Maximum nonlocality and minimum uncertainty using magic states

Abstract

We prove that magic states from the Clifford hierarchy give optimal solutions for tasks involving nonlocality and entropic uncertainty with respect to Pauli measurements. For both the nonlocality and uncertainty tasks, stabilizer states are the worst possible pure states so our solutions have an operational interpretation as being highly non-stabilizer. The optimal strategy for a qudit version of the Clauser-Horne-Shimony-Holt (CHSH) game in prime dimensions is achieved by measuring maximally entangled states that are isomorphic to single-qudit magic states. These magic states have an appealingly simple form and our proof shows that they are "balanced" with respect to all but one of the mutually unbiased stabilizer bases. Of all equatorial qudit states, magic states minimize the average entropic uncertainties for collision entropy and also, for small prime dimensions, min-entropy -- a fact that may have implications for cryptography.

11 pages, 2 figures

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Cited by in corpus (13)

• Diagonal gates in the Clifford hierarchy
• Qutrit and Ququint Magic States
• Magic State Distillation with the Ternary Golay Code
• Generalized XOR games with $d$ outcomes and the task of non-local computation
• Approximate stabilizer rank and improved weak simulation of Clifford-dominated circuits for qudits
• States that are far from being stabilizer states
• Classical codes in quantum state space
• Multipartite Nonlocality in Clifford Networks
• A trace distance-based geometric analysis of the stabilizer polytope for few-qubit systems
• No quantum solutions to linear constraint systems in odd dimension from Pauli group and diagonal Cliffords
• Harvesting stabilizer entropy and non-locality from a quantum field
• Qudit Clauser-Horne-Shimony-Holt Inequality and Nonlocality from Wigner Negativity
• No-cost Bell nonlocality certification from quantum tomography and its applications in quantum-magic-resource witnessing