How one local change can leave many readable records in a quantum chain

The work combines a mathematical proof with numerical simulations, not a laboratory experiment. It was submitted to arXiv on November 8, 2026; the supplied source does not establish peer-reviewed publication.

A recognizable reference makes the difference

The researchers encode one classical bit through a choice between two preparations. For one value, they leave a reference state untouched. For the other, they apply a local operation. Both preparations then evolve under exactly the same interaction rules.

Their mechanism, called dynamical selection, depends on those preparations behaving differently. The reference retains a recognizable local pattern, while the locally disturbed state spreads and relaxes. Separate observers can detect departures from that pattern without examining the whole chain.

This is not automatic. If both preparations settle into the same local thermal state, small regions can lose access to the distinction even though the full system preserves it. Nor does a disturbance reaching a distant location necessarily mean it leaves records in many locations simultaneously.

The authors count nonoverlapping regions whose measurement outcomes reveal at least a specified amount of information about the initial bit. These records may be noisy and correlated. Ten records do not represent ten independent input bits, and a fractional-bit information value is not a percentage accuracy. Replicating this classical label does not clone an arbitrary unknown quantum state.

What the proof guarantees

The central theorem connects record formation to a contrast in entanglement entropy, which measures how a region is entangled with the rest of a pure system.

At a shared observation time, the reference must have entropy bounded by a system-size-independent constant for every contiguous interval—a uniform area law. The disturbed preparation must instead have entropy proportional to interval length across a macroscopic region—a volume law.

The physical argument is an entropy-capacity mismatch. Local blocks of the reference concentrate their probability in restricted sets of states. The disturbed branch cannot accommodate its extensive entropy while remaining similarly restricted on almost every block. Many blocks must therefore acquire detectable weight outside the reference pattern.

Under these assumptions, the proof guarantees a number of readable, fixed-size blocks proportional to chain length, each exceeding a fixed positive information threshold. It does not guarantee a nearly perfect bit in every block. Nor does it prove that a particular interaction model will dynamically produce the required entropy contrast. In the general theorem, measurement projectors may depend on location and observation time; the numerical examples use simple shared readout rules.

Two numerical demonstrations

The first model starts with spins paired into singlets, entangled two-spin states. Its interactions are constructed to leave this reference unchanged. A local operation converts one singlet into a triplet, activating dynamics that can spread triplet activity to neighboring pairs.

Using sparse-matrix and Krylov numerical evolution, the researchers studied periodic chains containing up to 20 spins. At observation times proportional to chain length, every pair carried more than half a bit of information in the tested 14-, 16-, 18- and 20-spin chains. Observers used the same binary test: singlet or not.

Larger observation blocks improved reliability. In the 16-, 18- and 20-spin chains, even the least informative four-pair block exceeded 0.96 bits. These calculations used joint probabilities directly, without assuming neighboring pairs were statistically independent.

The second example uses the constrained PXP model, relevant to Rydberg-atom systems. Its reference repeatedly returns close to a recognizable alternating spin pattern rather than remaining stationary.

In a stabilized 24-site simulation, measurements along the same fixed spin axis yielded twelve simultaneous records above a quarter-bit threshold near dimensionless time 49.6. High counts recurred at later sampled revival peaks. Ordinary, unstabilized PXP had no quarter-bit records from its seventh reference revival onward within the simulated window. All sites were evaluated at a common time for each revival.

The limits of the result

The numerical evidence concerns small periodic chains. Disturbances had time to circle the dimer rings, and the high-reliability four-pair blocks occupied 40–50% of those chains. Those results do not establish reliable small-fragment records in arbitrarily large systems.

The PXP observations likewise demonstrate records at selected revival times, not uninterrupted storage. Whether the necessary entropy contrast and record density persist as system size grows remains open.

The study nevertheless offers a concrete experimental target: prepare the two alternatives repeatedly, measure fixed local outcomes, and count how many disjoint regions retain readable evidence at one shared time. Rydberg-atom simulators are proposed as a platform for testing that prediction, not reported as having demonstrated it here.