No second law of entanglement manipulation after all

Many fruitful analogies have emerged between the theories of quantum entanglement and thermodynamics, motivating the pursuit of an axiomatic description of entanglement akin to the laws of thermodynamics. A long-standing open problem has been to establish a true second law of entanglement, and in particular a unique function that governs all transformations between entangled systems, mirroring the role of entropy in thermodynamics. Contrary to previous promising evidence, here we show that this is impossible and that no direct counterpart to the second law of thermodynamics can be established. This is accomplished by demonstrating the irreversibility of entanglement theory from first principles. Assuming only the most general microscopic physical constraints of entanglement manipulation, we show that entanglement theory is irreversible under all non-entangling transformations. We furthermore rule out reversibility without significant entanglement expenditure, showing that reversible entanglement transformations require the generation of macroscopically large amounts of entanglement according to certain measures. Our results not only reveal fundamental differences between quantum entanglement transformations and thermodynamic processes, but also showcase a unique property of entanglement that distinguishes it from other known quantum resources. A formal analysis of the physical limits of entanglement manipulation shows that it cannot be done reversibly, highlighting an important difference from thermodynamics.

Automated summary

Many analogies have been found between quantum entanglement theories and thermodynamics, leading to the pursuit of an axiomatic description for entanglement similar to thermodynamic laws. It has been a long-standing challenge to establish a true second law of entanglement, which governs all transformations between entangled systems. However, this study shows that it is impossible to establish a direct counterpart to the second law of thermodynamics for entanglement. The irreversibility of entanglement theory is demonstrated based on the most general microscopic physical constraints of entanglement manipulation.