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

A key challenge in scaling up quantum systems is the potential for correlated decay, which can significantly reduce the lifetime of states of interest. This talk answers the following question: what is the maximal decay rate of a quantum system, and how does it scale with system size? First, we reformulate the problem of maximal decay rate into finding the ground state energy of a 2-local Hamiltonian. While finding the ground state is widely believed to be hard, it is possible to efficiently find upper and lower bounds. In particular, using ideas from quantum approximation theory and semidefinite programming relaxations, we provide 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 (which describes dissipative couplings between atoms) and agnostic of the specific microscopic interactions. For many classes of physically-relevant systems, the bounds are tight, resulting in scaling laws with system size. For arrays of atoms in free space, the scaling depends only on the dimensionality and interaction range. These laws serve as upper limits on how fast any quantum state can decay, and offer valuable insights for research in quantum optics, quantum information processing, and metrology.