Abstract
Quantum entanglement is usually considered a fragile quantity and decoherence through coupling to an external environment, such as a thermal reservoir, can quickly destroy the entanglement resource. This doesn't have to be the case and the environment can be engineered to assist in the formation of entanglement. We investigate a system of qubits and higher dimensional spins interacting only through their mutual coupling to a reservoir. We explore the entanglement of multipartite and multidimensional system as mediated by the bath and show that at low temperatures and intermediate coupling strengths multipartite entanglement may form between qubits and between higher spins, i.e., qudits. We characterise the multipartite entanglement using an entanglement witness based upon the structure factor and demonstrate its validity versus the directly calculated entanglement of formation, suggesting possible experiments for its measure.
Highlights
Entanglement between systems with few degrees of freedom is often a fragile property as their interaction with a much larger environment drives decoherence
Steady state two-qubit entanglement can be generated by engineered dissipation in trapped ions[15] and superconducting qubits[16], and noise assisted quantum transport has been reported[17,18]
These experimental results challenge the general assumption that dissipation is always detrimental to quantum information processing, rather they demonstrate that it might be a resource that can be engineered and harnessed
Summary
Chee Kong Lee[1,2], Mojdeh S. First we consider a general open quantum system coupled to a bath and we examine the equilibrium reduced density matrix of non-interacting qudits through the analytical polaron treatment, complemented by a numerically exact path-integral approach. The number of degrees of freedom of the bath is assumed to be much larger than that of the qudits, according to the Poincaré recurrence theorem the time-scale on which the bath feeds back the energy to the subsystems is enormous This separation of time-scales allows us to smooth the oscillator modes and instead of {ωn} we characterise the bath with a continuous spectral density J(ω). The cut-off with reciprocal of a fixed ωc, the cut-off and constant system-bath coupling frequency, τ ∝ 1 governs the relaxation time of the bath This form of the spectral density is commonly used in the study of tunnωcelling effects in solid state systems[33].
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