Werner states from diagrams

• URL: http://arxiv.org/abs/2302.05572v2
• Date: Tue, 9 May 2023 14:10:36 GMT
• Title: Werner states from diagrams
• Authors: David W. Lyons, Cristina Mullican, Adam Rilatt, Jack D. Putnam
• Abstract summary: We present two results on multiqubit Werner states, defined to be those states that are invariant under the collective action of any given single-qubit unitary. Motivated by the desire to characterize entanglement properties of Werner states, we construct a basis for the real linear vector space of Werner invariant Hermitian operators on the Hilbert space of pure states. It follows that any mixed Werner state can be written as a mixture of these basis operators with unique coefficients.
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• License: http://creativecommons.org/licenses/by-nc-sa/4.0/
• Abstract: We present two results on multiqubit Werner states, defined to be those states that are invariant under the collective action of any given single-qubit unitary that acts simultaneously on all the qubits. Motivated by the desire to characterize entanglement properties of Werner states, we construct a basis for the real linear vector space of Werner invariant Hermitian operators on the Hilbert space of pure states; it follows that any mixed Werner state can be written as a mixture of these basis operators with unique coefficients. Continuing a study of "polygon diagram" Werner states constructed in earlier work, with a goal to connect diagrams to entanglement properties, we consider a family of multiqubit states that generalize the singlet, and show that their 2-qubit reduced density matrices are separable.

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