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arxiv: 2602.20819 · v1 · submitted 2026-02-24 · 🪐 quant-ph

Quantum discord of mixed states under noisy channels in the curved spacetime

Yuxuan Xiong , Zhiling Pi , Tinggui Zhang , Xiaofen Huang This is my paper

Pith reviewed 2026-05-15 19:59 UTC · model grok-4.3

classification 🪐 quant-ph
keywords quantum discordSchwarzschild black holenoisy quantum channelsHawking accelerationtwo-qubit mixed statesphase dampingphase flipbit flip
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The pith

Accessible quantum discord in two-qubit states degrades with Hawking acceleration but never suffers sudden death under standard noise channels in Schwarzschild spacetime.

A machine-rendered reading of the paper's core claim, the machinery that carries it, and where it could break.

The paper applies the geometric measure of quantum discord to two-qubit mixed states evolving in the background of a Schwarzschild black hole while passing through phase-damping, phase-flip, and bit-flip channels. It derives analytical complementary relations that link the discords of the accessible and inaccessible subsystems. The accessible discord decreases steadily as the Hawking acceleration grows, yet remains positive at all finite accelerations, while the inaccessible discord rises monotonically from zero. For the bit-flip and phase-flip channels the discord is symmetric in the decay probability. These results matter because they show how quantum correlations behave when both gravitational redshift and ordinary decoherence act together, a regime relevant to any quantum-information task performed near a black hole.

Core claim

For two-qubit mixed states in Schwarzschild spacetime subject to phase-damping, phase-flip or bit-flip noise, the geometric quantum discord of the accessible subsystem decreases monotonically with rising Hawking acceleration without sudden death, the discord of the inaccessible subsystem increases monotonically from zero, and closed-form complementary relations hold between the two quantities; in the bit-flip and phase-flip cases the discord is symmetric under interchange of the decay probability with its complement.

What carries the argument

Geometric measure of quantum discord evaluated on the reduced density matrices obtained after tracing out the inaccessible region in the Schwarzschild metric under the three Pauli noise channels.

If this is right

  • Analytical complementary relations allow the inaccessible discord to be obtained directly from the accessible one without recomputing the full density matrix.
  • Absence of sudden death implies that some quantum correlations remain available for information processing at arbitrarily large but finite accelerations.
  • Identical qualitative behavior across the three channels indicates that the degradation pattern is insensitive to the precise form of the Pauli noise.
  • Symmetry of the discord with respect to decay probability in the flip channels supplies a simple predictive rule for how correlations change when the noise strength varies.

Where Pith is reading between the lines

These are editorial extensions of the paper, not claims the author makes directly.

  • The persistence of accessible discord without sudden death suggests that certain quantum-communication protocols could still function in the vicinity of a black-hole horizon provided the acceleration is not infinite.
  • The complementary relations may extend to other correlation measures such as entanglement of formation, offering a unified description of quantum resources near black holes.
  • Repeating the calculation for rotating or charged black holes would test whether the monotonic degradation and absence of sudden death are universal features of stationary spacetimes.

Load-bearing premise

The geometric measure continues to quantify quantum correlations faithfully when the two-qubit system is placed in curved Schwarzschild spacetime and subjected to the standard noise channels.

What would settle it

An explicit calculation of the geometric discord that shows sudden death at a finite value of the Hawking acceleration, or a numerical violation of any of the derived complementary relations, would falsify the central claims.

Figures

Figures reproduced from arXiv: 2602.20819 by Tinggui Zhang, Xiaofen Huang, Yuxuan Xiong, Zhiling Pi.

Figure 1
Figure 1. Figure 1: Plot quantum discords D(ρAIBI ) , D(ρAIBII ) and D(ρAIIBII ) when Hawking acceler￾ation ra = rb = r for various state parameters. In the similarly way, we calculate the another three reduce density matrices and the corre￾sponding discords (see detailed calculations in the Appendix), their analytical expressions can be written out explicitly in the following, D(ρAIBII ) = (2p − 1)2 18 cos2 ra sin2 rb, (11) … view at source ↗
Figure 2
Figure 2. Figure 2: Plot quantum discords D(ρAIBI ), D(ρAIBII ) and D(ρAIIBII ) under phase damping noisy when ra = rb = r. The upper three subfigures are the cases that discord is a function of acceleration parameter r with several different values of state parameter p for k = 1 3 . The lower three subfigures are the cases that discord is a function of both acceleration parameter r and decay probability parameter k. In case … view at source ↗
Figure 3
Figure 3. Figure 3: Plot quantum discords D(ρAIBI ), D(ρAIBII ) and D(ρAIIBII ) for the phase flip channel when ra = rb = r. The upper subfigures are the cases that discord is a function of acceleration parameter r for k = 1 3 . The lower subfigures are the cases that discord is a function of both acceleration parameter r and decay probability parameter k. In [PITH_FULL_IMAGE:figures/full_fig_p009_3.png] view at source ↗
Figure 4
Figure 4. Figure 4: Plot quantum discords D(ρAIBI ), D(ρAIBII ) and D(ρAIIBII ) for the bit flip channel when ra = rb = r. The upper subfigures are the cases that discord is a function of acceleration parameter r for k = 1 3 . The lower subfigures are the cases that discord is a function of both acceleration parameter r and decay probability parameter k. trade-off relations of quantum discords about reduced density matrices a… view at source ↗
read the original abstract

We focus our attention on two-qubit mixed states as initial states, and apply the geometric measure of quantum discord to investigate quantum discord properties in the background of a Schwarzschild black hole under phase damping, phase flip and bit flip channels, respectively. Several analytical complementary relationships based on quantum discords for bipartite subsystems are proposed. For the three channel noises, the behaviors of discords are similar, the accessible discords always degrade as the Hawking acceleration rising, but sudden death never occurs, while the inaccessible discords increase from zero monotonically. Interestingly, in the case of the bit flip channel and phase flip channel, the discords perform symmetrically with the decay probability rising.

Editorial analysis

A structured set of objections, weighed in public.

Desk editor's note, referee report, simulated authors' rebuttal, and a circularity audit. Tearing a paper down is the easy half of reading it; the pith above is the substance, this is the friction.

Referee Report

2 major / 1 minor

Summary. The manuscript examines the geometric measure of quantum discord for two-qubit mixed states in Schwarzschild spacetime under phase-damping, phase-flip, and bit-flip channels. It reports several analytical complementary relationships between accessible and inaccessible discords, claiming that accessible discords degrade monotonically with increasing Hawking acceleration without sudden death, inaccessible discords increase from zero, and symmetric behaviors appear for bit-flip and phase-flip channels as a function of decay probability.

Significance. If the geometric discord measure remains a faithful quantifier once redshift, Unruh/Hawking mode mixing, and the standard noise channels are incorporated, the results would provide concrete analytical insights into the combined effects of gravitational redshift and decoherence on quantum correlations, including the absence of sudden death and the reported monotonicity and symmetry properties.

major comments (2)
  1. [Section defining the geometric discord and the combined channel map] The central application of the geometric measure of quantum discord (defined via the Hilbert-Schmidt distance to the nearest classical-quantum state) is performed without deriving or justifying its faithfulness for two-qubit states in Schwarzschild coordinates; the measure is known to be basis-dependent, and the paper does not check whether the algebraic expression survives the coordinate transformation, redshift factors, or mode mixing induced by the accelerated observers.
  2. [Results section presenting the analytical relations and numerical plots] The abstract asserts several analytical complementary relationships, yet the provided text contains no explicit formulas, intermediate steps, or verification that the reported monotonicity and symmetry hold independently of parameter choices in the initial mixed states or the specific form of the Hawking temperature factor.
minor comments (1)
  1. [Abstract] In the abstract, the clause 'as the Hawking acceleration rising' is grammatically incorrect and should read 'as the Hawking acceleration rises'.

Simulated Author's Rebuttal

2 responses · 0 unresolved

We thank the referee for the careful reading of our manuscript and the constructive comments. We address each major comment below and indicate the revisions we plan to incorporate.

read point-by-point responses

  1. Referee: [Section defining the geometric discord and the combined channel map] The central application of the geometric measure of quantum discord (defined via the Hilbert-Schmidt distance to the nearest classical-quantum state) is performed without deriving or justifying its faithfulness for two-qubit states in Schwarzschild coordinates; the measure is known to be basis-dependent, and the paper does not check whether the algebraic expression survives the coordinate transformation, redshift factors, or mode mixing induced by the accelerated observers.

    Authors: We acknowledge that the geometric discord is basis-dependent in general and that the manuscript does not contain an explicit derivation of its faithfulness under the Schwarzschild coordinate transformations. Our calculations apply the standard Bogoliubov transformations to define the accessible and inaccessible modes for the accelerated observers, after which the geometric discord is evaluated in the natural basis of those modes. This procedure follows the approach used in prior works on quantum correlations in curved spacetime. To strengthen the presentation, we will add a concise justification subsection citing the relevant literature on the applicability of the Hilbert-Schmidt geometric discord to two-qubit states after relativistic mode mixing. The numerical and analytical results themselves are unaffected, as they are obtained directly from the transformed density matrices. revision: partial

  2. Referee: [Results section presenting the analytical relations and numerical plots] The abstract asserts several analytical complementary relationships, yet the provided text contains no explicit formulas, intermediate steps, or verification that the reported monotonicity and symmetry hold independently of parameter choices in the initial mixed states or the specific form of the Hawking temperature factor.

    Authors: We agree that the main text would be improved by including the explicit analytical expressions. In the revised manuscript we will insert the full closed-form expressions for the accessible and inaccessible geometric discords under each of the three channels, together with the intermediate steps that yield the complementary relations. We will also add a short analytical argument demonstrating that the monotonic degradation of accessible discord (without sudden death) and the monotonic rise of inaccessible discord hold for the family of initial two-qubit mixed states considered, and that the symmetry observed for the bit-flip and phase-flip channels is independent of the precise value of the Hawking temperature factor. These additions will be supported by the existing numerical plots. revision: yes

Circularity Check

0 steps flagged

No significant circularity; discord derivations rest on standard definitions

full rationale

The paper computes geometric quantum discord for two-qubit mixed states after applying Hawking/Unruh mode transformations and standard phase-damping/phase-flip/bit-flip channels. Explicit analytical expressions for accessible and inaccessible discords are obtained directly from the post-channel density matrices without fitting parameters or reducing to self-citations by construction. Complementary relationships follow from algebraic manipulation of those expressions. Any prior citations on the geometric measure or curved-spacetime channels supply independent background rather than load-bearing premises that collapse the present results. The validity assumption for the measure in Schwarzschild coordinates is an external modeling choice, not a definitional loop.

Axiom & Free-Parameter Ledger

0 free parameters · 2 axioms · 0 invented entities

The work rests on standard quantum-information definitions of geometric discord and on the usual Schwarzschild metric plus Hawking temperature; no new free parameters or entities are introduced.

axioms (2)
  • domain assumption Geometric measure of quantum discord is an appropriate quantifier for the correlations in this setting
    Invoked to define the central quantity studied.
  • domain assumption Standard Kraus-operator representations of phase-damping, phase-flip, and bit-flip channels remain valid in curved spacetime
    Used to model the noise.

pith-pipeline@v0.9.0 · 5408 in / 1207 out tokens · 40173 ms · 2026-05-15T19:59:18.868190+00:00 · methodology

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Reference graph

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