Every quantum system is open. Whether it is a single trapped ion or a vast array of thousands of neutral atoms, a quantum device continually exchanges energy and information with its surroundings, and that exchange leads to decoherence and decay of the fragile quantum states on which future technologies depend. For decades, physicists have understood how decay works for a lone emitter, but the collective case—where many particles decay together through shared interactions with the same environment—has remained stubbornly difficult to characterize. Now, a team of researchers led by Wai-Keong Mok of the California Institute of Technology and Ana Asenjo-Garcia of Columbia University, working alongside John Preskill and colleagues, has established rigorous, universal bounds on how fast a large quantum system can possibly decay, and shown that in many important cases those bounds translate into exact scaling laws with system size. The work, published in Nature Physics, connects the physics of dissipation to the abstract theory of computational complexity in a way that may ultimately shape how quantum computers and simulators are built.

The central question the team addressed sounds deceptively simple: given a large quantum system coupled to its environment, what is the maximal rate at which it can decay, and how does that rate grow as the system gets bigger? In a collection of many particles, vacuum fluctuations of the electromagnetic field—or of phonons, magnons, and other collective excitations—mediate long-range dissipative interactions that can never be switched off. When emitters are packed closely together, their decay becomes correlated and collectively enhanced, a phenomenon famously exemplified by Dicke superradiance, in which a dense ensemble of excited atoms emits a burst of light far brighter than the sum of independent emissions. Correlated decay can be a curse, shortening coherence times in quantum processors and degrading the signal-to-noise ratio of atomic clocks, or a blessing, enabling new light sources and the dissipative preparation of entangled many-body states. Knowing the worst-case decay rate is therefore essential for both diagnosing the limits of quantum hardware and exploiting dissipation as a resource.

Computing that maximal decay rate exactly, however, is extraordinarily hard. The researchers showed that the problem is formally equivalent to finding the ground-state energy of a generic two-local spin Hamiltonian, a task known to be quantum Merlin–Arthur complete—believed to be intractable even for a quantum computer. Except in trivial limits, such as non-interacting qubits or fully symmetric all-to-all models, no exact solution exists. Rather than surrender to this complexity, the team turned it to their advantage. By importing tools from Hamiltonian complexity theory into the study of out-of-equilibrium open quantum dynamics, they derived general upper and lower bounds on the maximal decay rate that hold for a broad class of Markovian many-body quantum systems, encompassing arbitrary Hamiltonian interactions, coherent driving, diverse decoherence channels, and even disorder in the dissipative couplings.

The mathematical framework rests on a Lindblad master equation describing N qubits whose collective dissipation is encoded in a Hermitian, positive semidefinite decoherence matrix. The instantaneous decay rate of the many-body system can be written as the expectation value of an auxiliary Hermitian Hamiltonian, which generically takes the form of an XY model on a weighted interaction graph with a local transverse field. Maximizing the decay rate over all possible quantum states then amounts to finding the ground-state energy of the negative of that auxiliary Hamiltonian—the very problem complexity theory tells us is hard. The team’s key insight was to bound this quantity using product states, simple unentangled states in which each qubit is treated independently with a carefully chosen phase. Remarkably, this approach yields bounds that remain valid for any state, including highly entangled ones, without relying on mean-field approximations. The physical message is striking: entanglement is not necessary for a system to dissipate at a rate near the theoretical maximum.

The resulting bounds take a compact form involving the largest eigenvalue of the decoherence matrix, the average single-qubit decay rate, and a parameter that measures how uniformly the brightest collective decay channel is spread across the system. When decay is delocalized—meaning the dominant collective jump operator has approximately uniform spatial support over all the qubits—the bounds become tight up to a constant factor, yielding an elegant scaling law: the maximal decay rate is proportional to the system size times the largest collective transition rate. This simple relation is far from obvious and does not hold for arbitrary systems; the authors even constructed explicit mathematical counterexamples showing that no universal scaling law depending only on system size and the spectrum of the decoherence matrix can exist in general. But for the physically relevant delocalized regime, the law holds, and it remains valid even when local Hamiltonian terms and local dissipation are included, since those contribute only subleading corrections.

The researchers then applied their machinery to the platform of greatest experimental relevance: ordered arrays of atoms in free space, which have become a workhorse for quantum computing, quantum simulation, atomic clocks, and spin squeezing. Here the decoherence matrix is proportional to the electromagnetic Green’s function evaluated at the resonance frequency, a long-ranged function with oscillating sign that makes the problem genuinely non-trivial. By analyzing divergences of the transition rates in reciprocal space—divergences that appear in two- and three-dimensional lattices as constructive interference of photon emission is enhanced—they found that the maximal decay rate scales as N raised to the power of three-halves minus one over twice the array dimensionality. This dimensional scaling is universal in the strictest sense: it is independent of lattice geometry, lattice constant, and atomic polarization, all of which enter only as prefactors. For one-dimensional arrays, the decay effectively behaves as though the atoms were non-interacting, while for two- and three-dimensional arrays the collective enhancement grows with size.

To validate these analytical predictions, the team employed a semidefinite-programming relaxation, a numerical technique borrowed from approximation algorithms that can be solved in polynomial time. They proved rigorously that the semidefinite-programming solution approximates the true maximal decay rate up to a constant factor, establishing a universal relation valid for arbitrary systems regardless of whether decay is delocalized. Numerical simulations for arrays with lattice constants comparable to the resonance wavelength confirmed the predicted dimensional scaling with excellent agreement. The analysis also mapped out the crossover between regimes: for arrays much smaller than the wavelength, Dicke’s quadratic scaling is recovered, while for very widely spaced atoms the ensemble behaves as independent emitters. For intermediate, physically relevant spacings, the crossover to superlinear collective decay requires a number of atoms that grows rapidly with the lattice constant, explaining why current experiments with a few hundred atoms have not yet observed the full dimensional scaling.

The implications ripple across quantum science. The scaling laws set rigorous upper bounds on transient superradiant bursts from extended atomic arrays and on the intensity and optimal pump rate of superradiant lasing, ruling out such lasing for one-dimensional free-space arrays while suggesting that a superradiant lasing phase transition might occur in two and three dimensions. They also determine the threshold drive intensity for driven-dissipative Dicke phase transitions in free space, consistent with recent numerical studies of collective resonance fluorescence. Perhaps most consequentially for technology, the authors estimated the impact of collective decay on Rydberg atom quantum processors, where microwave transitions have wavelengths of roughly ten millimeters and typical experiments already sit within the collective decay regime. Their analysis of a two-dimensional array of tweezer-trapped rubidium atoms performing parallel entangling gates suggests that in a next-generation 40-by-200 array, collectively enhanced leakage could contribute roughly one-third of the total gate error budget—a non-negligible share that grows as arrays scale up.

Quantum error correction faces its own reckoning with these results. In the worst case, the error rate per qubit from correlated decay scales with the maximal decay rate divided by system size, which grows with array size in two dimensions and above, meaning that corrections must be applied on timescales that shorten as processors expand. Yet the news is not uniformly grim: the researchers proved that typical stabilizer states—the random-looking states that populate the code space of many error-correcting schemes—decay at nearly the rate of independent emitters, protected by random phases between qubits. The danger lies in structured states, since even simple product states can be superradiant. Looking forward, the authors point to quantum metrology, where carefully prepared Dicke and squeezed states may hit fundamental limits imposed by correlated decay, and to theoretical extensions of their approximation techniques to higher-order observables, driven-dissipative steady states, interacting fermions and bosons, and even maximal absorption rates relevant to quantum batteries. What began as a question about how fast quantum systems fall apart has yielded a unifying framework for the limits of dissipation itself.

Subject of Research: Universal scaling laws governing the maximal correlated decay rate of many-body open quantum systems

Article Title: Universal scaling laws for correlated decay of many-body quantum systems

Article References: Mok, W.-K., Poddar, A., Sierra, E., Rusconi, C. C., Preskill, J., & Asenjo-Garcia, A. (2026). Universal scaling laws for correlated decay of many-body quantum systems. Nature Physics. https://doi.org/10.1038/s41567-026-03448-4

Image Credits: AI Generated

DOI: 10.1038/s41567-026-03448-4

Keywords: quantum decay, decoherence, superradiance, open quantum systems, atomic arrays, Lindblad master equation, quantum complexity theory, semidefinite programming, Rydberg atoms, quantum error correction, Dicke scaling, quantum optics