second law reversible entanglement battery

Quantum Entanglement Gets Its Own Second Law—Two Centuries After Carnot

Establishing a Second Law for Quantum Systems

Just over two centuries after the French physicist Sadi Carnot laid down the second law of thermodynamics, an international research team has now revealed an equivalent principle for quantum systems. This newly established second law of entanglement manipulation shows that, akin to heat or energy in classical thermodynamics, quantum entanglement can be reversibly manipulated—an idea that had long remained contentious.

The research, appearing in Physical Review Letters on 2 July 2025, advances our understanding of the fundamentals of entanglement and delivers key guidance on how best to handle entanglement and related quantum phenomena in real-world settings.

Entanglement—A Hallmark and Resource of Quantum Mechanics

Defining Entanglement and Its Historical Context

Entanglement is widely regarded as the defining hallmark of quantum mechanics. When two microscopic particles become entangled, measuring a quantum property of one and then examining the other will always reveal a perfect correlation, even if the pair is separated by enormous distances. Thus, knowledge of one particle's state instantly disclose the state of its partner.

Entanglement was proposed nearly 90 years ago as a means of highlighting the perceived absurdity of quantum theory if taken as a complete description of nature. Yet today, it is no longer viewed as absurd.

Modern Applications in Quantum Information Science

Following extensive verification of entanglement's existence in the real world, it has become a foundational resource in quantum information science—enabling quantum teleportation, secure quantum cryptography and delivering clear advantages in computing, communication and precision metrology.

Thermodynamic Parallels and the Quest for Reversibility

Entanglement Entropy Mirrors Thermodynamic Entropy

Although entanglement remains at odds with our everyday understanding of reality, researchers have uncovered compelling parallels with a far more familiar domain: thermodynamics. Indeed, numerous similarities now link the frameworks of entanglement and thermodynamic theory. One such example is "Entanglement Entropy", a property of idealized, noiseless quantum systems that mirrors the function of thermodynamic entropy.

The Challenge of a Quantum Second Law

The second law of thermodynamics tells us that systems progress towards higher entropy, with true reversibility being both efficient and exceptionally rare. A corresponding principle within quantum theory has, however, remained frustratingly out of grasp. Crucially, this notion of reversibility involves the ability of an external agent to  change and then exactly restore a system's state without incurring any loss—not a literal reversal of time.

"Identifying a second law akin to that of thermodynamics has long been an open question in quantum information science," explains study co-author Tulja Varun Kondra. "This challenge has served as our principal motivation."

Surpassing LOCC Limits with an Entanglement Battery

The Alice-and Bob LOCC Scenario

A great deal of research on this problem has centred around a scenario where two distant parties—commonly referred to as Alice and Bob—wish to exchange quantum information but are limited to performing local operations on their respective systems and communicating via classical means, such as telephone or the internet. This restriction, known as local operations and classical communication (LOCC), ensures that they cannot influence the inherently nonlocal aspects of entanglement between their quantum systems.

Introducing the Entanglement Battery

"it is well established that under LOCC operations, entanglement is an irreversible resource," notes senior author Alexander Streltsov. "This led us to ask whether it might be possible to surpass LOCC constraints and restore reversibility." The team found that the answer is yes —provided Alice and Bob are equipped with an additional entangled system, known as an entanglement battery.

Much like a conventional battery stores energy for performing work in thermodynamic processes, an entanglement battery stores and supplies entanglement. It may be employed during quantum state transformations, with its own state adjusted as part of the operation. The one constraint: Alice and Bob must ensure the battery's level of entanglement is never diminished.

Rendering Mixed-State Transformations Reversible

Just as an ordinary battery enables processes that would otherwise be unachievable, an entanglement battery offers the same advantage. By supplementing standard LOCC operations with this hypothetical device, the team showed that any transformation between mixed entangled states could, in fact, be rendered fully reversible.

Implications and Future Directions

Toward Universal Second Laws for All Quantum States

This breakthrough marks a major step forward in the ongoing debate regarding the general reversibility of entanglement manipulation. More crucially, the researchers have demonstrated that their methods extend beyond mixed-state transformations, employing the entanglement battery to test reversibility in broader contexts. Such findings pave the way for a set of second laws applicable to all quantum states.

Potential Impact on Quantum Technologies

The entanglement battery could prove valuable beyond the scope of entanglement theory itself. Notably, its principles extend to multi-particle systems, offering new insights into complex quantum networks and the potential development of next-generation quantum technologies.

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