Capacity of entanglement for a nonlocal Hamiltonian

The notion of capacity of entanglement is the quantum information theoretic counterpart of the heat capacity which is defined as the second cumulant of the entanglement spectrum. Given any bipartite pure state, we can define the capacity of entanglement as the variance of the modular Hamiltonian in the reduced state of any of the subsystems. Here, we study the dynamics of this quantity under a nonlocal Hamiltonian. Specifically, we address the following question: Given an arbitrary nonlocal Hamiltonian, what is the capacity of entanglement that the system can possess? As a useful application, we show that the quantum speed limit for creating the entanglement is not only governed by the fluctuation in the nonlocal Hamiltonian, but also depends inversely on the time average of the square root of the capacity of entanglement. Furthermore, we discuss this quantity for a general self-inverse Hamiltonian and provide a bound on the rate of capacity of entanglement. Towards the end, we generalize the capacity of entanglement for bipartite mixed states based on the relative entropy of entanglement and show that the above definition reduces to the capacity of entanglement for pure bipartite states. Our results can have several applications in diverse areas of physics.