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Physical Review A

Scalable approach to generation of large symmetric Dicke states

Sachin Kasture

Published Apr 27, 2018• 12 citations
Publisher

Abstract

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 $N$ for $N$ qubits. This scheme will allow scalable entanglement generation of distant qubits.

DOI
10.1103/physreva.97.043862

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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.
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.
Multipartite entanglement is an essential quantum resource for various distributed quantum applications. One promising method for preparing multipartite entanglement is to interfere independent photons at linear optical interference setups. While heralding the successful interference and thereby the state generation is often costly, postselecting entangled states provides an achievable alternative in this framework. We introduce a family of interference schemes for postselecting symmetric qudit Dicke states, useful resources in quantum communication and variational quantum computing. We present schemes with and without ancillary photons and show that using ancillary photons can exceed the upper bound on the success probability of schemes without ancillary photons. Our results accommodate a wide range of linear optical schemes, providing multiple viable approaches for postselecting Dicke states.
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.