Compared to scribbling mathematical expressions for entangled quantum states on a sheet of paper, producing real entanglement is a tricky task. In the lab, physicists can only claim a prepared quantum state is entangled after it passes an entanglement verification test, and all conventional testing strategies have a major drawback: they destroy the entanglement in the process of certifying it. This means that, post-certification, experimenters must prepare the system in the same state again if they want to use it – but this assumes they trust their source to reliably produce the same state each time.

In a new study, physicists led by Hyeon-Jin Kim from the Korea Advanced Institute of Science and Technology (KAIST) found a way around this trust assumption. They did this by refining conventional entanglement certification (EC) strategies in a way that precludes complete destruction of the initial entanglement, making it possible to recover it (albeit with probability <1) along with its certification.

### A Mysterious State with a Precise Definition

Entanglement, as mysterious as it is made to sound, has a very precise definition within quantum mechanics. According to quantum theory, composite systems (that is, two or more systems considered as a joint unit) are either separable or entangled. In a separable system, as the name might suggest, each subsystem can be assigned an independent state. In an entangled system, however, this is not possible because the subsystems can’t be seen as independent; as the maxim goes, “the whole is greater than its parts”. Entanglement plays a crucial role in many fields, including quantum communication, quantum computation, and demonstrations of how quantum theory differs from classical theory. Being able to verify it is thus imperative.

In the latest work, which they describe in a paper published in Science Advances, Kim and colleagues studied EC tests involving multiple qubits – the simplest possible quantum systems. Conventionally, there are three EC strategies. The first, called witnessing, applies to experimental situations where two (or more) devices making measurements on each subsystem are completely trusted. In the second, termed steering, one of the devices is fully trusted, but the other isn’t. The third strategy, called Bell nonlocality, applies when none of the devices are trusted. For each of these strategies, one can derive inequalities which, if violated, certify entanglement.

### Weak Measurement is the Key

Kim and colleagues reconditioned these strategies in a way that enabled them to recover the original entanglement post-certification. The key to their success was a process called weak measurement.

In quantum mechanics, a measurement is any process that probes a quantum system to obtain information from it, and the theory models measurements in two ways: projective or “strong” measurements and non-projective or “weak” measurements. Conventional EC strategies employ projective measurements, which completely destroy the entanglement. Weak measurements, in contrast, don’t disturb the subsystems as sharply, allowing for the possibility of recovering the initial entangled state.

The team introduced a control parameter for the strength of measurement on each subsystem and rederived the certifying inequality to incorporate these parameters. They then iteratively prepared their qubit system in the state to be certified and measured a fixed sub-unit value (weak measurement) of the parameters. After all the iterations, they collected statistics to check for the violation of the certification inequality. Once a violation occurred, meaning that the state is entangled, they implemented further suitable weak measurements of the same strength on the same subsystems to recover the initial entangled state with some probability R (for “reversibility”).

### Lifting the Trust Assumption

The physicists also demonstrated this theoretical proposal on a photonic setup called a Sagnac interferometer. As predicted, they found that as the measurement strength increases, the reversibility R goes down and the degree of entanglement decreases, while the certification level increases. This implies the existence of a measurement strength “sweet spot” such that the certification levels remain somewhat high without too much loss of entanglement and hence reversibility.

In an ideal experiment, the entanglement source would be trusted to prepare the same state in every iteration, and destroying entanglement in order to certify it would be benign. But a realistic source may never output a perfectly entangled state every time, making it vital to filter out useful entanglement soon after it is prepared. The KAIST team demonstrated this by applying their scheme to a noisy source that produces a multi-qubit mixture of an entangled and a separable state as a function of time. By employing weak measurements at different time steps and checking the value of the witness, the team certified and recovered the entanglement from the mixture, lifting the trust assumption, and using it further for a Bell nonlocality experiment.

### Frequently Asked Questions

#### What is entanglement?

Entanglement is a phenomenon in quantum mechanics where two or more particles become correlated in such a way that the state of one particle cannot be described independently of the state of the others. It is an essential aspect of quantum theory and is used in various applications such as quantum communication and quantum computation.

#### What is entanglement certification?

Entanglement certification is the process of verifying whether a prepared quantum state is truly entangled. Often, this involves performing measurements on the system and checking if certain inequalities are violated. The certification step is crucial in ensuring the reliability of an entangled state for further use in quantum applications.

#### What is weak measurement?

Weak measurement is a type of measurement in quantum mechanics that does not disturb the system as sharply as projective or strong measurements. It allows for the extraction of limited information from the system while preserving its entanglement. Weak measurements play a key role in the entanglement certification scheme described in the article.

#### Why is recovering the initial entangled state important?

Recovering the initial entangled state after certification is important because it allows for the reuse of the entangled system without the need for preparing the state again from scratch. This is particularly useful when dealing with realistic sources that may not produce perfectly entangled states every time. The ability to recover the initial entangled state increases the practicality and efficiency of utilizing entanglement in quantum applications.