There is no “second law of entanglement” after all, study claims

Non-returnable tangle manipulation. Our main result in Theorem 1 shows that the two-piece state of 3 cannot be reversibly manipulated under NE transitions. We can only extract the log2(3/2) ≈7/12 synapse bits per copy of ω3 asymptotically, but only one full synapse bit per copy is required to generate it. Theory 1 can be strengthened and extended in several ways. credit: nature physics (2023). DOI: 10.1038/s41567-022-01873-9

The second law of thermodynamics is often considered to be one of the few laws of physics that is completely 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 events, determining which processes are reversible and which are not. It explains why an ice cube placed on a hot stove always melts, and why pressurized gas always flies out of a container (and never back inside) when a valve is opened into the atmosphere.

Only states of equal entropy and energy can be reversibly converted from one state to another. This state of reversal led to the discovery of thermodynamic processes such as the (ideal) Carnot cycle, which constitute an upper limit on how efficiently one can convert heat into work, or vice versa, by circulating a closed system through various temperatures and pressures. Our understanding of this process supported rapid economic development during the Western Industrial Revolution.

Quantum entropy

The beauty of the second law of thermodynamics is that it is applicable to any microscopic system, regardless of the minute details. In quantum systems, entanglement might be one such detail: a quantum connection that causes the separate components of a system to share properties. It is interesting that quantum entanglement shares many profound similarities with thermodynamics, although quantum systems are mostly studied in the microscopic order.

Scientists have unveiled the idea of ​​”entanglement entropy” that accurately mimics the role of thermodynamic entropy, at least for ideal quantum systems completely isolated from their surroundings.

“Quantum entanglement is a key resource that underlies much of the power of quantum computers in the future. To use it effectively, we need to learn how to manipulate it,” says quantum information researcher Ludovico Lamy. The key question became whether entanglement could always be manipulated in reverse, in a direct analogy to the Carnot cycle. Crucially, this reflectivity should prove, at least in theory, even for disturbing (“mixed”) quantum systems that are not completely isolated from their environment.

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

There is no second law of entanglement

To solve this long-standing open question, research by Lamy (formerly at the University of Ulm and currently at QuSoft and the University of Amsterdam) and Bartos Regula (University of Tokyo) has shown that manipulation of entanglement is essentially irreversible, rendering any hope of establishing a second law of entanglement .

This new result relies on constructing a specific quantum state that is very “expensive” to create using pure entanglement. Creating this state will always cause some of this entanglement to be lost, as the invested entanglement cannot be fully recovered. As a result, it is inherently impossible to transfer this state to another and back again. The existence of such cases was not previously known.

Since the approach used here does not presuppose the exact transduction protocols used, it rules out the possibility of reversing crosslinking in all possible settings. It applies to all protocols, assuming they don’t themselves generate new tangles. Lamy explains, “Using crosslinking would be like running a distillery in which alcohol from elsewhere is secretly added to the drink.”

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

This could mean that describing quantum entanglement is not as simple as scientists had hoped. Rather than being a flaw, the much greater complexity of entanglement theory compared to the classical laws of thermodynamics may allow us to use entanglement to accomplish feats that would otherwise be entirely unimaginable. “For now, what we know for sure is that the entanglement conceals a much richer and more complex structure that we would have given credit for,” Lamy concludes.

The paper has been published in the journal nature physics.

more information:
Ludovico Lamy et al., There is no second law to manipulate entanglement after all, nature physics (2023). DOI: 10.1038/s41567-022-01873-9

Provided by the University of Amsterdam

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