The entanglement of two microscopic systems links their properties. Manipulating this unique quantum phenomenon enables cryptography, communication and computation.

Although comparisons have been made between quantum entanglement and the classical physics of heat, the current study shows the limitations of these equations. Entanglement is considerably more complex than we previously thought.

The second law of thermodynamics is one of the few laws of physics that can be said to be absolutely and undeniably true. By law, the “entropy” of a closed system, a physical property, can never decrease. Everyday events are given an ‘arrow of time’ to indicate which processes are reversible and which are not. It explains why an ice cube placed on a hot stove will always melt and why when a valve is opened to the atmosphere, compressed gas will always fly out of the container (and never come back).

Only states with equal entropy and energy can change from one to the other in a reversible way. The discovery of thermodynamic processes such as the (idealized) Carnot cycle, which sets a limit on how effectively one can convert heat into work or vice versa by cycling a closed system through different temperatures and pressures, was made possible by the reversibility condition. Our understanding of this process was the basis for the tremendous economic growth of the Western Industrial Revolution.

The second law of thermodynamics applies to any macroscopic system, regardless of the microscopic details. Entanglement, a quantum connection that causes isolated components of the system to share functions, may be one of these details in quantum systems. Interestingly, despite the fact that quantum systems are often explored in the microscopic realm, thermodynamics and quantum entanglement show many striking parallels. Scientists have discovered a concept known as “entanglement entropy” that, at least for idealized quantum systems completely isolated from their environment, exactly matches the function of thermodynamic entropy.

Quantum information researcher Ludovico Lami said: *“Quantum entanglement is a key resource that underpins much of the power of future quantum computers. To make effective use of it, we need to learn how to manipulate it. A fundamental question became whether entanglement can always be reversibly manipulated, in direct analogy to the Carnot cycle. Crucially, this reversibility should hold, at least in theory, even for noisy (‘mixed’) quantum systems that have not been kept perfectly isolated from their environment.”*

To solve this long-standing open question, scientists are demonstrating that manipulating entanglement is fundamentally irreversible, dashing any hopes of establishing a second law of entanglement.

The development of a particular quantum state, which is extremely “expensive” to establish with pure entanglement, is necessary for this new conclusion. Since the invested entanglement cannot be recovered, there will always be some loss of this entanglement when this state is created. As a result, it is essentially impossible to change this condition from one to the other and vice versa. The existence of such states had not been recognized before.

Lami explains: *“Because the approach used here does not assume which exact transformation protocols are used, it rules out the reversibility of entanglement in all possible environments. It applies to all protocols assuming they do not generate new entanglement. Using entanglement operations would be the same like running a distillery where alcohol from elsewhere is secretly added to the drink.”*

*“We can conclude that no single quantity, such as entanglement entropy, can tell us everything there is to know about the permissible transformations of entangled physical systems. The theory of entanglement and thermodynamics are thus governed by fundamentally different and irreconcilable laws.”*

*“This may mean that describing quantum entanglement is not as easy as scientists had hoped. However, rather than being a drawback, the much greater complexity of the theory of entanglement compared to the classical laws of thermodynamics may allow us to to use entanglement to achieve feats that would otherwise be completely unimaginable.”What we now know for sure is that entanglement hides an even richer and more complicated structure for which we assumed it.”*

**Magazine reference:**

- Lami, L., Regula, B. Yet no second law of entanglement manipulation. Wet. Physically. 19, 184-189 (2023). DOI: 10.1038/s41567-022-01873-9