Stabilizer Rényi entropy

Abstract

We introduce a novel measure for the quantum property of nonstabilizerness - commonly known as "magic" - by considering the Rényi entropy of the probability distribution associated to a pure quantum state given by the square of the expectation value of Pauli strings in that state. We show that this is a good measure of nonstabilizerness from the point of view of resource theory and show bounds with other known measures. The stabilizer Rényi entropy has the advantage of being easily computable because it does not need a minimization procedure. We present a protocol for an experimental measurement by randomized measurements. We show that the nonstabilizerness is intimately connected to out-of-time-order correlation functions and that maximal levels of nonstabilizerness are necessary for quantum chaos.

References in corpus (9)

• Application of a resource theory for magic states to fault-tolerant quantum computing
• Aspects of generic entanglement
• Many-body quantum magic
• Conformal field theories are magical
• Quantum Chaos is Quantum
• Catalysis and activation of magic states in fault tolerant architectures
• The Clifford group fails gracefully to be a unitary 4-design
• Transitions in entanglement complexity in random quantum circuits by measurements
• Random Matrix Theory of the Isospectral twirling

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