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Register a new userEntanglement dynamics under local Lindblad evolution
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The phenomenon of entanglement sudden death (ESD) in finite dimensional composite open systems is described here for both bi-partite as well as multipartite cases, where individual subsystems undergo Lindblad type heat bath evolution. ESD is found to be generic for non-zero temperature of the bath. At T=0, one-sided action of the heat bath on pure entangled states of two qubits does not show ESD.
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We study the time evolution of quantum entanglement for a specific class of quantum dynamics, namely the locally scrambled quantum dynamics, where each step of the unitary evolution is drawn from a random ensemble that is invariant under local (on-site) basis transformations. In this case, the average entanglement entropy follows Markovian dynamics that the entanglement property of the future state can be predicted solely based on the entanglement properties of the current state and the unitary operator at each step. We introduce the entanglement feature formulation to concisely organize the entanglement entropies over all subsystems into a many-body wave function, which allows us to describe the entanglement dynamics using an imaginary-time Schrodinger equation, such that various tools developed in quantum many-body physics can be applied. The framework enables us to investigate a variety of random quantum dynamics beyond Haar random circuits and Brownian circuits. We perform numerical simulations for these models and demonstrate the validity and prediction power of the entanglement feature approach.
We characterize the early stages of the approach to equilibrium in isolated quantum systems through the evolution of the entanglement spectrum. We find that the entanglement spectrum of a subsystem evolves with at least three distinct timescales. First, on an o(1) timescale, independent of system or subsystem size and the details of the dynamics, the entanglement spectrum develops nearest-neighbor level repulsion. The second timescale sets in when the light-cone has traversed the subsystem. Between these two times, the density of states of the reduced density matrix takes a universal, scale-free 1/f form; thus, random-matrix theory captures the local statistics of the entanglement spectrum but not its global structure. The third time scale is that on which the entanglement saturates; this occurs well after the light-cone traverses the subsystem. Between the second and third times, the entanglement spectrum compresses to its thermal Marchenko-Pastur form. These features hold for chaotic Hamiltonian and Floquet dynamics as well as a range of quantum circuit models.
We investigate the time evolution of entanglement for bipartite systems of arbitrary dimensions under the influence of decoherence. For qubits, we determine the precise entanglement decay rates under different system-environment couplings, including finite temperature effects. For qudits, we show how to obtain upper bounds for the decay rates and also present exact solutions for various classes of states.
We consider the natural generalization of the Schr{o}dinger equation to Markovian open system dynamics: the so-called the Lindblad equation. We give a quantum algorithm for simulating the evolution of an $n$-qubit system for time $t$ within precision $epsilon$. If the Lindbladian consists of $mathrm{poly}(n)$ operators that can each be expressed as a linear combination of $mathrm{poly}(n)$ tensor products of Pauli operators then the gate cost of our algorithm is $O(t, mathrm{polylog}(t/epsilon)mathrm{poly}(n))$. We also obtain similar bounds for the cases where the Lindbladian consists of local operators, and where the Lindbladian consists of sparse operators. This is remarkable in light of evidence that we provide indicating that the above efficiency is impossible to attain by first expressing Lindblad evolution as Schr{o}dinger evolution on a larger system and tracing out the ancillary system: the cost of such a textit{reduction} incurs an efficiency overhead of $O(t^2/epsilon)$ even before the Hamiltonian evolution simulation begins. Instead, the approach of our algorithm is to use a novel variation of the linear combinations of unitaries construction that pertains to channels.
We study the entanglement dynamics for two independent superconducting qubits each affected by a bistable impurity generating random telegraph noise (RTN) at pure dephasing. The relevant parameter is the ratio $g$ between qubit-RTN coupling strength and RTN switching rate, that captures the physics of the crossover between Markovian and non-Markovian features of the dynamics. For identical qubit-RTN subsystems, a threshold value $g_mathrm{th}$ of the crossover parameter separates exponential decay and onset of revivals; different qualitative behaviors also show up by changing the initial conditions of the RTN. We moreover show that, for different qubit-RTN subsystems, when both qubits are very strongly coupled to the RTN an increase in entanglement revival amplitude may occur during the dynamics.
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