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arXiv:quant-ph/0703137 · Physical Review Letters

Generation of Symmetric Dicke States of Remote Qubits with Linear Optics

C. Thiel, Joachim von Zanthier, Thierry Bastin, E. Solano, G. S. Agarwal

Published Nov 7, 2007• 88 citations
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Abstract

We propose a method for generating all symmetric Dicke states, either in the long-lived internal levels of N massive particles or in the polarization degrees of freedom of photonic qubits, using linear optical tools only. By means of a suitable multiphoton detection technique, erasing Welcher-Weg information, our proposed scheme allows the generation and measurement of an important class of entangled multiqubit states.

DOI
10.1103/physrevlett.99.193602

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We propose a method for generating all symmetric Dicke states, either in the long-lived internal levels of N massive particles or in the polarization degrees of freedom of photonic qubits, using linear optical tools only. By means of a suitable multiphoton detection technique, erasing Welcher-Weg information, our proposed scheme allows the generation and measurement of an important class of entangled multiqubit states.
In this paper, we present an approach to generating arbitrary symmetric Dicke states with distant trapped ions and linear optics. Distant trapped ions can be prepared in the symmetric Dicke states by using two photon-number-resolving detectors and a polarization beam splitter. The atomic symmetric Dicke states are robust against decoherence, for atoms are in a metastable level. We discuss the experimental feasibility of our scheme with current technology. Finally, we discuss the classification of arbitrary n-qubit symmetric Dicke states under statistical local operation and classical communication and prove the existence of [n/2] inequivalent classes of genuine entanglement of n-qubit symmetric Dicke states.
Symmetric Dicke states represent a class of genuinely entangled multipartite states with superior resistance to loss and entanglement characteristics, even for low fidelity. A scalable and resource-intensive method is proposed using hybrid spatiotemporal encoding using only linear optics for generation of all symmetric Dicke states for both atomic and photonic qubits. Compared to purely spatial encoding, this method shows orders-of-magnitude improvement in success probability while also reducing the hardware complexity by a factor NNN for NNN qubits. This scheme will allow scalable entanglement generation of distant qubits.
Entanglement is a fundamental feature of quantum mechanics and a key resource for quantum information processing. Among multipartite entangled states, Dicke states ∣Dnk⟩|D_n^k\rangle∣Dnk​⟩ are distinguished by their permutation symmetry, which provides robustness against particle loss and enables applications for quantum communication and computation. Although Dicke states have been realized in various platforms, most optical implementations rely on postselection, which destroys the state upon detection and prevents its further use. A heralded optical scheme is therefore highly desirable. Here, we present a linear-optical heralded scheme for generating arbitrary Dicke states ∣Dnk⟩|D_n^k\rangle∣Dnk​⟩ with 3n+k3n+k3n+k photons through the framework of the linear quantum graph (LQG) picture. By mapping the scheme design into the graph-finding problem, and exploiting the permutation symmetry of Dicke states, we overcome the structural complexity that has hindered previous approaches. Our results provide a resource-efficient pathway toward practical heralded preparation of Dicke states for quantum technologies.
We propose a scheme enabling the universal coupling of angular momentum of NNN remote noninteracting qubits using linear optical tools only. Our system consists of NNN single-photon emitters in a $\ensuremath{\Lambda}$ configuration that are entangled among their long-lived ground-state qubits through suitably designed measurements of the emitted photons. In this manner, we present an experimentally feasible algorithm that is able to generate any of the 2N{2}^{N}2N symmetric and nonsymmetric total angular momentum eigenstates spanning the Hilbert space of the NNN-qubit compound.