### Abstract

In our logical interpretation, edges are assigned logical formulas in a special logical system, called BV, an instance of a deep inference system. We demonstrate that BV, with its mix of commutative and noncommutative connectives, is precisely the right logic for such analysis. We show that the commutative tensor encodes (possible) entanglement, and the noncommutative seq encodes causal precedence. With this interpretation, the locative slices are precisely the derivable strings of formulas. Several new technical results about BV are developed as part of this analysis.

Original language | English |
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Title of host publication | Categories and Types in Logic, Language, and Physics |

Editors | C. Casadio, B. Coecke, M. Moortgat, P. Scott |

Publisher | Springer |

Pages | 90-107 |

Number of pages | 18 |

Volume | 8222 |

ISBN (Electronic) | 978-3-642-54789-8 |

ISBN (Print) | 978-3-642-54788-1 |

DOIs | |

Publication status | Published - 31 Dec 2014 |

### Publication series

Name | Lecture Notes in Computer Science |
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Publisher | Springer |

Volume | 8222 |

### Fingerprint

### Cite this

*Categories and Types in Logic, Language, and Physics*(Vol. 8222, pp. 90-107). (Lecture Notes in Computer Science; Vol. 8222). Springer. https://doi.org/10.1007/978-3-642-54789-8_6

**A logical basis for quantum evolution and entanglement.** / Blute, Richard; Guglielmi, A; Ivanov, Ivan; Panangaden, Prakash; Straßburger, Lutz.

Research output: Chapter in Book/Report/Conference proceeding › Chapter

*Categories and Types in Logic, Language, and Physics.*vol. 8222, Lecture Notes in Computer Science, vol. 8222, Springer, pp. 90-107. https://doi.org/10.1007/978-3-642-54789-8_6

}

TY - CHAP

T1 - A logical basis for quantum evolution and entanglement

AU - Blute, Richard

AU - Guglielmi, A

AU - Ivanov, Ivan

AU - Panangaden, Prakash

AU - Straßburger, Lutz

PY - 2014/12/31

Y1 - 2014/12/31

N2 - We reconsider discrete quantum causal dynamics where quantum systems are viewed as discrete structures, namely directed acyclic graphs. In such a graph, events are considered as vertices and edges depict propagation between events. Evolution is described as happening between a special family of spacelike slices, which were referred to as locative slices. Such slices are not so large as to result in acausal influences, but large enough to capture nonlocal correlations.In our logical interpretation, edges are assigned logical formulas in a special logical system, called BV, an instance of a deep inference system. We demonstrate that BV, with its mix of commutative and noncommutative connectives, is precisely the right logic for such analysis. We show that the commutative tensor encodes (possible) entanglement, and the noncommutative seq encodes causal precedence. With this interpretation, the locative slices are precisely the derivable strings of formulas. Several new technical results about BV are developed as part of this analysis.

AB - We reconsider discrete quantum causal dynamics where quantum systems are viewed as discrete structures, namely directed acyclic graphs. In such a graph, events are considered as vertices and edges depict propagation between events. Evolution is described as happening between a special family of spacelike slices, which were referred to as locative slices. Such slices are not so large as to result in acausal influences, but large enough to capture nonlocal correlations.In our logical interpretation, edges are assigned logical formulas in a special logical system, called BV, an instance of a deep inference system. We demonstrate that BV, with its mix of commutative and noncommutative connectives, is precisely the right logic for such analysis. We show that the commutative tensor encodes (possible) entanglement, and the noncommutative seq encodes causal precedence. With this interpretation, the locative slices are precisely the derivable strings of formulas. Several new technical results about BV are developed as part of this analysis.

UR - http://cs.bath.ac.uk/ag/p/LBQEE.pdf

UR - http://dx.doi.org/10.1007/978-3-642-54789-8_6

U2 - 10.1007/978-3-642-54789-8_6

DO - 10.1007/978-3-642-54789-8_6

M3 - Chapter

SN - 978-3-642-54788-1

VL - 8222

T3 - Lecture Notes in Computer Science

SP - 90

EP - 107

BT - Categories and Types in Logic, Language, and Physics

A2 - Casadio, C.

A2 - Coecke, B.

A2 - Moortgat, M.

A2 - Scott, P.

PB - Springer

ER -