Impossibility of Quantum Bit Commitment, a Categorical Perspective
Bit commitment is a cryptographic task in which Alice commits a bit to Bob such that she cannot change the value of the bit after her commitment and Bob cannot learn the value of the bit before Alice opens her commitment. According to the Mayers−Lo−Chau (MLC) no-go theorem, ideal...
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| Format: | Article |
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MDPI AG
2020-03-01
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| Series: | Axioms |
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| Online Access: | https://www.mdpi.com/2075-1680/9/1/28 |
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| author | Xin Sun Feifei He Quanlong Wang |
| author_facet | Xin Sun Feifei He Quanlong Wang |
| author_sort | Xin Sun |
| collection | DOAJ |
| description | Bit commitment is a cryptographic task in which Alice commits a bit to Bob such that she cannot change the value of the bit after her commitment and Bob cannot learn the value of the bit before Alice opens her commitment. According to the Mayers−Lo−Chau (MLC) no-go theorem, ideal bit commitment is impossible within quantum theory. In the information theoretic-reconstruction of quantum theory, the impossibility of quantum bit commitment is one of the three information-theoretic constraints that characterize quantum theory. In this paper, we first provide a very simple proof of the MLC no-go theorem and its quantitative generalization. Then, we formalize bit commitment in the theory of dagger monoidal categories. We show that in the setting of dagger monoidal categories, the impossibility of bit commitment is equivalent to the unitary equivalence of purification. |
| first_indexed | 2024-12-14T00:56:04Z |
| format | Article |
| id | doaj.art-73b48c90daf04f59bd250e8d5e9a4a4a |
| institution | Directory Open Access Journal |
| issn | 2075-1680 |
| language | English |
| last_indexed | 2024-12-14T00:56:04Z |
| publishDate | 2020-03-01 |
| publisher | MDPI AG |
| record_format | Article |
| series | Axioms |
| spelling | doaj.art-73b48c90daf04f59bd250e8d5e9a4a4a2022-12-21T23:23:34ZengMDPI AGAxioms2075-16802020-03-01912810.3390/axioms9010028axioms9010028Impossibility of Quantum Bit Commitment, a Categorical PerspectiveXin Sun0Feifei He1Quanlong Wang2Department of Foundation of Computer Science, Catholic University of Lublin, 20950 Lublin, PolandInstitute of Logic and Cognition, Sun Yat-sen University, Guangzhou 510275, ChinaDepartment of Computer Science, University of Oxford, Oxford OX13QD, UKBit commitment is a cryptographic task in which Alice commits a bit to Bob such that she cannot change the value of the bit after her commitment and Bob cannot learn the value of the bit before Alice opens her commitment. According to the Mayers−Lo−Chau (MLC) no-go theorem, ideal bit commitment is impossible within quantum theory. In the information theoretic-reconstruction of quantum theory, the impossibility of quantum bit commitment is one of the three information-theoretic constraints that characterize quantum theory. In this paper, we first provide a very simple proof of the MLC no-go theorem and its quantitative generalization. Then, we formalize bit commitment in the theory of dagger monoidal categories. We show that in the setting of dagger monoidal categories, the impossibility of bit commitment is equivalent to the unitary equivalence of purification.https://www.mdpi.com/2075-1680/9/1/28bit commitmentcategorical quantum mechanicsquantum foundation |
| spellingShingle | Xin Sun Feifei He Quanlong Wang Impossibility of Quantum Bit Commitment, a Categorical Perspective Axioms bit commitment categorical quantum mechanics quantum foundation |
| title | Impossibility of Quantum Bit Commitment, a Categorical Perspective |
| title_full | Impossibility of Quantum Bit Commitment, a Categorical Perspective |
| title_fullStr | Impossibility of Quantum Bit Commitment, a Categorical Perspective |
| title_full_unstemmed | Impossibility of Quantum Bit Commitment, a Categorical Perspective |
| title_short | Impossibility of Quantum Bit Commitment, a Categorical Perspective |
| title_sort | impossibility of quantum bit commitment a categorical perspective |
| topic | bit commitment categorical quantum mechanics quantum foundation |
| url | https://www.mdpi.com/2075-1680/9/1/28 |
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