Quantum Speed Limit for Change of Basis
- URL: http://arxiv.org/abs/2212.12352v1
- Date: Fri, 23 Dec 2022 14:10:13 GMT
- Title: Quantum Speed Limit for Change of Basis
- Authors: Moein Naseri, Chiara Macchiavello, Dagmar Bru\ss, Pawe{\l} Horodecki,
and Alexander Streltsov
- Abstract summary: We extend the notion of quantum speed limits to collections of quantum states.
For two-qubit systems, we show that the fastest transformation implements two Hadamards and a swap of the qubits simultaneously.
For qutrit systems the evolution time depends on the particular type of the unbiased basis.
- Score: 55.500409696028626
- License: http://arxiv.org/licenses/nonexclusive-distrib/1.0/
- 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 $d$. 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.
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