Einstein never had his bar mitzvah but the theory of relativity has been confirmed over and over again. Einstein called the notion of quantum entanglement ‘spooky’; yet it turned out to be as real as God’s ongoing interactive spiritual relationships (covenants) with the intelligent creatures God caused to evolve throughout the universe.
Describing quantum entanglement will not be 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 physicists to use entanglement to achieve feats otherwise completely inconceivable.
The second law of thermodynamics is often considered to be one of only a few physical laws that is absolutely and unquestionably true. The law states that the amount of ‘entropy’—a physical property—of any closed system can never decrease. It adds an ‘arrow of time’ to everyday occurrences, determining which processes are reversible and which are not. It explains why an ice cube placed on a hot stove will always melt, and why compressed gas will always fly out of its container (and never back in) 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.
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 featured in a famous list of open problems in quantum information theory.
Resolving this long-standing open question, research carried out by Lami (currently at QuSoft and the University of Amsterdam) and Bartosz Regula (University of Tokyo) demonstrates that manipulation of entanglement is fundamentally irreversible, putting an end to 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. Creation of this state will always result in a loss of some of this entanglement, as the invested entanglement cannot be fully recovered. 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. This is the bases of monotheism.
Rather than being a drawback, however, the vastly greater complexity of the theory of entanglement (covenants) may allow humans to use religious entanglement to achieve feats (like achieving the Messianic Age) 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. (phys.org 1/24/2023)
The paper is published in the journal Nature Physics. For more information: Ludovico Lami et al, No second law of entanglement manipulation after all, Nature Physics (2023). DOI: 10.1038/s41567-022-01873-9