Quantum, classical and intermediate II: the vanishing vector space structure

Diederik Aerts; Bob Coecke; Thomas Durt; Frank Valckenborgh

Quantum, classical and intermediate II: the vanishing vector space structure

Diederik Aerts, Bob Coecke, Thomas Durt, Frank Valckenborgh

Research output: Contribution to journal › Article › peer-review

Abstract

We propose an approach where physical entities are described by the set of their states, and the set of their relevant experiments. In this framework we will study a general entity that is neither quantum nor classical. We show that the collection of eigenstate sets forms a closure structure on the set of states. We also illustrate this framework on a concrete physical example, the ε-example. This leads us to a model for a continuous evolution from the linear closure in vector space to the standard topological closure.

Original language	English
Pages (from-to)	241-266
Number of pages	26
Journal	Tatra Mountains Mathematical Publications
Volume	10
Publication status	Published - 1997
Externally published	Yes

Keywords

Poincaré sphere
ε-model
state
Hilbert lattice

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title = "Quantum, classical and intermediate II: the vanishing vector space structure",

abstract = "We propose an approach where physical entities are described by the set of their states, and the set of their relevant experiments. In this framework we will study a general entity that is neither quantum nor classical. We show that the collection of eigenstate sets forms a closure structure on the set of states. We also illustrate this framework on a concrete physical example, the ε-example. This leads us to a model for a continuous evolution from the linear closure in vector space to the standard topological closure.",

keywords = "Poincar{\'e} sphere, ε-model, state, Hilbert lattice",

author = "Diederik Aerts and Bob Coecke and Thomas Durt and Frank Valckenborgh",

year = "1997",

language = "English",

volume = "10",

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journal = "Tatra Mountains Mathematical Publications",

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publisher = "Mathematical Institute, Slovak Academy of Sciences",

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TY - JOUR

T1 - Quantum, classical and intermediate II

T2 - the vanishing vector space structure

AU - Aerts, Diederik

AU - Coecke, Bob

AU - Durt, Thomas

AU - Valckenborgh, Frank

PY - 1997

Y1 - 1997

N2 - We propose an approach where physical entities are described by the set of their states, and the set of their relevant experiments. In this framework we will study a general entity that is neither quantum nor classical. We show that the collection of eigenstate sets forms a closure structure on the set of states. We also illustrate this framework on a concrete physical example, the ε-example. This leads us to a model for a continuous evolution from the linear closure in vector space to the standard topological closure.

AB - We propose an approach where physical entities are described by the set of their states, and the set of their relevant experiments. In this framework we will study a general entity that is neither quantum nor classical. We show that the collection of eigenstate sets forms a closure structure on the set of states. We also illustrate this framework on a concrete physical example, the ε-example. This leads us to a model for a continuous evolution from the linear closure in vector space to the standard topological closure.

KW - Poincaré sphere

KW - ε-model

KW - state

KW - Hilbert lattice

M3 - Article

VL - 10

SP - 241

EP - 266

JO - Tatra Mountains Mathematical Publications

JF - Tatra Mountains Mathematical Publications

SN - 1210-3195

ER -