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arXiv:2608.05473

Surviving correlations across a horizon: reflected entropy for bosonic fields in non-inertial frames and black hole spacetimes

Sayid Mondal

hep-thgr-qcquant-phSubmitted Aug 5, 2026• Announced Aug 7, 2026• 0 citations• Revised Aug 12, 2026 (v2)
v1 · Aug 5, 2026v2 · Aug 12, 2026
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Abstract

We study the reflected entropy and the Markov gap for modes of a free bosonic field shared by inertial observers (Alice, Charlie) and a uniformly accelerated one (Bob), for a bipartite Bell state and the tripartite Werner (W) and Greenberger--Horne--Zeilinger (GHZ) states. The bosonic Bogoliubov transformation spans an infinite-dimensional Fock space with an unbounded squeezing parameter unlike the fermionic case. By identifying a conserved charge, we block-diagonalize the reduced density matrices into exact two-dimensional sectors, yielding closed or semi-analytic forms for all three states. Although bosonic entanglement is known to vanish asymptotically, the Alice--Bob reflected entropy instead saturates at a nonzero floor, retaining the surviving classical correlation, and converges to the value Alice shares with Bob's causally disconnected partner. Crucially, only the inter-wedge reflected entropy diverges, linearly in the squeezing parameter---the sharp distinction from the fermionic case, where it stays bounded---while the Markov gaps saturate. The construction transfers verbatim to a Schwarzschild black hole, where the saturation values become mass-independent constants.

Comments
21 pages, 4 figures; minor revision and references added; comments are welcome!

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We study the reflected entropy and the Markov gap for modes of a free bosonic field shared by inertial observers (Alice, Charlie) and a uniformly accelerated one (Bob), for a bipartite Bell state and the tripartite Werner (W) and Greenberger--Horne--Zeilinger (GHZ) states. The bosonic Bogoliubov transformation spans an infinite-dimensional Fock space with an unbounded squeezing parameter unlike the fermionic case. By identifying a conserved charge, we block-diagonalize the reduced density matrices into exact two-dimensional sectors, yielding closed or semi-analytic forms for all three states. Although bosonic entanglement is known to vanish asymptotically, the Alice--Bob reflected entropy instead saturates at a nonzero floor, retaining the surviving classical correlation, and converges to the value Alice shares with Bob's causally disconnected partner. Crucially, only the inter-wedge reflected entropy diverges, linearly in the squeezing parameter---the sharp distinction from the fermionic case, where it stays bounded---while the Markov gaps saturate. The construction transfers verbatim to a Schwarzschild black hole, where the saturation values become mass-independent constants.
We explore the reflected entropy and the Markov gap between two modes of a free fermionic field as observed by accelerating observers. This is done for both a bipartite system, which is described by the Bell state, and tripartite systems, which are represented by the Werner and Greenberger-Horne-Zeilinger states. The reflected entropy of the fermionic modes degrades monotonically as a result of the Unruh effect, eventually reaching a nonzero minimum value in the limit of infinite acceleration. Furthermore, we show that the Markov gap exhibits monotonic behavior with regard to acceleration in all three cases. In addition, we suggest a function for reflected entropy which decreases monotonically with decreasing Unruh temperature for all states. Finally, we confirm that the reflected entropy for our system does reduce under the partial tracing of the degrees of freedom for our states.
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We review a recently introduced unified approach to the analytical quantification of correlations in Gaussian states of bosonic scalar fields by means of Renyi-2 entropy. This allows us to obtain handy formulae for classical, quantum, total correlations, as well as bipartite and multipartite entanglement. We apply our techniques to the study of correlations between two modes of a scalar field as described by observers in different states of motion. When one or both observers are in uniform acceleration, the quantum and classical correlations are degraded differently by the Unruh effect, depending on which mode is detected. Residual quantum correlations, in the form of quantum discord without entanglement, may survive in the limit of an infinitely accelerated observer Rob, provided they are revealed in a measurement performed by the inertial Alice.
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The investigation of nonclassical correlations in curved spacetimes offers key insights into the intersection of quantum information theory and gravitational physics. This paper studies two nonlocal correlation measures, non local advantage of quantum coherence (NAQC) and Bell nonlocality (BN) in a ddd-dimensional spherically symmetric Einstein-Gauss-Bonnet (EGB) black hole spacetime. We consider two observers (Alice and Rob) initially sharing a maximally entangled Bell state: Alice freely falls into the black hole (inertial Kruskal frame), while Rob accelerates outside the horizon (non-inertial Schwarzschild-like frame). The Unruh-Hawking effect modifies Rob's field modes, requiring Bogoliubov transformations to relate the two frames. We derive the mixed bipartite density matrix for fermionic fields and analytical expressions for NAQC and BN, which depend on Hawking temperature (itself governed by ααα, ddd, and rhr_hrh​). Our results show both correlations degrade monotonically with increasing Hawking temperature, confirm the NAQC-BN hierarchical relationship persists in EGB spacetime, and highlighting the impact of high curvature corrections on quantum resources.