Wigner's friend's black hole adventure: an argument for complementarity?

TL;DR

The paper investigates unitarity tensions in Wigner's friend scenarios and black hole information puzzles by unifying extended Wigner's friend paradoxes with cloning and firewall arguments in a 4D Schwarzschild setting. It develops no-go theorems showing that there is no consistent post-quantum description of interior and exterior black hole physics if no observer can experimentally falsify quantum predictions, using a Hardy-state protocol and Hawking-radiation decoding as core tools. By combining extended Wigner's friend reasoning with firewall logic, the work sharpens monogamy-of-entanglement and no-signalling constraints, arguing that quantum theory cannot be locally violated or globally extended without contradicting observable correlations. The results emphasize subtleties in black hole puzzles—such as superposed geometries, gauge invariance, and observer-dependence—and outline future directions for both theoretical refinement and experimental analogues to probe these foundational issues.

Abstract

At the heart of both black hole physics and Wigner's friend scenarios lies the question of unitarity. In Wigner's friend setups, sealed-lab measurements are modeled unitarily, probing the measurement problem. In black hole physics, the unitarity problem concerns information preservation in evaporation. We extend a recent analogy between these two puzzles exposed by Hausmann and Renner [arXiv:2504.03835v1] by constructing new paradoxes that merge black hole physics with extensions of the Wigner's friend scenario into a unified argument. This unified construction allows us to sharpen the cloning and firewall paradoxes, which leave room for a post-quantum theory to consistently describe the physics of black holes. We close this loophole, showing that no such theory exists if no observer can experimentally falsify quantum theory's predictions. We conclude by briefly highlighting subtleties in assumptions commonly used in black hole puzzles.

Figures (5)

• Figure 1: Initial set-up of our first protocol (a) and pictured in a Penrose diagram (b) for a black hole formed from collapse. Alice and Bob measure $S_A,S_B$ and fall into the black hole. Ursula and Wigner catch their Hawking radiation (yellow wiggly arrow) upon which they perform an operation, after which they fall into the black hole to retrieve the outcomes of Alice and Bob (green wiggly arrow).
• Figure 2: Stepwise explanation of the EWF-firewall protocol. (1) Alice and Bob hold a maximally entangled state, obtained from high entanglement between early and late radiation, perform their measurements with outcomes $a,b$ and verify the correlation $p(a,b)$; this verification action is then undone by Ursula. (2) Alice falls into the black hole and measures a qubit $S_W$ that is maximally entangled with Bob's qubit, obtained from high entanglement across the horizon, verifying the correlation $p(a,a_w)$, while Bob remains outside. (3) Ursula catches the Hawking radiation of Alice's lab, undoes her measurement and performs a measurement with outcome $u$ so that she can verify the correlation $p(u,b)$ with Bob. Next, Wigner undoes this verification, and Bob falls into the black hole. (4) Wigner catches the Hawking radiation from Bob's lab, undoes Bob's measurement and performs a measurement with outcome $w$, verifying the correlation $p(u,w)$ with Ursula. Summarizing, in steps (1), (2), (3) and (4), the correlations $p(a,b),p(a,a_w),p(u,b)$ and $p(u,w)$ are verified. The final picture $(f)$ shows how seemingly all outcomes $a_w,a,b,u,w$ coexist, contradicting the fact that the verified correlations violate the CHSH inequality and cannot arise from a single, global probability distribution. We comment on these Penrose diagrams and locations of information recovery in \ref{['sec:implications']}.
• Figure 3: To include discussion about evaporation of black holes and unitarity, the post-evaporation spacetime must be pictured as well. Two possibilities are (a): continuing past the singularity, and (b) the same continuation but for a nonsingular black hole; see also Refs. Ashtekar_2005hawking2016softSchindler_2020Ashtekar_2020Ashtekar_2025hiscock1981modelshiscock1981parttwoHayward_2006Ashtekar_2011ashtekar_surprises_2011Stephens_1994barenboim2024noCarballo-Rubio:2025fncalmheiri2019entropy.
• Figure 4: A critique of the cloning paradox (a), with the state $\ket{\psi}$ cloned on a spatial surface, and the firewall paradox (c), with three systems violating monogamy of entanglement, the inside mode highly entangled with the mode just outside the horizon and the early radiation also highly entangled with the same late mode just outside the radiation. Diagrams (b) and (d) giving an alternative views for the cloning and firewall paradox, respectively. Namely, in order to recover the information, it is only at or near $I^+$ that one must be able to reconstruct the state $\ket{\psi}$ of an infalling system from the radiation and potentially remaining gravitational degrees of freedom. Similarly, it is only at or near $I^+$ that the early radiation must be highly entangled with the late radiation. Furthermore, the experiences of infalling observers might be quite different as they get entangled with the superposed, backreacted geometry (in which a notion of single spatial slices may be questionable as well).
• Figure 5: The LF-black hole protocol in a Penrose diagram; $x,y$ denote choices by Charlie and Bob, respectively, and the smaller black dots denote operations by Alice, Ursula, Bob, Wigner and Charlie.

Theorems & Definitions (7)

• Theorem 1
• Theorem 2
• Theorem 3: Firewall paradox
• Theorem 4: EWF and firewalls
• Theorem 5
• proof : Proof of \ref{['th:theorem_nosignalling']}.
• Theorem 6: No-signalling firewall argument