Qubits entanglement and radiation recovery

5 October 2026. Michael requested adding quantum entanglement and qubits, then hashing at Hawking radiation “and back.” This record extends the research model while distinguishing a quantum recovery channel from a classical hash. The experiment below is a two-qubit control; no black-hole evaporation or quantum-gravity dynamics were simulated.

Closest established framework

Hayden and Preskill, Black holes as mirrors studies recovery of information deposited in an evaporating black hole, assuming unitary, rapidly mixing dynamics and extensive control of the radiation. Their result depends on the black hole’s entanglement history and access to emitted radiation. It does not describe an ordinary light ray returning outward through a classical event horizon.

Yoshida and Kitaev, Efficient decoding for the Hayden–Preskill protocol supplies explicit idealized recovery procedures and discusses their success probabilities and computational cost. These are relevant models for a future implementation, not evidence that this project has implemented their decoder or realized the underlying physics.

Proposed registers and flow

  • M: incoming message qubits.

  • B: modeled black-hole qubits.

  • E: earlier radiation entangled with B.

  • C: remaining interior after a specified unitary U acts on M and B.

  • D: newly emitted radiation.

The proposed recovery experiment is M+B through U to C+D, with a decoder acting only on the allowed exterior registers D+E. A separate inaccessible reference entangled with M can assess entanglement recovery without revealing M to the decoder. Required declarations include the initial state, circuit U, register sizes, emission schedule, decoder, noise model, and permitted access. A simple inverse that secretly accesses C is not recovery from exterior radiation alone.

This register model is a research specification. No full Hayden–Preskill circuit, thermal Hawking spectrum, changing spacetime, or detector was implemented in this turn. The initial control below uses a much simpler two-qubit release schedule to isolate the role of correlations.

Executed two-qubit control

Script: entangled_return_control.py. Results: entangled-return-results.json.

For classical two-bit messages 00, 01, 10 and 11, initialize the corresponding computational-basis state. Apply a Hadamard gate to the first qubit, then a controlled-NOT from the first to the second. This maps the four inputs to the four Bell states. For example:

00 -> (|00> + |11>)/sqrt(2)
10 -> (|00> - |11>)/sqrt(2)

First permit access to one qubit. Its full reduced density matrix is I/2 for every message. A computational-basis measurement yields 0 or 1 with equal probability. Indeed, no measurement of that single subsystem can distinguish the four inputs, since their reduced states are identical.

Next permit access to both qubits with coherence preserved, analogous only to an assumed later stage in which all of this tiny system has become accessible. Apply the inverse circuit. All four messages were recovered with fidelity approximately 0.9999999999999996, consistent with one to numerical precision. This demonstrates a reversible joint encoding, not a gravitational escape mechanism.

As a destructive comparison, dephase both qubits in the computational basis before applying the inverse. Recovery probability falls to approximately 0.5 for each message. Phase information distinguishing the plus and minus Bell states has been lost. Measurement in another basis or a different protocol has different behavior; the claim is specific to this declared operation.

Hashing at the radiation boundary

The exact one-qubit measurement distribution is [0.5,0.5] for all four inputs. Its canonical serialization was hashed with SHAKE256 to eight bytes using the prefix Bell-local-distribution-v1 followed by a null byte. Every message produced:

1594685f91b9b228

This is a collision introduced by using an identical reduced description for different global messages. It is not a discovered collision in SHAKE256, whose input was identical each time. An actual random measurement outcome is also insufficient to identify the input and would not give a deterministic message hash.

The simulation can inspect density matrices directly because it stores the state mathematically. A physical observer cannot read a density matrix from a single unknown qubit; obtaining such a description requires additional preparation and measurement resources.

The recovery branch must retain and process the quantum information needed by its decoder. A classical hash may fingerprint a classical measurement record or a recovered classical message, but the hash alone cannot replace that quantum information. For general unknown quantum messages, classical tomography, copying, and serialization must not be assumed available for free.

Result and next step

Adding entanglement changes where information resides: a subsystem can look random while the joint state carries recoverable information in correlations. This supports investigating the radiation-recovery model. It does not establish a reversible 64-bit hash or a new source of computational hardness.

The next meaningful quantum experiment would implement a specified small Hayden–Preskill recovery circuit with early radiation, a declared scrambler, and exterior-only decoding. Measure recovery fidelity versus radiation access and noise, alongside decoding cost. Keep a classical hash of recovered classical test messages as a verification aid. A white-hole label is optional terminology; the operational requirement is an explicitly defined decoder with no access to forbidden registers.