No second law of entanglement manipulation after all

TL;DR

This paper proves that a second law-like principle does not exist for quantum entanglement, demonstrating the irreversibility of entanglement transformations under general physical constraints, unlike thermodynamics.

Contribution

It establishes the fundamental irreversibility of entanglement manipulation and rules out the existence of a unique entanglement measure analogous to entropy.

Findings

Entanglement theory is irreversible under all non-entangling transformations.

Reversible entanglement transformations require large amounts of entanglement generation.

No single function governs all entanglement transformations, unlike thermodynamic entropy.

Abstract

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 which 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 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 which distinguishes it from other known quantum resources.