We consider the environment-affected dynamics of N self-interacting particles living in one-dimensional double wells. Two topics are dealt with. First, we consider the production of entangled states of two-level systems. We show that by adiabatically varying the well biases, we may dynamically generate maximally entangled states, starting from initially unentangled product states. Entanglement degradation due to a common type of environmental influence is then computed by solving a master equation. However, we also demonstrate that entanglement production is unaffected if the system-environment coupling is of the type that induces ``motional narrowing.'' As our second but related topic, we construct a different master equation that seamlessly merges error protection/detection dynamics for quantum information with the environmental couplings responsible for producing the errors in the first place. Adiabatic avoided crossing schemes are used in both topics.
We consider the environment-affected dynamics of N self-interacting particles living in one-dimensional double wells. Two topics are dealt with. First, we consider the production of entangled states of two-level systems. We show that by adiabatically varying the well biases, we may dynamically generate maximally entangled states, starting from initially unentangled product states. Entanglement degradation due to a common type of environmental influence is then computed by solving a master equation. However, we also demonstrate that entanglement production is unaffected if the system-environment coupling is of the type that induces ``motional narrowing.'' As our second but related topic, we construct a different master equation that seamlessly merges error protection/detection dynamics for quantum information with the environmental couplings responsible for producing the errors in the first place. Adiabatic avoided crossing schemes are used in both topics.
We study the Markovian dynamics of a collection of n quantum systems coupled to an irreversible environmental channel consisting of a stream of entangled qubits. Within the framework of repeated quantum interactions, we derive the master equation for the joint-state dynamics of the n quantum systems. We investigate the evolution of the joint state for two-qubit environments where the presence of antidiagonal coherences in the state of the bath qubits (in the local energy basis) is essential for preserving and generating entanglement between two remote quantum systems. However, maximally entangled bath qubits, such as Bell states, exhibit exceptional behavior, where the master equation does not have a unique steady state and can destroy entanglement between the systems. For the general case of n-qubit environments we show that antidiagonal coherences that arise from multibody entanglement in the bath qubits do not affect the composite system evolution in the weak-coupling regime.
Considering two non-interacting qubits in the context of open quantum systems, it is well known that their common environment may act as an entangling agent. In a perturbative regime the influence of the environment on the system dynamics can effectively be described by a unitary and a dissipative contribution. For the two-spin Boson model with (sub-) Ohmic spectral density considered here, the particular unitary contribution (Lamb shift) easily explains the buildup of entanglement between the two qubits. Furthermore it has been argued that in the adiabatic limit, adding the so-called counterterm to the microscopic model compensates the unitary influence of the environment and, thus, inhibits the generation of entanglement. Investigating this assertion is one of the main objectives of the work presented here. Using the hierarchy of pure states (HOPS) method to numerically calculate the exact reduced dynamics, we find and explain that the degree of inhibition crucially depends on the parameter s determining the low frequency power law behavior of the spectral density J(ω)∼ωse−ω/ωc . Remarkably, we find that for resonant qubits, even in the adiabatic regime (arbitrarily large ωc ), the entanglement dynamics is still influenced by an environmentally induced Hamiltonian interaction. Further, we study the model in detail and present the exact entanglement dynamics for a wide range of coupling strengths, distinguish between resonant and detuned qubits, as well as Ohmic and deep sub-Ohmic environments. Notably, we find that in all cases the asymptotic entanglement does not vanish and conjecture a linear relation between the coupling strength and the asymptotic entanglement measured by means of concurrence. Further we discuss the suitability of various perturbative master equations for obtaining approximate entanglement dynamics.
We investigate the effect of magnetic field and charge noise on the generation of entanglement between two Heisenberg exchange-coupled electron spins in a double quantum dot. We focus on exchange-driven evolution that would ideally take an initial unentangled tensor product state to a maximally entangled state in the absence of noise. The presence of noise obviously adversely affects the attainment of maximal entanglement, which we study quantitatively and exactly. To quantify the effects of noise, we calculate two-qubit coherence times and entanglement fidelity, both of which can be extracted from simulations or measurements of the return probability as a function of interaction time, i.e., the time period during which the exchange coupling remains effective between the two spins. We perform these calculations for a broad range of noise strengths that includes the regime of recent experiments. We find that the two types of noise reduce the amount of entanglement in qualitatively distinct ways and that, although charge noise generally leads to faster decoherence, the relative importance of the two types of noise in entanglement creation depends sensitively on the strength of the exchange coupling. Our results can be used to determine the level of noise suppression needed to reach quantum error correction thresholds. We provide quantitative guidance for the requisite noise constraints necessary to eventually reach the >99 fidelity consistent with the quantum error correction threshold.
Abstract We show that, during adiabatic evolution, any changes in entanglement can be attributed to a succession of avoided energy level crossings at which eigenvalues swap their eigenvectors. These swaps mediate the generation and redistribution of entanglement in multipartite systems. The efficiency of this redistribution depends on the narrowness of the avoided level crossings and thus constrains the speed of adiabatic evolution. Moreover, we relate the amount of entanglement involved to the ruggedness of the energy landscape, which directly affects the hardness of a computational problem. This enables an analysis of computational complexity and quantum advantage from the point of view of entanglement requirements. Applied to adiabatic quantum computation, our findings directly relate the computation’s speed to its utilization of entanglement as a resource. The same principles extend to gate-based discretized adiabatic quantum algorithms, including those for Hamiltonian simulation and combinatorial optimization.
Quantum technologies able to manipulating single quantum systems, are presently developing. Among the dowries of the quantum realm, entanglement is one of the basic resources for the novel quantum revolution. Within this context, one is faced with the problem of protecting the entanglement when a system state is manipulated. In this paper, we investigate the effect of the classical driving field on the generation entanglement between two qubits interacting with a bosonic environment. We discuss the effect of the classical field on the generation of entanglement between two (different) qubits and the conditions under which it has a constructive role in protecting the initial-state entanglement from decay induced by its environment. In particular, in the case of similar qubits, we locate a stationary sub-space of the system Hilbert space, characterized by states non depending on the environment properties as well as on the classical driving-field. Thus, we are able to determine the conditions to achieve maximally entangled stationary states after a transient interaction with the environment. We show that, overall, the classical driving field has a constructive role for the entanglement protection in the strong coupling regime. Also, we illustrate that a factorable initial-state can be driven in an entangled state and, even, in an entangled steady-state after the interaction with the environment.
Quantum technologies able to manipulating single quantum systems, are presently developing. Among the dowries of the quantum realm, entanglement is one of the basic resources for the novel quantum revolution. Within this context, one is faced with the problem of protecting the entanglement when a system state is manipulated. In this paper, we investigate the effect of the classical driving field on the generation entanglement between two qubits interacting with a bosonic environment. We discuss the effect of the classical field on the generation of entanglement between two (different) qubits and the conditions under which it has a constructive role in protecting the initial-state entanglement from decay induced by its environment. In particular, in the case of similar qubits, we locate a stationary sub-space of the system Hilbert space, characterized by states non depending on the environment properties as well as on the classical driving-field. Thus, we are able to determine the conditions to achieve maximally entangled stationary states after a transient interaction with the environment. We show that, overall, the classical driving field has a constructive role for the entanglement protection in the strong coupling regime. Also, we illustrate that a factorable initial-state can be driven in an entangled state and, even, in an entangled steady-state after the interaction with the environment.