Interference, Dependence and Bell’s Theorem Samson Abramsky Department of Computer Science, University of Oxford Samson Abramsky (Department of Computer Science, University of Oxford) Interference, Dependence and Bell’s Theorem 1 / 18
Our Themes Samson Abramsky (Department of Computer Science, University of Oxford) Interference, Dependence and Bell’s Theorem 2 / 18
Our Themes Interference and dependence are closely related concepts, the first being the observational phenomenon connected to the second. Interference refers to the behaviour of some parts of a system influencing the behaviour of another part of the system. Dependence specifies the relation which determines those parts of the system that influence the computation of another part of the system. Samson Abramsky (Department of Computer Science, University of Oxford) Interference, Dependence and Bell’s Theorem 2 / 18
Our Themes Interference and dependence are closely related concepts, the first being the observational phenomenon connected to the second. Interference refers to the behaviour of some parts of a system influencing the behaviour of another part of the system. Dependence specifies the relation which determines those parts of the system that influence the computation of another part of the system. This workshop will bring together researchers working on interference and dependence from both the modelling and programming research communities to discuss connections and challenges. Samson Abramsky (Department of Computer Science, University of Oxford) Interference, Dependence and Bell’s Theorem 2 / 18
Our Themes Interference and dependence are closely related concepts, the first being the observational phenomenon connected to the second. Interference refers to the behaviour of some parts of a system influencing the behaviour of another part of the system. Dependence specifies the relation which determines those parts of the system that influence the computation of another part of the system. This workshop will bring together researchers working on interference and dependence from both the modelling and programming research communities to discuss connections and challenges. I want to make the following points: Samson Abramsky (Department of Computer Science, University of Oxford) Interference, Dependence and Bell’s Theorem 2 / 18
Our Themes Interference and dependence are closely related concepts, the first being the observational phenomenon connected to the second. Interference refers to the behaviour of some parts of a system influencing the behaviour of another part of the system. Dependence specifies the relation which determines those parts of the system that influence the computation of another part of the system. This workshop will bring together researchers working on interference and dependence from both the modelling and programming research communities to discuss connections and challenges. I want to make the following points: Interference and dependence are not only pervasive in Computer Science, but throughout the sciences. Samson Abramsky (Department of Computer Science, University of Oxford) Interference, Dependence and Bell’s Theorem 2 / 18
Our Themes Interference and dependence are closely related concepts, the first being the observational phenomenon connected to the second. Interference refers to the behaviour of some parts of a system influencing the behaviour of another part of the system. Dependence specifies the relation which determines those parts of the system that influence the computation of another part of the system. This workshop will bring together researchers working on interference and dependence from both the modelling and programming research communities to discuss connections and challenges. I want to make the following points: Interference and dependence are not only pervasive in Computer Science, but throughout the sciences. In fact, they play a key rˆ ole in fundamental results such as Bell’s theorem in the foundations of quantum mechanics — seminal for subsequent developments in quantum information and computation. Samson Abramsky (Department of Computer Science, University of Oxford) Interference, Dependence and Bell’s Theorem 2 / 18
Our Themes Interference and dependence are closely related concepts, the first being the observational phenomenon connected to the second. Interference refers to the behaviour of some parts of a system influencing the behaviour of another part of the system. Dependence specifies the relation which determines those parts of the system that influence the computation of another part of the system. This workshop will bring together researchers working on interference and dependence from both the modelling and programming research communities to discuss connections and challenges. I want to make the following points: Interference and dependence are not only pervasive in Computer Science, but throughout the sciences. In fact, they play a key rˆ ole in fundamental results such as Bell’s theorem in the foundations of quantum mechanics — seminal for subsequent developments in quantum information and computation. There is a fascinating interplay between logical structure, probability, observational ideas — with implications for the nature of physical reality! Samson Abramsky (Department of Computer Science, University of Oxford) Interference, Dependence and Bell’s Theorem 2 / 18
The Basic Scenario a a · · d b d b c c Alice Bob Samson Abramsky (Department of Computer Science, University of Oxford) Interference, Dependence and Bell’s Theorem 3 / 18
The Basic Scenario a a · · d b d b c c Alice Bob Think e.g. of making observations at different nodes of a network. Samson Abramsky (Department of Computer Science, University of Oxford) Interference, Dependence and Bell’s Theorem 3 / 18
The Basic Scenario a a · · d b d b c c Alice Bob Think e.g. of making observations at different nodes of a network. Different quantities which can be measured. Samson Abramsky (Department of Computer Science, University of Oxford) Interference, Dependence and Bell’s Theorem 3 / 18
The Basic Scenario a a · · d b d b c c Alice Bob Think e.g. of making observations at different nodes of a network. Different quantities which can be measured. Observations: tuples of values. Repeated observations give sets of such tuples. Samson Abramsky (Department of Computer Science, University of Oxford) Interference, Dependence and Bell’s Theorem 3 / 18
The Basic Scenario a a · · d b d b c c Alice Bob Think e.g. of making observations at different nodes of a network. Different quantities which can be measured. Observations: tuples of values. Repeated observations give sets of such tuples. Can we tell from this observational history if there is interference/dependence between different parts of the system? Samson Abramsky (Department of Computer Science, University of Oxford) Interference, Dependence and Bell’s Theorem 3 / 18
The Basic Scenario a a · · d b d b c c Alice Bob Think e.g. of making observations at different nodes of a network. Different quantities which can be measured. Observations: tuples of values. Repeated observations give sets of such tuples. Can we tell from this observational history if there is interference/dependence between different parts of the system? Cf. ‘measurement-based verification’. Samson Abramsky (Department of Computer Science, University of Oxford) Interference, Dependence and Bell’s Theorem 3 / 18
A Probabilistic Model Of An Experiment Samson Abramsky (Department of Computer Science, University of Oxford) Interference, Dependence and Bell’s Theorem 4 / 18
A Probabilistic Model Of An Experiment A B (0 , 0) (1 , 0) (0 , 1) (1 , 1) a b 1 / 2 0 0 1 / 2 a ′ b 3 / 8 1 / 8 1 / 8 3 / 8 b ′ a 3 / 8 1 / 8 1 / 8 3 / 8 a ′ b ′ 1 / 8 3 / 8 3 / 8 1 / 8 Samson Abramsky (Department of Computer Science, University of Oxford) Interference, Dependence and Bell’s Theorem 4 / 18
A Probabilistic Model Of An Experiment A B (0 , 0) (1 , 0) (0 , 1) (1 , 1) a b 1 / 2 0 0 1 / 2 a ′ b 3 / 8 1 / 8 1 / 8 3 / 8 b ′ a 3 / 8 1 / 8 1 / 8 3 / 8 a ′ b ′ 1 / 8 3 / 8 3 / 8 1 / 8 Is this ‘reasonable’ or not? Samson Abramsky (Department of Computer Science, University of Oxford) Interference, Dependence and Bell’s Theorem 4 / 18
A Probabilistic Model Of An Experiment A B (0 , 0) (1 , 0) (0 , 1) (1 , 1) a b 1 / 2 0 0 1 / 2 a ′ b 3 / 8 1 / 8 1 / 8 3 / 8 b ′ a 3 / 8 1 / 8 1 / 8 3 / 8 a ′ b ′ 1 / 8 3 / 8 3 / 8 1 / 8 Is this ‘reasonable’ or not? How can we tell? Samson Abramsky (Department of Computer Science, University of Oxford) Interference, Dependence and Bell’s Theorem 4 / 18
A Probabilistic Model Of An Experiment A B (0 , 0) (1 , 0) (0 , 1) (1 , 1) a b 1 / 2 0 0 1 / 2 a ′ b 3 / 8 1 / 8 1 / 8 3 / 8 b ′ a 3 / 8 1 / 8 1 / 8 3 / 8 a ′ b ′ 1 / 8 3 / 8 3 / 8 1 / 8 Is this ‘reasonable’ or not? How can we tell? What does reasonable mean?? Samson Abramsky (Department of Computer Science, University of Oxford) Interference, Dependence and Bell’s Theorem 4 / 18
A Simple Observation Samson Abramsky (Department of Computer Science, University of Oxford) Interference, Dependence and Bell’s Theorem 5 / 18
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