# Two Roads to Classicality

@inproceedings{Coecke2017TwoRT, title={Two Roads to Classicality}, author={Bob Coecke and John H. Selby and Sean Tull}, year={2017} }

Mixing and decoherence are both manifestations of classicality within quantum theory, each of which admit a very general category-theoretic construction. We show under which conditions these two 'roads to classicality' coincide. This is indeed the case for (finite-dimensional) quantum theory, where each construction yields the category of C*-algebras and completely positive maps. We present counterexamples where the property fails which includes relational and modal theories. Finally, we…

## 19 Citations

### CPM Categories for Galois Extensions

- PhilosophyElectronic Proceedings in Theoretical Computer Science
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By considering a generalisation of the CPM construction, we develop an infinite hierarchy of probabilistic theories, exhibiting compositional decoherence structures which generalise the traditional…

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It is shown that defining a notion of purity for processes in general process theories has to make reference to the leaks of that theory, a feature missing in standard definitions; hence, a refined definition is proposed and the resulting notion ofurity for quantum, classical and intermediate theories is studied.

### A no-go theorem for theories that decohere to quantum mechanics

- Philosophy, PhysicsProceedings of the Royal Society A: Mathematical, Physical and Engineering Sciences
- 2018

This work asks whether there exists an operationally defined theory superseding quantum theory, but which reduces to it via a decoherence-like mechanism and proves that no such post-quantum theory exists if it is demanded that it satisfy two natural physical principles: causality and purification.

### Entanglement is Necessary for Emergent Classicality in All Physical Theories.

- Physics, PhilosophyPhysical review letters
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It is shown that any theory with a classical limit must contain entangled states, thus establishing entanglement as an inevitable feature of any theory superseding classical theory.

### Reconstructing quantum theory from diagrammatic postulates

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A reconstruction of finite-dimensional quantum theory where all of the postulates are stated entirely in diagrammatic terms, making them intuitive, and necessary additional axioms for a process theory to correspond to the Hilbert space model are characterised.

### Categorical Probabilistic Theories

- Physics
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A minimal number of operationally motivated axioms are adopted which provide clean categorical foundations, in the style of CQM, for the treatment of the problems that OPTs are concerned with.

### Compositional resource theories of coherence

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This work shows that resource theories of coherence can instead be defined purely compositionally, that is, working with the mathematics of process theories, string diagrams and category theory, and opens the door to the development of novel tools which would not be accessible from the linear algebraic mind set.

### Hyper-decoherence in Density Hypercubes

- Computer ScienceElectronic Proceedings in Theoretical Computer Science
- 2021

This work demonstrates the existence of a probabilistic hyper-decoherence of density hypercubes to quantum systems and calculate the associated hyper-phase group.

### A Diagrammatic Derivation of the Hermitian Adjoint

- Mathematics
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We show that the physical principle, “the adjoint associates to each state a ‘test’ for that state”, fully characterises the Hermitian adjoint for pure quantum theory, therefore providing the adjoint…

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It is shown that update structures survive decoherence and are sufficiently general to capture quantum observables, pinpointing the additional assumptions required to make the two coincide.

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