Entanglement rates for Renyi, Tsallis and other entropies

Abstract

We provide an upper bound on the maximal entropy rate at which the entropy of the expected density operator of a given ensemble of two states changes under nonlocal unitary evolution. A large class of entropy measures in considered, which includes Renyi and Tsallis entropies. The result is derived from a general bound on the trace-norm of a commutator, which can be expected to find other implementations. We apply this result to bound the maximal rate at which quantum dynamics can generate entanglement in a bipartite closed system with Renyi and Tsallis entanglement entropy taken as measures of entanglement in the system.

References in corpus (14)

• Strong converse for the classical capacity of entanglement-breaking and Hadamard channels via a sandwiched Renyi relative entropy
• Asymptotically scale-invariant occupancy of phase space makes the entropy Sq extensive
• Quantum hypothesis testing and the operational interpretation of the quantum Renyi relative entropies
• Charged-particle multiplicities in pp interactions at sqrt(s) = 900 GeV measured with the ATLAS detector at the LHC
• Nonlinear Relativistic and Quantum Equations with a Common Type of Solution
• Non-extensive Statistical Mechanics and Black Hole Entropy From Quantum Geometry
• On the capacities of bipartite Hamiltonians and unitary gates
• Entanglement rates and area laws
• Quantum phases with differing computational power
• Upper bounds on entangling rates of bipartite Hamiltonians
• Quantum Skew Divergence
• Entanglement capability of self-inverse Hamiltonian evolution
• Entanglement-assisted local operations and classical communications conversion in the quantum critical systems
• Entanglement rates for bipartite open systems

Cited by in corpus (5)

• Speed limits and locality in many-body quantum dynamics
• Emergence of a second law of thermodynamics in isolated quantum systems
• Fundamental speed limits on entanglement dynamics of bipartite quantum systems
• The dynamical $\alpha$-Rényi entropies of local Hamiltonians grow at most linearly in time
• Limitations of Noisy Quantum Devices in Computational and Entangling Power