini et al. in New J Phys 14:013027, 2012) and a closely associated entanglement measure, the entanglement of formation. We conclude that, with respect to the correlation structure probed by inertial observers alone, the introduction of a Rindler observer gives rise to a correlation redistribution which can be quantified by the entanglement of formation. Given the informational meaning of the derived correlations, we discuss on the capacity of a quantum channel to communicate classical information between accelerated parties.