Abstract
We study genuine multipartite entanglement (GME) in a system of n qubits prepared in symmetric Dicke states and subjected to the influences of noise. We provide general, setup-independent expressions for experimentally favorable tools such as fidelity- and collective spin-based entanglement witnesses, as well as entangled-class discriminators and multi-point correlation functions. Besides highlighting the effects of the environment on large qubit registers, we also discuss strategies for the robust detection of GME. Our work provides techniques and results for the experimental communities interested in investigating and characterizing multipartite entangled states by introducing realistic milestones for setup design and associated predictions.
Highlights
We study genuine multipartite entanglement (GME) in a system of n qubits prepared in symmetric Dicke states and subjected to the influences of noise
Symmetric Dicke states having k = n/2 are interesting in virtue of the fact that they are associated with the largest eigenvalues of the set of observables {J2, Jz}
A remarkable contribution has come from the introduction and use of entanglement witness operators, which with often only modest experimental effort allow for the discrimination between separable, biseparable and fully GME states without requiring the complete knowledge of the state at hand
Summary
We use an effective picture for the action of a completely positive trace-preserving map given by the operator-sum representation [20] Within this formalism, a single-qubit noisy process is described by a set of Kraus operators {Kμ}, satisfying the completeness property μ Kμ†Kμ = 1ˆ1, such that, calling ρ0 the initial state of a qubit, its evolution is given by ρch = $ch(ρ0) = μ Kμρ0Kμ†. We start by considering the Kraus decomposition of a zerotemperature amplitude damping (AD) mechanism This physically corresponds to an energy dissipation process: the system undergoing AD has a finite probability e−γ to lose an excitation (here, γ is an effective dimensionless rate characterizing the whole process). The effect of a DP channel is to effectively add white noise to a given singlequbit state This correspondence will become useful in our study. Our task is to provide an analysis as general as possible of the effects of such environmental channels on a variety of experimentally viable tools for multipartite entanglement
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