Capacity of Entanglement for Non-local Hamiltonian

TL;DR

This paper explores the capacity of entanglement in bipartite quantum systems under non-local Hamiltonians, linking it to quantum speed limits and extending the concept to mixed states, with broad potential applications.

Contribution

It introduces a dynamic analysis of the capacity of entanglement under non-local Hamiltonians and generalizes the concept to mixed states based on relative entropy.

Findings

Quantum speed limit depends on capacity of entanglement

Bound on the rate of capacity of entanglement for self-inverse Hamiltonians

Generalization of capacity to bipartite mixed states

Abstract

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 non-local Hamiltonian. Specifically, we address the question: Given an arbitrary non-local Hamiltonian what is the capacity of entanglement that the system can possess? As an useful application, we show that the quantum speed limit for creating the entanglement is not only governed by the fluctuation in the non-local Hamiltonian, but also depends inversely on the time average of 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 the capacity of entanglement. Towards the end, we generalise 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.