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

Increasing the density of quantum devices opens avenues to explore novel regimes of many-body quantum dynamics and enhance the performance of various quantum applications. At the same time, this effort poses new challenges as densely packed systems exhibit correlated dissipation, significantly impacting the decay rate of correlated quantum states. It is thus natural to ask: What is the maximum decay rate of a system with correlated dissipation? Addressing this question for large numbers of particles is however complicated by the exponential scaling of the Hilbert space dimension. In this talk, I will present an alternative method that circumvents this difficulty. We reformulate the problem of maximal decay rate into finding the ground state energy of a 2-local Hamiltonian. Leveraging ideas from quantum approximation theory and semidefinite programming relaxations developed for Hamiltonian systems, we provide rigorous analytical bounds for the maximal decay rate of generic many-body quantum systems. Our bounds are universal in that they only depend on global properties of the decoherence matrix and agnostic of the specific microscopic interactions. For many classes of physical systems, the bounds are tight, resulting in scaling laws with system size. As a particular application, I will discuss Superfluorescence in extended systems. Our general method allows us to derive rigorous scalings for the radiation burst, illustrating its broader applicability in understanding complex quantum phenomena.