Entanglement has now become the key resource in quantum information theory. It is being used in quantum teleportation and quantum cryptography, quantum computing, communication, and precision measurements.
More than 200 years after Sadi Carnot introduced the second law of thermodynamics, scientists have discovered a similar rule for the quantum world. This new “second law of entanglement” demonstrates that quantum entanglement can be altered and reversed in a controlled manner, much like the behavior of energy in classical thermodynamics. Until now, many researchers doubted this was possible.
The study could advance the understanding of entanglement’s basic properties. It also offers significant insight into effectively regulating entanglement and other quantum phenomena in practice.
Scientists have noticed many parallels between quantum entanglement and thermodynamics. One key example is entanglement entropy, which behaves like thermodynamic entropy, a measure of disorder, but in ideal, perfectly controlled quantum systems.
There is no second law of entanglement after all, suggests a study
But there’s been a missing piece: a quantum version of the second law of thermodynamics. This classical law states that systems naturally tend toward greater disorder (higher entropy) and that while reversing a process perfectly is theoretically possible, it’s extremely rare and requires ideal conditions.
In the quantum world, reversibility doesn’t mean rewinding time. Instead, it means that an outside agent can change a quantum system’s state and then return it to its original state without losing any information, a form of perfect control. Until now, proving this kind of reversibility for entanglement had been elusive.
For a long time, scientists in quantum information science have been searching for a rule analogous to the second law of thermodynamics, but applicable to the quantum world. This has been a central unsolved puzzle.
To tackle this problem, researchers often envision two people, typically referred to as Alice and Bob, who are separated and wish to share quantum information. However, there’s a catch: they can only interact with their local quantum systems and communicate with each other using conventional methods, such as a phone or the internet.
This setup, known as LOCC (Local Operations and Classical Communication), simplifies things. It also means that, regardless of what Alice and Bob do, they can’t directly alter the deep, nonlocal connection —the entanglement —between their quantum systems.
Under LOCC operations, entanglement is irreversible. Considering this, researchers in this study posed the question: Can we somehow go beyond LOCC in a meaningful way and recover reversibility?
They found the answer that it is possible, as long as Alice and Bob share an additional entangled system: an entanglement battery.
Like an ordinary battery stores energy, an entanglement battery injects and stores entanglement. Imagine Alice and Bob have access to a special kind of battery, not one that stores electricity, but one that stores entanglement. This entanglement battery can be used to help them change the state of their quantum systems. They’re allowed to charge or drain the battery during the process, but there’s one strict rule: they can’t reduce the total amount of entanglement in the battery.
Just like a regular battery lets you do things you couldn’t do otherwise, this entanglement battery lets Alice and Bob perform quantum operations that would typically be impossible under LOCC rules alone. With its help, the researchers showed that any transformation involving mixed quantum states can be made perfectly reversible, a breakthrough in quantum information science.
The idea of an entanglement battery can be expanded into a broader concept: a resource battery. This is an extra quantum system that facilitates a transformation, as long as it doesn’t reduce the key resource being utilized, whether that’s entanglement, coherence, or something else.
Lead author of the study Alexander Streltsov said, “We can have a battery that is supposed to preserve coherence or free energy, and then we can formulate a reversible framework in this setting where, instead of entanglement, we reversibly manipulate that particular resource of our system.”
“Though many of these other principles of reversibility have already been confirmed via other approaches, our technique offers a unified proof framework based on well-established physical principles.”
Journal Reference:
- Ray Ganardi, Tulja Varun Kondra, Nelly H. Y. Ng, and Alexander Streltsov. Second Law of Entanglement Manipulation with an Entanglement Battery. Physical Review Letters, 2025; 135 (1) DOI: 10.1103/kl56-p2vb