Where Does Handedness Go? Exact Minimal Joint Measurements after Environmental Decoherence of a Chiral Molecule

In plain words

A chiral molecule comes in a left and a right form. Its energy eigenstates are even mixtures of both, yet real molecules are found handed. One standard explanation is the environment. Collisions keep telling the two forms apart, and the information about handedness ends up in correlations between the molecule and what it hit. This paper asks the converse question. If you only know the molecule's parity populations and the record's own coherence, you cannot predict what happens next. Which joint measurements of molecule and record must you add, and how few will do?

The answer is exact in a minimal model: one two level molecule, one record qubit, and 35 registered future probabilities. The coarse description fails as badly as it can. Measuring molecule and record separately is not enough; what matters is how their outcomes vary together. One joint setting can fix one prediction and leave a neighbouring one broken. A reconstruction that is linear in the data needs four joint settings. On the states that can actually occur, three are necessary and sufficient at a five percent worst case error. Six three setting families are in fact exact, and all 66 pairs of settings fail.

The gap between four and three comes from nonlinear constraints that physical histories obey, which no linear rule can use. It is an instance, at the level of specific predictions, of the known fact that restricting the possible states reduces what must be measured. Every verdict is backed by an explicit pair of indistinguishable histories or an exact bound. The paper also says what a lab test would need: a collision partner that can be controlled and read out jointly with the molecule.

What it shows

• Separate measurements of molecule and record cannot recover the lost predictions; joint correlations are required.
• A linear reconstruction of all 35 targets needs four joint settings, in exactly nine minimal families.
• On reachable states three settings are necessary and sufficient, and six three setting families are exact.
• Every one of the 66 pairs of settings fails, each with an exact certificate.

What it does not claim

The model is deliberately minimal: one record, one collision step, no parity violation. It says nothing about many records or any particular laboratory molecule, and robustness to calibration errors for the three setting families is not established.

Cite

Tsiokos, I. (2026). Where Does Handedness Go? Exact Minimal Joint Measurements after Environmental Decoherence of a Chiral Molecule. Zenodo. https://doi.org/10.5281/zenodo.23057726