A significant advancement in quantum technology has been achieved through the derivation of an exact mathematical expression vital for refining noisy quantum entanglement. This theoretical breakthrough by a RIKEN mathematical physicist and a collaborator from the University of Amsterdam revisits and corrects flawed theories from approximately two decades ago.
Quantum entanglement, famously described by Einstein as “spooky action at a distance,” creates connections between particles that produce quantum correlations beyond classical physics capabilities. For quantum technologies to function properly, they require pure entangled states, yet real-world laboratories typically produce weak, noisy versions.
Scientists address this challenge through entanglement distillation (or purification), which refines multiple noisy entangled states into fewer but stronger entangled pairs. As Bartosz Regula of the RIKEN Center for Quantum Computing explains, “Entanglement distillation is essential because there is this gap between the pure entanglement that quantum protocols require and the noisy entanglement we can prepare in the lab.“
Mathematically determining the speed at which entanglement can be distilled from noisy quantum states has been extremely challenging. The researchers have now derived an exact expression under less stringent conditions called dually non-entangling (DNE) operations. This is only the second time such an exact expression has been derived in this field.
The breakthrough helps clarify questions dating back twenty years regarding the connection between entanglement distillation and relative entropy. Earlier mathematical proofs contained flaws that this new work addresses. The researchers were surprised when an exact expression emerged from their work, though Regula notes this was “a nice surprise.”
Since the expression involves approximations with numerous quantum states, experimental verification remains distant. “This is a case where theory is far ahead of experiments,” Regula notes, as experimentalists currently manage only tens or hundreds of quantum bits, far fewer than needed to observe these theoretical rates.
The findings confirm that entanglement can be distilled from any entangled state under DNE operations and demonstrate that entanglement theory under these operations exhibits strong irreversibility. This theoretical advancement positions the field for future experimental breakthroughs once quantum technology catches up.
Reference: “Distillable entanglement under dually non-entangling operations” by Ludovico Lami, and Bartosz Regula, 22 November 2024, Nature Communications. DOI: 10.1038/s41467-024-54201-5
