Weaker end connections could improve quantum energy transfer

Energy arriving at a destination is not necessarily energy that can be turned into useful work. That distinction matters for quantum batteries, where the arrangement of a system’s quantum state determines how much work can be extracted. A new theoretical preprint asks how well that work potential can travel along a chain of interacting spins.

R. C. Krisnanda, M. S. Ukhtary and Abdurrouf report that weakening the connections at both ends can substantially improve delivery compared with a uniformly coupled chain. Their calculations also reveal a trade-off: interactions reaching beyond adjacent spins can shorten the wait, but generally reduce the maximum extractable energy received. The study was submitted to arXiv on November 9, 2026; it is a preprint, not an experimental demonstration.

What needs to arrive?

The central quantity is ergotropy: the maximum work that an ideal, reversible quantum manipulation can extract from a state while returning the system’s energy-setting conditions to their original form. It is not simply the energy stored above the ground state. Some states contain energy but offer no ergotropy under these permitted operations.

The researchers model a straight chain of two-level quantum systems, or spins. The first spin acts as the sender and the last as the receiver. Initially, every spin except the sender is in its lowest-energy state. The sender can begin in various pure states or statistical mixtures.

Interactions are then switched on, allowing an excitation to move through the chain. The authors calculate the receiver’s evolving quantum state and determine its ergotropy. Because sender and receiver have matching local energy levels, faithful transfer of the sender’s state would preserve its extractable work.

Why weaken the ends?

The study compares a chain with equal interaction strengths against one whose endpoint connections are reduced by an adjustable factor. It examines both nearest-neighbor interactions and longer-range interactions that fall with the cube of distance.

Weak endpoint connections favor collective states concentrated near the chain’s ends. These states can support effective transfer between sender and receiver without requiring precise adjustment of every interior connection. But weaker connections can also make transfer slow.

To include that timing constraint, the researchers search for the largest receiver ergotropy within a fixed observation window, from zero to 1,000 in the model’s time units. They optimize the endpoint coupling separately for each chain length. Those units are not a measured delivery time for a particular device.

For the examined chains, weakened endpoint connections outperform uniform coupling, especially at larger lengths. Calculations extending to 100 spins show that the receiver can retain nearly the initial ergotropy for the selected example state.

Odd and even chain lengths behave differently. In the nearest-neighbor model, their allowed collective energy states have different structures near the middle of the spectrum. Under weak coupling, these differences let long odd-length chains reach strong transfer sooner. Consequently, they achieve higher optimized ergotropy within the finite waiting window. This is a timing-dependent advantage, not a general claim that odd chains always transfer more.

Two contributions respond differently

The authors also separate ergotropy associated with population inversion—having the excited level more occupied than the ground level—from ergotropy associated with quantum coherence between energy levels.

Imperfect transmission affects these contributions differently. The receiver’s excited-state population scales with the square of the transfer amplitude, while its coherence scales with the amplitude itself. For some starting states, the receiver therefore loses the population-inversion contribution while retaining a coherence contribution.

The coherence contribution can even exceed its initial value in certain cases. That does not establish an increase in total extractable work: the two contributions need not change together.

Faster is not necessarily better

Adding longer-range interactions generally lowers peak receiver ergotropy but makes that peak arrive sooner, particularly for longer chains. Averaging transfer efficiency over initial qubit states also favors the weakened nearest-neighbor chain among the configurations compared.

These are results for specified mathematical models, not a demonstrated energy-delivery technology. The central calculations assume controlled interactions and ideal quantum evolution; environmental disturbances and implementation constraints remain important practical questions. The findings nevertheless identify a concrete design choice worth investigating: endpoint coupling should be tuned alongside the distance of transfer and the time available, rather than simply made as strong as possible.