On Hamiltonians Generating Optimal-Speed Evolutions

Abstract

We present a simple derivation of the formula for the Hamiltonian operator(s) that achieve the fastest possible unitary evolution between given initial and final states. We discuss how this formula is modified in pseudo-Hermitian quantum mechanics and provide an explicit expression for the most general optimal-speed quasi-Hermitian Hamiltonian. Our approach allows for an explicit description of the metric- (inner product-) dependence of the lower bound on the travel time and the universality (metric-independence) of the upper bound on the speed of unitary evolutions.

Published version

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Cited by in corpus (18)

• Pseudo-Hermitian Representation of Quantum Mechanics
• Quantum speed limits: from Heisenberg's uncertainty principle to optimal quantum control
• Geometry and response of Lindbladians
• Shortcuts to adiabaticity for non-Hermitian systems
• Bypassing the bandwidth theorem with PT symmetry
• Action quantum speed limits
• Time-dependent Hamiltonians with 100% evolution speed efficiency
• Time-optimal CNOT between indirectly coupled qubits in a linear Ising chain
• Qubit Geodesics on the Bloch Sphere from Optimal-Speed Hamiltonian Evolutions
• Observing a Changing Hilbert-Space Inner Product
• Classical and quantum speed limits
• Non-Hermitian Quantum Systems and Time-Optimal Quantum Evolution
• Family of Exact and Inexact Quantum Speed Limits for Completely Positive and Trace-Preserving Dynamics
• Distinguishability times and asymmetry monotone-based quantum speed limits in the Bloch ball
• Entanglement Efficiencies in PT-Symmetric Quantum Mechanics
• Entanglement between uncoupled modes with time-dependent complex frequencies
• Optimal-speed unitary quantum time evolutions and propagation of light with maximal degree of coherence
• The operational foundations of PT-symmetric and quasi-Hermitian quantum theory