Insider Brief
- Researchers have demonstrated that entangled quantum states can be reversibly transformed using an auxiliary system called an entanglement battery.
- The conversion rate between two quantum states is determined by the ratio of their entanglement values, provided the battery retains at least the same amount of entanglement.
- The framework also applies to quantum thermodynamics, where a free energy battery allows reversible transformations governed by free energy rather than entanglement.
Physicists have long compared quantum entanglement to thermodynamics. Now, an international team of researchers has taken steps to formalize the analogy by proposing a kind of “second law” for quantum entanglement — one that enables the reversible manipulation of entangled quantum states using what they call an entanglement battery.
Published in Physical Review Letters, the study solves a longstanding open problem in quantum information theory: how to transform one entangled state into another without losing entanglement, and under what conditions such transformations can be reversed. The researchers add that, if it holds, this conceptual milestone could have implications for foundational quantum science. The technique could even find its way into practical quantum technologies.
The researchers write: “Our setting allows us to consider different entanglement quantifiers which give rise to unique principles governing state transformations, effectively constituting diverse manifestations of a“second law” of entanglement manipulation. These findings resolve a long-standing open question on the reversible manipulation of entangled states and are also applicable to multipartite entanglement and other quantum resource theories, including quantum thermodynamics.”
A Reversible Law for a Quantum Resource
Entanglement is often described as a resource, much like energy. Just as thermodynamic systems obey laws about how energy can be transferred or converted, quantum systems appear to follow laws governing the flow and transformation of entanglement. Until now, however, scientists had no general rule for reversibly converting mixed entangled states—those that exhibit noise or uncertainty.
The new study, led by Ray Ganardi and colleagues from the University of Warsaw, Nanyang Technological University and other institutions, introduces a framework in which any entangled state can be transformed into another with no net loss of entanglement, as long as the transformation is assisted by a shared auxiliary system known as an entanglement battery.
The battery, conceptually similar to a catalyst in chemistry, temporarily supplies or absorbs entanglement but must be returned with at least the same amount of entanglement as it started. When this condition is met, the transformation between states becomes reversible, and the cost of conversion is determined by a quantifiable ratio between the entanglement of the two states.
To try to explain this with a more classical example, think of the entanglement battery like a power supply in an electrical circuit. It can deliver or absorb entanglement during a state transformation, just as a battery can supply or store energy in a circuit. But to preserve reversibility, the battery must end with the same charge it started with — that means no net energy lost or gained. When this condition is met, converting one quantum state into another is like running an ideal circuit, much like voltage or current ratios in classical systems.
Conversion Is a Ratio of Entanglement
At the heart of the study is a straightforward rule: the rate at which one entangled state can be converted into another is determined by comparing how much entanglement each state contains.
In technical terms, the researchers define the conversion rate between two quantum states — let’s call them Q (the starting state) and O (the target state) — as the maximum number of copies of O you can create from a given number of copies of Q, without losing entanglement overall. This rate is expressed as a simple ratio: the amount of entanglement in Q divided by the amount in O.
According to the researchers, the amount of entanglement is measured using a mathematical tool called an “entanglement quantifier.” One example is squashed entanglement, which has properties that make it especially well-suited for this framework. Importantly, this measure must behave predictably when you combine states (additivity), respond smoothly to small changes (continuity), and apply consistently across many copies of a state (asymptotic behavior).
So in plain terms: if the starting state has twice as much entanglement as the target, you can convert one copy of the starting state into two copies of the target, assuming you use an entanglement battery to assist the process and preserve the overall entanglement.
How It Works: Swapping States with a Battery
The process works in a setup where two parties, traditionally named Alice and Bob, each hold part of an entangled system. They also share a separate, entangled ancillary system, the battery. A transformation from one state to another state involves using local operations and classical communication (LOCC), a standard model in quantum information.
To transform these states, Alice and Bob are allowed to shift some entanglement into or out of the battery, provided its overall entanglement doesn’t decrease. If the battery ends the procedure just as entangled as before — or more so — the transformation is deemed successful under the reversible framework.
The researchers show that this setup allows any two entangled states to be reversibly transformed into each other in the asymptotic limit. Even for a finite number of copies, reversibility holds if the entanglement ratio is a rational number.
Implications Beyond Entanglement
While the study focuses on entanglement, the implications extend into other domains of quantum resource theory. In particular, the authors generalize the approach to quantum thermodynamics by introducing a “free energy battery.”
For clarification, because free energy battery sounds more than a bit speculative, in the context of this study free energy battery does not mean a device that magically generates free energy. That would violate the laws of physics, particularly the first and second laws of thermodynamics. Instead, a free energy battery is a theoretical tool used in quantum thermodynamics. It stores free energy — that is, a combination of internal energy and entropy — and can supply or absorb it during quantum state transformations.
Under their framework, the researchers also show that transformations between quantum states obey a second law based on free energy — even when the states are “coherent,” meaning they contain quantum superpositions that challenge classical thermodynamic assumptions. The findings provide an operational interpretation of catalytic thermodynamic processes in quantum systems.
This generalization brings clarity to an open problem in quantum thermodynamics: whether the classical second law can be extended to fully quantum regimes that include coherent effects. The study answers affirmatively, provided a suitable battery system is introduced.
The findings could also have implications for quantum computing, particularly in how entanglement is managed and optimized across large-scale systems.
Entanglement is a core resource in quantum algorithms, communications and error correction, but has traditionally been treated as a one-way, lossy commodity. By introducing a reversible framework for entanglement manipulation, the study suggests that quantum processors could reuse and redistribute entanglement more efficiently, much like how energy is recycled in classical systems.
This could potentially reduce overhead in quantum circuit design, improve the efficiency of entanglement distribution in quantum networks, and provide new tools for managing resources in modular or distributed quantum architectures. While the framework remains theoretical, it lays the groundwork for future protocols that treat entanglement not as something to burn through, but as something to conserve, store, and deploy strategically.
Limitations and Caution
The study’s conclusions depend heavily on the choice of entanglement measure. While squashed entanglement satisfies the necessary properties for reversibility, not all entanglement quantifiers do. Measures like geometric entanglement can allow for misleading results, including scenarios where entanglement appears to increase arbitrarily, a violation of resource conservation principles.
The battery itself also introduces practical constraints when we move outside lab settings. Though theoretically elegant, the requirement that it not lose entanglement may be difficult to ensure in real-world settings, which is always a challenge for quantum work. While classical communication is often considered essential for LOCC, the optimal protocols described in the study may also bypass it entirely in certain cases, raising questions about the role of communication in entanglement management.
There’s also the issue of correlated final states. The study assumes that the battery and the main system are uncorrelated at the end of the transformation, but allows for a relaxed version where correlations are permitted, provided the entanglement in the battery doesn’t drop. These assumptions affect which entanglement measures are valid under the model.
Future Directions
These limitations aren’t necessarily a wall to future research and the authors suggest several paths forward. One is identifying which entanglement measures satisfy the conditions needed for reversible transformations. While it was previously believed that the regularized relative entropy of entanglement might uniquely govern such transformations, this study shows that others—like squashed entanglement—also qualify.
Another is exploring the extent to which similar “battery-assisted” reversibility can be extended across quantum resource theories, from coherence and asymmetry to thermodynamics and beyond. The broader goal is to develop a unified view of how quantum resources can be stored, manipulated, and recovered efficiently — without loss.
The study also opens up avenues for experimental testing. While entanglement batteries are currently theoretical, they provide a blueprint for building controlled systems that manage entanglement like a currency. Such systems could one day improve the efficiency of quantum computers, communications networks, and sensors by minimizing waste and maximizing resource reuse.
The research team included Ganardi and Alexander Streltsov, both from the Centre for Quantum Optical Technologies at the University of Warsaw, with Streltsov also affiliated with the Polish Academy of Sciences; Nelly H. Y. Ng from the School of Physical and Mathematical Sciences at Nanyang Technological University, with Ng also affiliated with the Centre for Quantum Technologies at the National University of Singapore; and Tulja Varun Kondra from the Institute for Theoretical Physics III at Heinrich Heine University Düsseldorf. Ganardi is also affiliated with Nanyang Technological University.
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