Scientists Prove That There Is No “Second Law of Entanglement”

Quantum Physics Waves Concept

The second law of entanglement states that the total amount of entanglement in a closed system cannot increase over time. In other words, entanglement is a conserved resource that can be neither created nor destroyed.

The power of the second law

The second law of thermodynamics is widely considered one of the most universally true physical laws. It dictates that the entropy, a measure of physical disorder, of any isolated system can never decrease over time. It adds an ‘arrow of time’ to everyday occurrences, determining which processes are reversible and which are not. It explains why an ice cube on a hot stove will always melt and why compressed gas will always escape its container and never return when a valve is opened to the atmosphere.

Only states of equal entropy and energy can be reversibly converted from one to the other. This reversibility condition led to the discovery of thermodynamic processes such as the (idealized) Carnot cycle, which poses an upper limit to how efficiently one can convert heat into work, or the other way around, by cycling a closed system through different temperatures and pressures. Our understanding of this process underpinned the rapid economic development during the Western Industrial Revolution.

Quantum entropy

The beauty of the second law of thermodynamics is its applicability to any macroscopic system, regardless of the microscopic details. In quantum systems, one of these details may be entanglement: a quantum connection that makes separated components of the system share properties. Intriguingly, quantum entanglement shares many profound similarities with thermodynamics, even though quantum systems are mostly studied in the microscopic regime. Scientists have uncovered a notion of ‘entanglement entropy’ that precisely mimics the role of the thermodynamical entropy, at least for idealized quantum systems that are perfectly isolated from their surroundings.

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

It was conjectured that a ‘second law of entanglement’ could be established, embodied in a single function that would generalize the entanglement entropy and govern all entanglement manipulation protocols. This conjecture is featured in a famous list of open problems in quantum information theory.

No second law of entanglement

Resolving this long-standing open question, research carried out by Lami (previously at the University of Ulm and currently at QuSoft and the University of Amsterdam) and Bartosz Regula (University of Tokyo) demonstrates that manipulation of entanglement is fundamentally irreversible, putting to rest any hopes of establishing a second law of entanglement. This new result relies on the construction of a particular quantum state which is very ‘expensive’ to create using pure entanglement. Creating this state will always result in a loss of some of this entanglement, as the invested entanglement cannot be fully recovered. As a result, it is inherently impossible to transform this state into another and back again. The existence of such states was previously unknown.

Because the approach used here does not presuppose what exact transformation protocols are used, it rules out the reversibility of entanglement in all possible settings. It applies to all protocols, assuming they don’t generate new entanglement themselves. Lami explains: “Using entangling operations would be like running a distillery in which alcohol from elsewhere is secretly added to the beverage.”

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

This may mean that describing quantum entanglement is not as simple as scientists had hoped. Rather than being a drawback, however, the vastly greater complexity of the theory of entanglement compared to the classical laws of thermodynamics may allow us to use entanglement to achieve feats that would otherwise be completely inconceivable. “For now, what we know for certain is that entanglement hides an even richer and more complicated structure that we had given it credit for,” concludes Lami.

Reference: “No second law of entanglement manipulation after all” by Ludovico Lami and Bartosz Regula, 23 January 2023, Nature Physics.
DOI: 10.1038/s41567-022-01873-9

4 Comments on "Scientists Prove That There Is No “Second Law of Entanglement”"

  1. R. Michael Smith | February 16, 2023 at 3:09 pm | Reply

    If we are able to uncover the channel through which entanglement connects, we may be able to interrupt the connection much as an on- off switch. Of course, uncovering that channel, will lead to many other even more significant applications.

  2. Fixed gravity for you. | February 18, 2023 at 4:15 pm | Reply

    “The theory of entanglement and thermodynamics are thus governed by fundamentally different and incompatible sets of laws.”

    Heat flow and entropy increase are the domain of electricity/magnetism, when gravity is relatively weakest.

    Entanglement is assisted by the focus of highly-retroreflective cold nucleonic gravity flow expressing radiated kinetic spin information in a beamlike manner and acting as a priming conduit for electric and magnetic energy flows.

    Gravity’s cold retro-reflection is essentially counter-entropic or entropy-limiting in effect, and it’s apparently the most logical basis for any emergence of life as a planet cools, especially with a capacity for cold focus to amplify impact of near-neighbors in interactions particularly with hydrogen, oxygen and carbon and minimize the impacts of more distant gravity neighbors.

    Overlooking this cold gravity focus effect is apparently why astronomers were not expecting to see rings around objects so much smaller than fluffy gas giants, or multiple asteroids with roughly octahedral shapes.

    • Fixed gravity for you. | February 18, 2023 at 4:27 pm | Reply

      It’s also not too difficult to see how gravity focus operates between identical nuclei to increase decay rates on heavy elements, and how entanglement operates to disprove General Relativity.

      ,,,, and I’m still waiting for the site’s gravity pest to show up here.

  3. Fixed gravity for you. | February 18, 2023 at 4:41 pm | Reply

    “a capacity for cold focus to amplify impact of near-neighbors in interactions particularly with hydrogen, oxygen and carbon and minimize the impacts of more distant gravity neighbors”

    At the galactic scale, compressed masses and flattened shapes help to extend this “near” focus effect to cold matter creating dark filaments in the cold vacuum between galaxies. A field roll effect explains dark halos. No idea if anyone else sees it this way, but that doesn’t matter much to me since I’m retired.

Leave a comment

Email address is optional. If provided, your email will not be published or shared.