The Observer Notebook · 2026-10-05

Record cost at the tipping point

When checks start cutting entanglement apart, how many bits does the hidden record of outcomes hold?

Partly known

Take a row of qubits. Scramble neighbouring pairs with random two-qubit gates, layer after layer, like bricks in a wall. Between layers, check each qubit with odds p. With few checks, entanglement (shared quantum correlation) spreads across the whole row. With many, the checks cut it into short pieces. The switch happens at a tipping point near p = 0.16.

Every check also writes down an outcome. This entry prices that hidden record: how many bits of randomness nature produces per check, right at the tipping point.

LIVE

A brickwork circuit, watched

Live · exact statevector · random two-qubit gates + random checks DEMO SCALE · 10 QUBITS · THE REAL RUN USED 20 AND 24
p = 0.160

starting

left · newest layer at the bottom. Bricks are random two-qubit gates; a dot is a check (ember = read 1, slate = read 0) · right · entanglement between the left and right halves of the row (Rényi-2 entropy, in bits; 5 is the most 10 qubits can hold), with its running average in moss. Slide p from 0.05 to 0.3 and watch the average fall. The record counter adds up the Born-rule surprise of every check: that sum is the number of bits you would have to guess to get this exact run again.

0.947 ± 0.003bits per check at p_c
EXACT SIM
p_c = 0.15720 qubits; paper says 0.168
EXACT SIM
≈ 2^256repeats to post-select 20q × 80 steps
EXACT SIM
c_eff = 0.25 ± 0.03matches Zabalo et al 2022
PAPER
01

In plain words

The toolkit found the tipping point at p_c = 0.157 with 20 qubits, close to the paper's 0.168. At that point each check produces 0.947 ± 0.003 bits of fresh randomness, about 0.16 bits per qubit per step.

That number is why these experiments are so hard. To see the transition directly you must repeat one exact run, outcomes and all. For 20 qubits over 80 steps that is about 256 bits, so about 2256 repeats.

The universal part of the result, the effective central charge c_eff = 0.25 ± 0.03, matches Zabalo et al 2022. The record cost itself is real but belongs to this model. A 24-qubit run at p = 0.21 landed. Where the 20 and 24 qubit curves cross is still unresolved at about 1σ.

Prior artZabalo et al 2022 (arXiv 2107.03393).

Next clickc_eff for Haar gates (0.25) vs large local dimension (0.29), running in the lab.

The record cost is specific to this circuit model; only c_eff is the universal, already-known part. The demo is 10 qubits with Rényi-2 entropy, where the transition is smeared out, so it shows the trend and cannot locate p_c. The demo's bits-per-check readout is its own small-scale tally, not the 0.947 measurement. The toolkit findings and run files sit on the lab machine; the numbers here are quoted from the entry.

Nearby on the bench