Verification of phased Dicke states

Abstract

Dicke states are typical examples of quantum states with genuine multipartite entanglement. They are valuable resources in many quantum information processing tasks, including multiparty quantum communication and quantum metrology. Phased Dicke states are a generalization of Dicke states and include antisymmetric basis states as a special example. These states are useful in atomic and molecular physics besides quantum information processing. Here we propose practical and efficient protocols based on adaptive local projective measurements for verifying all phased Dicke states, including $W$ states and qudit Dicke states. To verify any $n$-partite phased Dicke state within infidelity $\epsilon$ and significance level $\delta$, the number of tests required is only $O(n{\epsilon }^{-1}\ln {\delta }^{-1})$, which is linear in $n$ and is exponentially more efficient than traditional tomographic approaches. In the case of $W$ states, the number of tests can be further reduced to $O(\sqrt{n}{\epsilon }^{-1}\ln {\delta }^{-1})$. Moreover, we construct an optimal protocol for any antisymmetric basis state; the number of tests required decreases (rather than increases) monotonically with $n$. This is the only optimal protocol known for multipartite nonstabilizer states.

arXiv comment14+12 pages, 4 figures, and 1 table; published in PRA

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• Collective randomized measurements in quantum information processing
• $q$-analog qudit Dicke states
• Efficient verification of Affleck-Kennedy-Lieb-Tasaki states
• Matrix product state approach for a quantum system at finite temperatures using random phases and Trotter gates
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• Universal and Efficient Quantum State Verification via Schmidt Decomposition and Mutually Unbiased Bases
• Linear Optical Schemes to Postselect High-Dimensional Dicke States
• Prescriptive preparation and verification of nonstabilizer states