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Witnessing multipartite entanglement by detecting coherence

Davide Girolami, Benjamin Yadin

Published Sep 14, 2015• 2 citations
OpenAlex

Abstract

The characterization of quantum coherence in the context of quantum information theory and its interplay with quantum correlations is currently subject of intense study. Several theoretical quantifiers of coherence have been proposed, and links to quantum correlation measures have been provided. We here propose an experimental strategy to witness the presence of entanglement in multipartite systems by evaluating coherence. We test our scheme by simulating coherence and entanglement detection in a three-qubit GHZ-diagonal state.

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The characterization of quantum coherence in the context of quantum information theory and its interplay with quantum correlations is currently subject of intense study. Several theoretical quantifiers of coherence have been proposed, and links to quantum correlation measures have been provided. We here propose an experimental strategy to witness the presence of entanglement in multipartite systems by evaluating coherence. We test our scheme by simulating coherence and entanglement detection in a three-qubit GHZ-diagonal state.
The characterization of quantum coherence in the context of quantum information theory and its interplay with quantum correlations is currently subject of intense study. Coherence in a Hamiltonian eigenbasis yields asymmetry, the ability of a quantum system to break a dynamical symmetry generated by the Hamiltonian. We here propose an experimental strategy to witness multipartite entanglement in many-body systems by evaluating the asymmetry with respect to an additive Hamiltonian. We test our scheme by simulating asymmetry and entanglement detection in a three-qubit Greenberger–Horne–Zeilinger (GHZ) diagonal state.
Quantum mechanics predicts the existence of correlations between composite systems that, although puzzling to our physical intuition, enable technologies not accessible in a classical world. Notwithstanding, there is still no efficient general method to theoretically quantify and experimentally detect entanglement of many qubits. Here we propose to detect entanglement by measuring the statistical response of a quantum system to an arbitrary nonlocal parametric evolution. We witness entanglement without relying on the tomographic reconstruction of the quantum state, or the realization of witness operators. The protocol requires two collective settings for any number of parties and is robust against noise and decoherence occurring after the implementation of the parametric transformation. To illustrate its user friendliness we demonstrate multipartite entanglement in different experiments with ions and photons by analyzing published data on fidelity visibilities and variances of collective observables.
Multipartite entanglement detection is crucial for the develop of quantum information science and quantum computation, communication, simulation and metrology tasks. In contrast to experiments, where several handreds of qubits have been entangled to build a quantum computer or a quantum simulator, theoretically only for lower dimensional quantum system such as two qubit system or two-mode Gaussian state and some special quantum states, efficient criteria have been developed to detect the entanglement. An efficient and practical entanglement detection method is anticipated to appear for current scalable quantum system. Based on the matched entanglement witness scheme and integrated uncertainty relations, we propose a quite general entanglement detection method for all kinds of multipartite entanglement of multimode continuous variable systems. With the covariance matrix of any randomly generated multimode continuous variable quantum state, our criterion can detect entanglement, genuine entanglement and other kinds of inseparabilities almost imidiately.
Along with the vast progress in experimental quantum technologies there is an increasing demand for the quantification of entanglement between three or more quantum systems. Theory still does not provide adequate tools for this purpose. The objective is, besides the quest for exact results, to develop operational methods that allow for efficient entanglement quantification. Here we put forward an analytical approach that serves both these goals. We provide a simple procedure to quantify Greenberger-Horne-Zeilinger-type multipartite entanglement in arbitrary three-qubit states. For two qubits this method is equivalent to Wootters' seminal result for the concurrence. It establishes a close link between entanglement quantification and entanglement detection by witnesses, and can be generalised both to higher dimensions and to more than three parties.
Along with the vast progress in experimental quantum technologies there is an increasing demand for the quantification of entanglement between three or more quantum systems. Theory still does not provide adequate tools for this purpose. The objective is, besides the quest for exact results, to develop operational methods that allow for efficient entanglement quantification. Here we put forward an analytical approach that serves both these goals. We provide a simple procedure to quantify Greenberger-Horne-Zeilinger-type multipartite entanglement in arbitrary three-qubit states. For two qubits this method is equivalent to Wootters' seminal result for the concurrence. It establishes a close link between entanglement quantification and entanglement detection by witnesses, and can be generalised both to higher dimensions and to more than three parties.