Quantum speed limit for qubit systems: Exact results

贺志, 姚春梅, Li Li +1 more

Muhammad Musadiq, Salman Khan, Muhammad Javed +1 more

We study the dynamic of quantum speed limit (QSL) time of a qubit coupled to a bath of noninteracting spins. The investigations are carried under both exact and approximate solutions of the model and the results of the two approaches are compared with each other. Under the exact solution and in the low temperature limit, QSL time becomes independent of the number of spins in the environment with potential capacity for quantum speed up. Beyond a critical value of temperature, there exists a frequency of the spins that reduces the capacity for speeding up quantum evolution. The effects of driving time, nonuniform frequencies of the bath’s spins and coupling strength on QSL time are also investigated.

Xue-Bing Wang, Wei Wu

Arun Kumar Pati, Brij Mohan, Sahil +1 more

The traditional quantum speed limits are not attainable for many physical processes, as they tend to be loose and fail to determine the exact time taken by quantum systems to evolve. To address this we derive exact quantum speed limits for the unitary dynamics of pure-state quantum systems that outperform the existing quantum speed limits. Using these exact quantum speed limits, we can precisely estimate the evolution time for two- and higher-dimensional quantum systems. Additionally, for both finite- and infinite-dimensional quantum systems, we derive an improved Mandelstam-Tamm bound for pure states and show that this bound always saturates for any unitary generated by self-inverse Hamiltonians. Furthermore, we show that our speed limits establish an upper bound on the quantum computational circuit complexity and yield a tighter quantum Cramér-Rao bound. These results will have a significant impact on our understanding of quantum physics as well as rapidly developing quantum technologies, such as quantum computing, quantum control, and quantum batteries.

Nikolai A. Sinitsyn

Moein Naseri, Chiara Macchiavello, Dagmar Bruß +2 more

Abstract Quantum speed limits provide ultimate bounds on the time required to transform one quantum state into another. Here, we introduce a novel notion of quantum speed limits for collections of quantum states, investigating the time for converting a basis of states into an unbiased one as well as basis permutation. Establishing an unbiased basis, we provide tight bounds for the systems of dimension smaller than 5, and general bounds for multi-qubit systems and the 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. Permuting a basis, we obtain the exact expression for the Hilbert space of dimension d. We also investigate speed limits for coherence generation, providing the minimal time to establish a certain amount of coherence with a unitary evolution.