States that are far from being stabilizer states

Abstract

Stabilizer states are eigenvectors of maximal commuting sets of operators in a finite Heisenberg group. States that are far from being stabilizer states include magic states in quantum computation, MUB-balanced states, and SIC vectors. In prime dimensions the latter two fall under the umbrella of Minimum Uncertainty States (MUS) in the sense of Wootters and Sussman. We study the correlation between two ways in which the notion of "far from being a stabilizer state" can be quantified, and give detailed results for low dimensions. In dimension 7 we identify the MUB-balanced states as being antipodal to the SIC vectors within the set of MUS, in a sense that we make definite. In dimension 4 we show that the states that come closest to being MUS with respect to all the six stabilizer MUBs are the fiducial vectors for Alltop MUBs.

21 pages, 8 figures

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Cited by in corpus (6)

• Application of a resource theory for magic states to fault-tolerant quantum computing
• The SIC Question: History and State of Play
• Maximum nonlocality and minimum uncertainty using magic states
• The Number Behind the Simplest SIC-POVM
• One-Shot Yield-Cost Relations in General Quantum Resource Theories
• Classical codes in quantum state space