Hayden–Preskill decoder: first experiment¶
Date: 2026-10-05. User instruction: “Lets try it.” The trampoline model remains paused.
What was run¶
An exact classical statevector simulation of the idealized Yoshida–Kitaev protocol, including postselection and one Grover amplification iteration. One message qubit A is entangled with a reference R. Three black-hole qubits B are maximally entangled with three accessible partner qubits B′. A known 16-by-16 unitary U scrambles AB. Its outputs are split into remaining system C and radiation D. The receiver uses D, B′, and a prepared auxiliary EPR pair, applying U* on their own registers. Neither R nor C is operated on by the decoder.
The full simulation has ten qubits, including the reference and auxiliary pair. U is a reproducible Haar-distributed unitary generated through complex Gaussian QR with seed 20261005. This represents idealized scrambling, not a geometry, physical evaporation process, emission temperature, or source of fresh physical randomness. Varying radiation size repartitions the same output state; it is not a time-resolved evaporation simulation.
Source: Yoshida and Kitaev, sections 2, 4, and 5. For the one-qubit diary the ideal postselection probability is 1/4; the construction’s Grover iteration count is one in the perfect-decoupling limit. We use that fixed count rather than optimizing it against observed answers.
Results for the fixed seed¶
Radiation qubits |
Remaining qubits |
Postselection acceptance |
Conditional entanglement fidelity |
One Grover iteration: unconditional fidelity |
|---|---|---|---|---|
0 |
4 |
100.00% |
25.00% |
25.00% |
1 |
3 |
44.55% |
56.11% |
50.13% |
2 |
2 |
30.73% |
81.36% |
83.48% |
3 |
1 |
26.21% |
95.37% |
96.31% |
4 |
0 |
25.00% |
100.00% |
100.00% |
Fidelity here measures overlap between the recovered reference–output state and the original EPR state. It checks preservation of quantum correlations, including phase. It is not a percentage of recovered text characters or a per-bit accuracy rate. The 25% control value corresponds to a maximally mixed two-qubit reference–output state. Acceptance alone does not certify an exact message: the zero-radiation row accepts trivially while recovering no information.
At three radiation qubits, delta = 0.04851608475518754. The model’s probability relation gives (1 + delta)/4 = 0.2621290211887969. Its fidelity bound gives 1/(1 + delta) = 0.9537288121178271, attained here within floating-point precision. The gap from perfect entanglement fidelity is 4.63 percentage points with postselection and 3.69 points after one Grover iteration. The four-radiation-qubit endpoint has no remaining hole; it is a useful limiting check, not evidence of recovery from a remaining inaccessible interior.
Controls at three radiation qubits¶
Change |
Postselection acceptance |
Conditional entanglement fidelity |
|---|---|---|
Correct decoder |
26.21% |
95.37% |
Identity evolution; message stays in C |
100.00% |
25.00% |
Independent, incorrect decoding unitary |
1.05% |
14.06% |
Unrecorded computational-basis measurement of D |
4.35% |
71.81% |
The dephasing control sums measurement branches incoherently. It does not assume all information is destroyed. The wrong-decoder result is one chosen control, not its ensemble average; the correct-decoder fidelity bound does not apply to it.
Six explicit input states (0, 1, +, −, +i, −i) were also passed through the postselected decoder. Their conditional state fidelities ranged from 96.15% to 97.54%. These are a different metric from the entanglement fidelity in the table.
Across 32 seeded scrambling unitaries, mean conditional entanglement fidelities for 0–4 radiation qubits were 25.00%, 57.15%, 84.86%, 96.67%, and 100.00%. At three radiation qubits the range was 91.61–99.11%. These are an ensemble check, not experimental confidence intervals.
Verification and interpretation¶
Checks passed for unitarity, normalized states, the paper’s probability/fidelity relation, no-radiation and full-radiation limits, and the identity control. Numerical values are exact matrix calculations up to floating-point error; no hardware shots were sampled. The Grover output always exists, but finite-size decoding fidelity can be below one.
The controlled experiment demonstrates recovery in this specified quantum information model. It does not demonstrate astrophysical Hawking decoding or establish a cryptographic hash. Coherent access to B′ and the specified operations is assumed. No white hole, neutrino scattering, or RedTail-X modification was introduced.
Reproduce¶
Run python3 hayden_preskill_trial.py from this directory. Requires NumPy (run used 2.5.2). It writes hayden-preskill-results.json, which includes full precision results and all 32-circuit summaries.