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Quantum theory sets a bound on the minimal time evolution between initial and target states. This bound is called as quantum speed limit time. It is used to quantify maximal speed of quantum evolution. The quantum evolution will be faster, if quantum speed limit time decreases. In this work, we study the quantum speed limit time of a quantum state in the presence of disturbance effects in an environment. We use the model which is provided by Masashi Ban in href{https://doi.org/10.1103/PhysRevA.99.012116}{Phys. Rev. A 99, 012116 (2019)}. In this model two quantum systems $mathcal{A}$ and $mathcal{S}$ interact with environment sequentially. At first, quantum system $mathcal{A}$ interacts with the environment $mathcal{E}$ as an auxiliary system then quantum system $mathcal{S}$ interacts with disturbed environment immediately. In this work, we consider dephasing coupling with two types of environment with different spectral density: Ohmic and Lorentzian. We observe that, non-Markovian effects will be appear in the dynamics of quantum system $mathcal{S}$ by the interaction of quantum system $mathcal{A}$ with the environment. Given the fact that quantum speed limit time reduces due to non-Markovian effects, we show that disturbance effects will reduce the quantum speed limit time.
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We investigate the roles of the relativistic effect on the speed of evolution of a quantum system coupled with amplitude damping channels. We find that the relativistic effect speed-up the quantum evolution to a uniform evolution speed of open quantum systems for the damping parameter $p_{tau}lesssim p_{tau_{c0}}.$ Moreover, we point out a non-monotonic behavior of the quantum speed limit time (QSLT) with acceleration in the damping limit $p_{tau_{c0}}lesssim p_{tau}lesssim p_{tau_{c1}},$ where the relativistic effect first speed-up and then slow down the quantum evolution process of the damped system. For the damping strength $p_{tau_{c1}}lesssim p_{tau}$, we observe a monotonic increasing behavior of QSLT, leads to slow down the quantum evolution of the damped system. In addition, we examine the roles of the relativistic effect on the speed limit time for a system coupled with the phase damping channels.
Quantum speed limit time defines the limit on the minimum time required for a quantum system to evolve between two states. Investigation of bounds on speed limit time of quantum system under non-unitary evolution is of fundamental interest, as it reveals interesting connections to quantum (non-)Markovianity. Here, we discuss the characteristics of quantum speed limit time as a function of quantum memory, quantified as the deviation from temporal self-similarity of quantum dynamical maps for CP-divisible as well as indivisible maps. This provides an operational meaning to CP-divisible (non-)Markovianity.
Memory effects play a fundamental role in the dynamics of open quantum systems. There exist two different views on memory for quantum noises. In the first view, the quantum channel has memory when there exist correlations between successive uses of the channels on a sequence of quantum systems. These types of channels are also known as correlated quantum channels. In the second view, memory effects result from correlations which are created during the quantum evolution. In this work we will consider the first view and study the quantum speed limit time for a correlated quantum channel. Quantum speed limit time is the bound on the minimal time which is needed for a quantum system to evolve from an initial state to desired states. The quantum evolution is fast if the quantum speed limit time is short. In this work, we will study the quantum speed limit time for some correlated unital and correlated non-unital channels. As an example for unital channels we choose correlated dephasing colored noise. We also consider the correlated amplitude damping and correlated squeezed generalized amplitude damping channels as the examples for non-unital channels. It will be shown that the quantum speed limit time for correlated pure dephasing colored noise is increased by increasing correlation strength, while for correlated amplitude damping and correlated squeezed generalized amplitude damping channels quantum speed limit time is decreased by increasing correlation strength.
We investigate if physical laws can impose limit on computational time and speed of a quantum computer built from elementary particles. We show that the product of the speed and the running time of a quantum computer is limited by the type of fundamental interactions present inside the system. This will help us to decide as to what type of interaction should be allowed in building quantum computers in achieving the desired speed.
We report on a time scaling technique to enhance the performances of quantum protocols in non-Hermitian systems. The considered time scaling involves no extra-couplings and yields a significant enhancement of the quantum fidelity for a comparable amount of resources. We discuss the application of this technique to quantum state transfers in 2 and 3-level open quantum systems. We derive the quantum speed limit in a system governed by a non-Hermitian Hamiltonian. Interestingly, we show that, with an appropriate driving, the time-scaling technique preserves the optimality of the quantum speed with respect to the quantum speed limit while reducing significantly the damping of the quantum state norm.
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