Rényi Entropy, Signed Probabilities, and the Qubit
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| Format: | Preprint |
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2020
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| _version_ | 1866914642675105792 |
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| author | Brandenburger, Adam La Mura, Pierfrancesco Zoble, Stuart |
| author_facet | Brandenburger, Adam La Mura, Pierfrancesco Zoble, Stuart |
| contents | The states of the qubit, the basic unit of quantum information, are $2 \times 2$ 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. |
| format | Preprint |
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arxiv_https___arxiv_org_abs_2010_02111 |
| institution | arXiv |
| publishDate | 2020 |
| record_format | arxiv |
| spellingShingle | Rényi Entropy, Signed Probabilities, and the Qubit Brandenburger, Adam La Mura, Pierfrancesco Zoble, Stuart Quantum Physics Mathematical Physics The states of the qubit, the basic unit of quantum information, are $2 \times 2$ 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. |
| title | Rényi Entropy, Signed Probabilities, and the Qubit |
| topic | Quantum Physics Mathematical Physics |
| url | https://arxiv.org/abs/2010.02111 |