Measuring Entanglement via SICs and 2-designs

Bin Chen, Tao Li, Shao-Ming Fei

S. L. Rolston

Matthew A. Graydon, D. M. Appleby

Complex projective t-designs, particularly SICs and full sets of MUBs, play an important role in quantum information. We introduce a generalization which we call conical t-designs. They include arbitrary rank symmetric informationally complete measurements (SIMs) and full sets of arbitrary rank mutually unbiased measurements (MUMs). They are deeply implicated in the description of entanglement (as we show in a subsequent paper). Viewed in one way a conical 2-design is a symmetric decomposition of a separable Werner state (up to a normalization factor). Viewed in another way it is a certain kind of polytope in the Bloch body. In the Bloch body picture SIMs and full sets of MUMs form highly symmetric polytopes (a single regular simplex in the one case; the convex hull of a set of orthogonal regular simplices in the other). We give the necessary and sufficient conditions for an arbitrary polytope to be what we call a homogeneous conical 2-design. This suggests a way to search for new kinds of projective 2-design.

Joonwoo Bae

In this work, we show that measurement in quantum 2-design, such as mutually unbiased bases (MUBs) or symmetric, informationally complete states (SICs), improves the capability of detecting entangled states both theoretically and experimentally. On the theoretical side, we show that measurement in quantum 2-design can detect entangled states twice compared to entanglement witnesses. On the implementation side, we present the scheme of entanglement detection with two detectors only of a Hong-Ou-Mandel interferometer. The experimental scheme applies single-copy level measurement followed by post-processing of measurement outcomes, which is feasible with current technologies.

Leah Henderson

Wei Deng, Yong Deng