Capacity of Entanglement for Non-local Hamiltonian

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.

12 pages, 4 figures, comments are welcome

References in corpus (12)

• Entanglement Spectrum as a Generalization of Entanglement Entropy: Identification of Topological Order in Non-Abelian Fractional Quantum Hall Effect States
• Identifying Topological Order by Entanglement Entropy
• Probing Hawking radiation through capacity of entanglement
• Upper bounds on entangling rates of bipartite Hamiltonians
• Entanglement Spectrum and Entanglement Thermodynamics of Quantum Hall Bilayers at nu=1
• Replica wormholes and capacity of entanglement
• Sum Uncertainty Relation in Quantum Theory
• Quantum speed limits for information and coherence
• Fundamental limits on quantum dynamics based on entropy change
• Closed formula for the relative entropy of entanglement in all dimensions
• Capacity of Entanglement in Local Operators
• Many-particle Entanglement in Multiple Quantum NMR Spectroscopy

Cited by in corpus (13)

• Speed limits and locality in many-body quantum dynamics
• Generalised quantum speed limit for arbitrary time-continuous evolution
• Probing RG flows, symmetry resolution and quench dynamics through the capacity of entanglement
• Stronger speed limit for observables: Tight bound for the capacity of entanglement, the modular Hamiltonian and the charging of a quantum battery
• Quantum Speed Limit in Terms of Coherence Variations
• Fundamental speed limits on entanglement dynamics of bipartite quantum systems
• Energetic cost for speedy synchronization in non-Hermitian quantum dynamics
• Family of Exact and Inexact Quantum Speed Limits for Completely Positive and Trace-Preserving Dynamics
• Evolution of capacity of entanglement and modular entropy in harmonic chains and scalar fields
• Stronger Quantum Speed Limit For Mixed Quantum States
• Probing the quantum speed limit and entanglement in flavor oscillations of neutrino-antineutrino system in curved spacetime
• The area and volume laws for entanglement of scalar fields in flat and cosmological spacetimes
• Influence of gravity on the quantum speed limit in neutrino oscillations