After all, there is no "second law of entanglement," the study claims

After all, there is no “second law of entanglement,” the study claims

Irreversibility of entanglement manipulation. Our main result in Theorem 1 shows that the two-qutrite state ω3 cannot be reversibly manipulated under NE transformations. We can only extract the log2(3/2)≈7/12 crossover bits per copy of asymptotic ω3, but a full crossover bit per copy is required to generate it. Theorem 1 can be strengthened and extended in several ways. Credit: The physics of nature (2023). DOI: 10.1038/s41567-022-01873-9

The second law of thermodynamics is often considered one of the few laws of physics that is absolutely and unequivocally 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 events, 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) when a valve is opened to atmosphere.

Only states of equal entropy and energy can be reversibly converted from one to the other. This condition of reversibility led to the discovery of thermodynamic processes such as the (idealized) Carnot cycle, which represents an upper limit on how efficiently heat can be converted to work, or vice versa, by cycling a closed system through various 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 can be entanglement: a quantum connection that causes the separate components of the system to share properties. Intriguingly, quantum entanglement has many profound similarities to thermodynamics, even though quantum systems are mostly studied in the microscopic regime.

Scientists have discovered a notion of “crossover entropy” that exactly mimics the role of thermodynamic entropy, at least for idealized quantum systems that are perfectly isolated from their surroundings.

“Quantum entanglement is a key resource that underlies great power of future quantum computers. To use it effectively, we need to learn how to manipulate it,” says quantum information researcher Ludovico Lami. A fundamental question became whether entanglement can always be manipulated reversibly, 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.

It was assumed that a “second law of entanglement” could be established, embodied in a single function that would generalize the entropy of entanglement and govern all entanglement manipulation protocols. This assumption appeared in a famous list of open problems in quantum information theory.

No second law of entanglement

Addressing this long-standing open question, research by Lami (formerly at the University of Ulm and now at QuSoft and the University of Amsterdam) and Bartosz Regula (University of Tokyo) demonstrates that entanglement manipulation is fundamentally irreversible, eliminating any hope of establish a second law of entanglement.

This new result is based on the construction of a certain 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.

Since the approach used here does not assume which exact transformation protocols are used, it rules out reversibility of entanglement in all possible settings. It applies to all protocols, assuming they do not themselves generate new entanglements. Lami explains, “Using tampering would be like running a distillery where alcohol from somewhere else is secretly added to the drink.”

Lami says: “We can conclude that no single quantity, such as entanglement entropy, can tell us everything we need to know about the allowed transformations of entangled physical systems. Entanglement theory 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. However, rather than being a drawback, the much greater complexity of entanglement theory compared to the classical laws of thermodynamics can allow us to use entanglement to achieve facts that would otherwise be completely inconceivable. “For now, what we know for sure is that the entanglement hides an even richer and more complicated structure than we’ve given it credit for,” Lami concludes.

The work is published in the journal The physics of nature.

More information:
Ludovico Lami et al., There is no second law of entanglement manipulation, after all, The physics of nature (2023). DOI: 10.1038/s41567-022-01873-9

Provided by the University of Amsterdam

Citation: After all, there is no ‘second law of entanglement’, claims study (2023, January 24) Retrieved January 24, 2023, from

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