Speed limits on correlations in bipartite quantum systems

Abstract

Quantum speed limit is bound on the minimum time a quantum system requires to evolve from an initial state to final state under a given dynamical process. It sheds light on how fast a desired state transformation can take place which is pertinent for design and control of quantum technologies. In this paper, we derive speed limits on correlations such as entanglement, Bell-CHSH correlation, and quantum mutual information of quantum systems evolving under dynamical processes. Our main result is speed limit on an entanglement monotone called negativity which holds for arbitrary dimensional bipartite quantum systems and processes. Another entanglement monotone which we consider is the concurrence. To illustrate efficacy of our speed limits, we analytically and numerically compute the speed limits on the negativity, concurrence, and Bell-CHSH correlation for various quantum processes of practical interest. We are able to show that for practical examples we have considered, some of the speed limits we derived are actually attainable and hence these bounds can be considered to be tight.

18 pages, 11 figures, published in Physical Review A

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• Quantum speed limit for Kirkwood-Dirac quasiprobabilities
• Quantum Velocity Limits for Multiple Observables: Conservation Laws, Correlations, and Macroscopic Systems
• Entanglement-assisted quantum speedup: Beating local quantum speed limits
• Family of Exact and Inexact Quantum Speed Limits for Completely Positive and Trace-Preserving Dynamics
• Optimal quantum speed for mixed states
• Quantum-imaginarity-based quantum speed limit
• Stronger Quantum Speed Limit For Mixed Quantum States
• A Unifying Quantum Speed Limit For Time-Independent Hamiltonian Evolution
• Generalized Entropic Quantum Speed Limits
• Quantum Speed Limits Based on the Sharma-Mittal Entropy
• Quantum speed limits based on Jensen-Shannon and Jeffreys divergences for general physical processes
• Influence of gravity on the quantum speed limit in neutrino oscillations
• Implementation of multiparticle quantum speed limits on observables