The Pareto Frontiers of Magic and Entanglement: The Case of Two Qubits
🤖 AI Summary
This work investigates the trade-off between magic, quantified by the second-order Rényi entropy $M_2$, and entanglement, measured by concurrence $\Delta$, in two-qubit systems, with a focus on the extremal bounds of magic for a given amount of entanglement. By integrating tools from quantum information theory with analytical optimization techniques, the study fully characterizes the Pareto frontier between these two quantum resources: the upper boundary of achievable magic consists of three distinct segments, while the lower boundary forms a single continuous curve. Furthermore, the authors derive four compact analytical expressions that explicitly parameterize all extremal states, thereby establishing a theoretical foundation for the coordinated manipulation of quantum resources.
Application Category
📝 Abstract
Magic and entanglement are two measures that are widely used to characterize quantum resources. We study the interplay between magic and entanglement in two-qubit systems, focusing on the two extremes: maximal magic and minimal magic for a given level of entanglement. We quantify magic by the Rényi entropy of order 2, $M_2$, and entanglement by the concurrence $Δ$. We find that the Pareto frontier of maximal magic $M_2^{(max)}(Δ)$ is composed of three separate segments, while the boundary of minimal magic $M_2^{(min)}(Δ)$ is a single continuous line. We derive simple analytical formulas for all these four cases, and explicitly parametrize all distinct quantum states of maximal or minimal magic at a given level of entanglement.
Problem
Research questions and friction points this paper is trying to address.
magic
entanglement
Pareto frontier
two-qubit systems
quantum resources
Innovation
Methods, ideas, or system contributions that make the work stand out.
Pareto frontier
magic
entanglement
two-qubit systems
Rényi entropy
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