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Constructor theory of information.

Deutsch D, Marletto C - Proc. Math. Phys. Eng. Sci. (2015)

Bottom Line: Although these laws are directly about information, independently of the details of particular physical instantiations, information is not regarded as an a priori mathematical or logical concept, but as something whose nature and properties are determined by the laws of physics alone.This theory solves a problem at the foundations of existing information theory, namely that information and distinguishability are each defined in terms of the other.It also explains the relationship between classical and quantum information, and reveals the single, constructor-theoretic property underlying the most distinctive phenomena associated with the latter, including the lack of in-principle distinguishability of some states, the impossibility of cloning, the existence of pairs of variables that cannot simultaneously have sharp values, the fact that measurement processes can be both deterministic and unpredictable, the irreducible perturbation caused by measurement, and locally inaccessible information (as in entangled systems).

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Affiliation: Centre for Quantum Computation, The Clarendon Laboratory , University of Oxford , Oxford OX1 3PU, UK.

ABSTRACT

We propose a theory of information expressed solely in terms of which transformations of physical systems are possible and which are impossible-i.e. in constructor-theoretic terms. It includes conjectured, exact laws of physics expressing the regularities that allow information to be physically instantiated. Although these laws are directly about information, independently of the details of particular physical instantiations, information is not regarded as an a priori mathematical or logical concept, but as something whose nature and properties are determined by the laws of physics alone. This theory solves a problem at the foundations of existing information theory, namely that information and distinguishability are each defined in terms of the other. It also explains the relationship between classical and quantum information, and reveals the single, constructor-theoretic property underlying the most distinctive phenomena associated with the latter, including the lack of in-principle distinguishability of some states, the impossibility of cloning, the existence of pairs of variables that cannot simultaneously have sharp values, the fact that measurement processes can be both deterministic and unpredictable, the irreducible perturbation caused by measurement, and locally inaccessible information (as in entangled systems).

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Hierarchy of measurers of variables of which x is a member. (Online version in colour.)
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RSPA20140540F1: Hierarchy of measurers of variables of which x is a member. (Online version in colour.)

Mentions: We now obtain a necessary and sufficient condition for a variable to be an observable. Consider any attribute x, and any measurable variable X of which it is a member. Now, let χ be the union of all attributes in X, and consider the variable X′={x,χ−x}, a coarsening of X. It must be measurable, because any measurer of measures it. In this section and in §8e, we shall repeatedly rely on the relations between measurers of X, X′, and the two Boolean variables and , which are represented in figure 1.Figure 1.


Constructor theory of information.

Deutsch D, Marletto C - Proc. Math. Phys. Eng. Sci. (2015)

Hierarchy of measurers of variables of which x is a member. (Online version in colour.)
© Copyright Policy - open-access
Related In: Results  -  Collection

License
Show All Figures
getmorefigures.php?uid=PMC4309123&req=5

RSPA20140540F1: Hierarchy of measurers of variables of which x is a member. (Online version in colour.)
Mentions: We now obtain a necessary and sufficient condition for a variable to be an observable. Consider any attribute x, and any measurable variable X of which it is a member. Now, let χ be the union of all attributes in X, and consider the variable X′={x,χ−x}, a coarsening of X. It must be measurable, because any measurer of measures it. In this section and in §8e, we shall repeatedly rely on the relations between measurers of X, X′, and the two Boolean variables and , which are represented in figure 1.Figure 1.

Bottom Line: Although these laws are directly about information, independently of the details of particular physical instantiations, information is not regarded as an a priori mathematical or logical concept, but as something whose nature and properties are determined by the laws of physics alone.This theory solves a problem at the foundations of existing information theory, namely that information and distinguishability are each defined in terms of the other.It also explains the relationship between classical and quantum information, and reveals the single, constructor-theoretic property underlying the most distinctive phenomena associated with the latter, including the lack of in-principle distinguishability of some states, the impossibility of cloning, the existence of pairs of variables that cannot simultaneously have sharp values, the fact that measurement processes can be both deterministic and unpredictable, the irreducible perturbation caused by measurement, and locally inaccessible information (as in entangled systems).

View Article: PubMed Central - PubMed

Affiliation: Centre for Quantum Computation, The Clarendon Laboratory , University of Oxford , Oxford OX1 3PU, UK.

ABSTRACT

We propose a theory of information expressed solely in terms of which transformations of physical systems are possible and which are impossible-i.e. in constructor-theoretic terms. It includes conjectured, exact laws of physics expressing the regularities that allow information to be physically instantiated. Although these laws are directly about information, independently of the details of particular physical instantiations, information is not regarded as an a priori mathematical or logical concept, but as something whose nature and properties are determined by the laws of physics alone. This theory solves a problem at the foundations of existing information theory, namely that information and distinguishability are each defined in terms of the other. It also explains the relationship between classical and quantum information, and reveals the single, constructor-theoretic property underlying the most distinctive phenomena associated with the latter, including the lack of in-principle distinguishability of some states, the impossibility of cloning, the existence of pairs of variables that cannot simultaneously have sharp values, the fact that measurement processes can be both deterministic and unpredictable, the irreducible perturbation caused by measurement, and locally inaccessible information (as in entangled systems).

No MeSH data available.


Related in: MedlinePlus