Abstract:

We introduce and explore two questions concerning spectra of operators that are of interest in the theory of entanglement in symmetric (i.e., bosonic) quantum systems. First, we investigate the inverse eigenvalue problem for symmetric entanglement witnesses — that is, we investigate what their possible spectra are. Second, we investigate the problem of characterizing which separable symmetric quantum states remain separable after conjugation by an arbitrary unitary acting on symmetric space — that is, which states are separable in every orthonormal symmetric basis. Both of these questions have been investigated thoroughly in the non-symmetric setting, and we contrast the answers that we find with their non-symmetric counterparts.

Authors:

• Gabriel Champagne
• Nathaniel Johnston
• Mitchell MacDonald
• Logan Pipes

Download:

• Published version from Linear Algebra and its Applications
• Preprint from arXiv:2108.10405 [quant-ph]
• Local preprint [pdf]

Cite as:

• G. Champagne, N. Johnston, M. MacDonald, and L. Pipes. Spectral properties of symmetric quantum states and symmetric entanglement witnesses. Linear Algebra and its Applications, 649:273–300, 2022.

Suplemenentary Material:

• symmetric-spectral-properties repo – MATLAB code to accompany the paper and implement many of its theorems and semidefinite programs

Related Papers:

• The inverse eigenvalue problem for entanglement witnesses – an earlier paper that considers the non-symmetric version of one of the problems considered in this paper