Rényi Entropy,Signed Probabilities,and the Qubit |
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| Authors: | Adam Brandenburger Pierfrancesco La Mura Stuart Zoble |
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| Affiliation: | 1.Stern School of Business, Tandon School of Engineering, NYU Shanghai, New York University, New York, NY 10012, USA;2.HHL—Leipzig Graduate School of Management, 04109 Leipzig, Germany;3.Signal Fox, Princeton, NJ 08542, USA |
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| Abstract: | The states of the qubit, the basic unit of quantum information, are 2 × 2 positive semi-definite Hermitian matrices with trace 1. We contribute to the program to axiomatize quantum mechanics by characterizing these states in terms of an entropic uncertainty principle formulated on an eight-point phase space. We do this by employing Rényi entropy (a generalization of Shannon entropy) suitably defined for the signed phase-space probability distributions that arise in representing quantum states. |
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| Keywords: | Ré nyi entropy, signed probability, uncertainty principle, qubit |
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