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Cloning quantum steering is a no-go

The task of cloning steering. (Courtesy: F-L Zhang)

Quantum steering – a strange, non-local phenomenon similar to quantum entanglement – cannot be perfectly replicated by any joint operation between the system being steered and an external system. This new “no-cloning” theorem is the result of work by researchers in China who studied the situation that arises when one of two parties sharing a quantum state does not trust the source of quantum particles being used to create that state. As well as being important for fundamental physics, the finding could have implications for quantum cryptography and quantum computing.

Conventional computers store information as “bits” that have a value of either 1 or 0. Quantum computers, in contrast, store information in two-level quantum systems such as the horizontal and vertical polarization states of photons or the “spin up” and “spin down” states of electrons. The states of these quantum bits, or qubits, are not limited to 0 and 1; they can also exist in an intermediate combination known as a superposition. However, the complete state of a quantum system can never be fully known, meaning that perfect duplication of qubits is forbidden. This is the so-called “no-cloning” theorem, and it forms the basis of quantum cryptography.

Another important principle is that two or more qubits can become entangled, meaning that they have a much closer relationship than is allowed by classical physics. When two qubits are entangled, measuring the state of one of them automatically tells you the state of the second, no matter how far apart they may be. For example, if you know the spin of one particle, you can determine that of the other.

Albert Einstein found this aspect of entanglement unsettling, as it implied that entangled particles could affect each other’s state in a non-local way – something he called “spooky action at a distance”. In a paper published in 1935, he and his colleagues Boris Podolsky and Nathan Rosen argued against this form of nonlocality, and it became known as the EPR paradox after their initials. Later research, however, showed that their argument is incorrect: the 2022 Nobel Prize for Physics went to a trio of experimentalists who, building on work by the late theorist John Stewart Bell, demonstrated that entanglement (and thus nonlocality) is indeed part of our physical world.

The “steering no-cloning principle”

Quantum entanglement is not the only form of nonlocality in quantum theory, though. Another type, known as quantum steering, was first introduced by Erwin Schrödinger as a generalization of the EPR paradox. In quantum entanglement, the two parties involved in a quantum transaction (known traditionally as Alice and Bob), both trust the source of quantum particles used to generate their respective states. Quantum steering introduces an asymmetry to this set-up: now only one source (Alice’s, for example) is trustworthy. This enables Alice to “steer” the state of the particles observed by Bob, which means that measurements she makes on her half of the entangled particle pair affect the state of Bob’s half in a way that cannot be explained classically.

The “steering no-cloning principle” demonstrated in the new work adds to our understanding of this form of nonlocality. “The original no-cloning theorem states that no physical operation can perfectly copy an unknown quantum state,” explains Fu-Lin Zhang, who led a team of researchers at the Department of Physics at Tianjin University and the Chern Institute of Mathematics at Nankai University. “Our finding indicates that the quantum steering in a known state cannot be perfectly copied if the state is ‘too quantum’.”

The researchers also found that a closely related type of quantum correlation called EPR steering can be partially cloned. EPR steering exists in states that can be used to convincingly demonstrate quantum steering even if the observer of the steered states does not the trust the measurer. It can therefore be regarded as a “stronger” quantum property than quantum steering, Zhang explains. “In quantum information tasks between Alice and Bob attacked by a third party, ‘Charlie’, using a cloning machine, our result sets thresholds on the EPR steering between Alice and Bob to exclude EPR steering between Alice and Charlie,” he tells Physics World.

“The no-cloning of quantum steering is a consequence of quantum superposition, as are the original no-cloning and no-go theorems,” he adds, “and our proof is based on the so-called no-broadcasting theorem, which is an extended no-cloning system of ‘mixed’ states (in composite systems).”

The researchers are now examining how degrees of “quantumness” affect other no-go theorems. “We are studying protocols of sharing nonlocality and other types of quantum information among multiple observers in the framework of quantum cloning,” Zhang reveals. “Such a topic of sharing nonlocality and information is fundamental in quantum information science.”

The work is detailed in Chinese Physics Letters.

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