Kirkwood-Dirac nonpositivity as a resource for quantum computing (Part 2): Bound-magic states

The Kirkwood–Dirac (KD) quasiprobability distribution provides a powerful and trending mathematical framework to represent quantum systems. For certain states, the KD distribution is a standard joint probability distribution. However, the KD distribution can signal nonclassical phenomena by admitting nonpositive entries. In Part 1 of this talk, we showed that in a real-qubit model of quantum computation, a KD nonpositive input state is a necessary condition for quantum advantage. Consequently, computations with KD-positive inputs can be efficiently classically simulated. Interestingly, KD-positive states may lie outside the stabilizer polytope. Such states constitute bound-magic states. In this talk, we leverage recent mathematical advances on the characterization of the KD-positive states’ geometry to construct large classes of previously unknown bound-magic states. Our analysis reveals that these bound-magic states occupy approximately 0.69% of the two-qubit state space. Compared to previous results, this constitutes a 15% increase in the volume of input states that admit efficient classical simulation.