The target was a particular photon number
In 2011 Sayrin and colleagues made a microwave field return toward a chosen photon number after it lost a photon. Atoms passed through a cavity and probed the stored light. A computer used their results to estimate the field state, then commanded a microwave source to apply small corrections. The loop combined measurement with an action on the light.
Measurement alone can narrow a field to a definite number state, meaning a state with exactly one photon number. The result is random, though: it need not be the number requested beforehand. Feedback adds a way to steer later results toward that target. Performance includes how often it succeeds and how long it takes, especially when success is declared only after favourable results appear.
Read the evidence: C. Sayrin et al. (2011), Real-Time Quantum Feedback Prepares and Stabilizes Photon Number States — author manuscript, arXiv:1107.4027; Nature 477, 73–77
The same average can hide very different states
Take a target of exactly two photons. An equal mixture of vacuum and four photons has the same mean photon number, yet it never contains two. A meter that reads only the mean would report no error; a measurement that resolves photon number would find nothing in the target state.
For this known pure target, fidelity means the probability of finding exactly the requested photon number in an ideal measurement. In the formula, n with the subscript t denotes the target number, rho describes the field state, and F is that probability. It measures how much of the state occupies the target; reconstructing an arbitrary field, including coherence between number components, requires additional information.
A displacement does not add exactly one photon
The actuator in 2011 applied a small displacement to the light field, the quantum version of adding a controlled wave. It did not supply exactly one photon whenever the computer suspected a loss. Even displacing an empty cavity creates a spread of possible photon numbers.
The sequence worked by alternating those controlled nudges with number-sensitive probes. The probes narrowed the possibilities, the computer used the available record to choose the next nudge, and subsequent probes checked its effect. The interplay let a correction with uncertain photon number help steer the state toward a definite target.
The estimate combined the preparation, probe calibration, earlier actions and the latest detected atom with a model of relaxation and detection errors. An undetected atom could still have interacted with the field. Atoms also needed time to reach the detector, leaving a delay between their effect on the light and the arrival of their results.
The raw atom result, the estimated photon-number distribution and the commanded microwave pulse formed three different time streams. A correction responded to the information available then. The field could already have changed again before the news arrived.
Read the evidence: C. Sayrin et al. (2011), Real-Time Quantum Feedback Prepares and Stabilizes Photon Number States — author manuscript, arXiv:1107.4027; Nature 477, 73–77
Fresh probes checked the prepared field
To check the prepared field, the researchers interrupted feedback and sent extra probe atoms. Those fresh data reconstructed the photon-number distribution independently of the feedback estimator, using the calibrated probe response. The paper compared both runs stopped after a fixed time and runs stopped once the estimated target probability had remained above a threshold.
Runs stopped at a threshold can end with higher fidelity because the procedure waits for favourable evidence. Runs stopped at a fixed time include some still recovering from a jump. Comparing their bars as if they came from one protocol hides the time cost and the definition of success. The distribution of waiting times is therefore part of the result.
Read the evidence: C. Sayrin et al. (2011), Real-Time Quantum Feedback Prepares and Stabilizes Photon Number States — author manuscript, arXiv:1107.4027; Nature 477, 73–77
Recovering after photon loss
In an ideal vacuum-loss channel, each photon survives independently with the same probability, so a number state loses its first photon at a rate proportional to the number of photons. Larger targets leave the controller less time to gather information and act, and thermal gain and experimental errors make the job harder still.
The task was to stabilize a known number state. Protecting arbitrary unknown encoded information is a different task, because learning photon number can destroy coherence that an encoding needs. Here the measured number was exactly the information the controller wanted. Repeated sensing and small actions let it bring the field back toward that specified state after quantum jumps.
An unknown message needs a different kind of check
For an encoded unknown qubit, the useful measurement asks about relations between data qubits. In a three-qubit repetition code, two checks ask whether neighbouring bits agree. Both a codeword built from zeros and one built from ones give the same answers. A superposition can keep its unknown relative amplitudes because the checks do not distinguish those two messages. One bit flip changes a characteristic pair of answers, called the syndrome, and selects a repair.
Those agreement checks miss phase errors. Such an error can leave every reported check quiet and still change a phase-sensitive message. The five-qubit code of Laflamme and colleagues, published in 1996, provides four checks that distinguish the fifteen single-qubit Pauli errors and the no-error case. With ideal checking, it protects an arbitrary qubit against an error on any one data qubit. Multiple faults or faulty checks need further protection. A final test against a known prepared target can assess an experiment, but that test consumes the state; it cannot be used to read every unknown message during error correction.
Read the evidence: IBM Quantum Learning, Stabilizer codes: repetition, five-qubit and syndrome decodingR. Laflamme et al. (1996), Perfect Quantum Error Correction Code