Distance Bounds on Quantum Dynamics

Abstract

We derive rigorous upper bounds on the distance between quantum states in an open system setting, in terms of the operator norm between the Hamiltonians describing their evolution. We illustrate our results with an example taken from protection against decoherence using dynamical decoupling.

7 pages

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• Near-optimal dynamical decoupling of a qubit
• Dynamical Quantum Error Correction of Unitary Operations with Bounded Controls
• Collision models can efficiently simulate any multipartite Markovian quantum dynamics
• Adiabaticity in open quantum systems
• Some general properties of unified entropies
• Automated Synthesis of Dynamically Corrected Quantum Gates
• Quantum simulation of dissipative collective effects on noisy quantum computers
• Speed limits in Liouville space for open quantum systems
• Environment-invariant measure of distance between evolutions of an open quantum system
• Reducing sequencing complexity in dynamical quantum error suppression by Walsh modulation
• Rigorous Bounds for Optimal Dynamical Decoupling
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• High fidelity quantum memory via dynamical decoupling: theory and experiment
• Optimized Dynamical Decoupling via Genetic Algorithms
• Suppressing Spectral Diffusion of the Emitted Photons with Optical Pulses
• Quantum Information Encoding, Protection, and Correction from Trace-Norm Isometries
• Continuity of the quantum Fisher information
• Amplification of quadratic Hamiltonians
• Dependence of the Quantum Speed Limit on System Size and Control Complexity
• Partitioned trace distances
• Pointer States via Engineered Dissipation
• Robustness of quantum algorithms against coherent control errors
• High Order Coherent Control Sequences of Finite-Width Pulses
• Quantum features and signatures of quantum-thermal machines
• Tight and attainable quantum speed limit for open systems
• Efficient quantum algorithm to simulate open systems through a single environmental qubit
• Quantum Speed Limit in Terms of Coherence Variations
• Unified entropies and quantum speed limits for nonunitary dynamics
• Optimal digital dynamical decoupling for general decoherence via Walsh modulation
• Bounds on Shannon distinguishability in terms of partitioned measures
• Resources needed for non-unitary quantum operations
• Sample-Optimal Quantum Process Tomography with Non-Adaptive Incoherent Measurements
• Time-energy tradeoff in unambiguous state discrimination POVM
• Correlations in Quantum Spin Systems from the Boundary Effect
• Simplifying the simulation of local Hamiltonian dynamics
• Quantum Speed Limits Based on the Sharma-Mittal Entropy
• Symmetry-Enhanced Performance of Dynamical Decoupling
• Low overhead universality and quantum supremacy using only $Z$-control
• A Shrinking Factor for Unitarily Invariant Norms under a Completely Positive Map