Quantum Speed Limit for Change of Basis
arXiv:2212.12352 · doi:10.1088/1367-2630/ad25a5
Abstract
Quantum speed limits provide ultimate bounds on the time required to transform one quantum state into another. Here, we extend the notion of quantum speed limits to collections of quantum states, investigating the time for converting a basis of states into an unbiased one. We provide tight bounds for systems of dimension smaller than 5, and general bounds for multi-qubit systems and Hilbert space dimension . For two-qubit systems, we show that the fastest transformation implements two Hadamards and a swap of the qubits simultaneously. We further prove that for qutrit systems the evolution time depends on the particular type of the unbiased basis. We also investigate speed limits for coherence generation, providing the minimal time to establish a certain amount of coherence with a unitary evolution.
arXiv comment13 pages, 2 figures
References in corpus (36)
- Quantum entanglement
- Quantifying Coherence
- Quantum Coherence as a Resource
- The classical-quantum boundary for correlations: discord and related measures
- Operational Resource Theory of Coherence
- The maximum speed of dynamical evolution
- Quantum speed limits: from Heisenberg's uncertainty principle to optimal quantum control
- Quantum speed limit for physical processes
- Quantum speed limit for non-Markovian dynamics
- Quantum speed limits in open system dynamics
- The fundamental limit on the rate of quantum dynamics: the unified bound is tight
- Quantum speed limits, coherence and asymmetry
- Generalized Geometric Quantum Speed Limits
- Geometric derivation of the quantum speed limit
- Operational Resource Theory of Imaginarity
- Quantum Speed Limits Across the Quantum-to-Classical Transition
- Quantum Speed Limit is Not Quantum
- Tightening Quantum Speed Limits for Almost All States
- Speed limit for open quantum systems
- Quantifying the Imaginarity of Quantum Mechanics
- One-shot coherence distillation
- Quantum Coherence Sets The Quantum Speed Limit For Mixed States
- Resource theory of imaginarity: Quantification and state conversion
- Quantum speed limits for leakage and decoherence
- Comment on "Geometric derivation of the quantum speed limit"
- Experimental progress on quantum coherence: detection, quantification, and manipulation
- On the Role of Coherence in Shor's Algorithm
- Quantum Speed Limit for States with a Bounded Energy Spectrum
- Probing Quantum Speed Limits with Ultracold Gases
- Quantum speed limits for information and coherence
- Resource speed limits: Maximal rate of resource variation
- Non-asymptotic assisted distillation of quantum coherence
- There is no general connection between the quantum speed limit and non-Markovianity
- Entanglement and coherence in Bernstein-Vazirani algorithm
- Energy-constrained discrimination of unitaries, quantum speed limits and a Gaussian Solovay-Kitaev theorem
- Quantum speed limit and divisibility of the dynamical map