# Hyper-decoherence in Density Hypercubes

@article{Hefford2020HyperdecoherenceID, title={Hyper-decoherence in Density Hypercubes}, author={James Hefford and Stefano Gogioso}, journal={Electronic Proceedings in Theoretical Computer Science}, year={2020} }

We study hyper-decoherence in three operational theories from the literature, all examples of the recently introduced higher-order CPM construction. Amongst these, we show the theory of density hypercubes to be the richest in terms of post-quantum phenomena. Specifically, we demonstrate the existence of a probabilistic hyper-decoherence of density hypercubes to quantum systems and calculate the associated hyper-phase group. This makes density hypercubes of significant foundational interest, as…

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## References

SHOWING 1-10 OF 26 REFERENCES

### Density Hypercubes, Higher Order Interference and Hyper-decoherence: A Categorical Approach

- Computer ScienceQI
- 2018

This work uses the recently introduced double-dilation construction by Zwart and Coecke to construct a new categorical probabilistic theory of density hypercubes and shows that the theory displays higher-order interference of order up to fourth.

### Two Roads to Classicality

- Mathematics
- 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…

### Higher-order CPM Constructions

- MathematicsElectronic Proceedings in Theoretical Computer Science
- 2019

We define a higher-order generalisation of the CPM construction based on arbitrary finite abelian group symmetries of symmetric monoidal categories. We show that our new construction is functorial,…

### 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.

### Categorical Probabilistic Theories

- Physics
- 2017

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.

### Reducing the number of non-Clifford gates in quantum circuits

- Computer SciencePhysical Review A
- 2020

We present a method for reducing the number of non-Clifford quantum gates, in particularly T-gates, in a circuit, an important task for efficiently implementing fault-tolerant quantum computations.…

### Reducing T-count with the ZX-calculus

- Computer Science
- 2019

A new method for reducing the number of T-gates in a quantum circuit based on the ZX-calculus is presented, which matches or beats previous approaches to T-count reduction on the majority of benchmark circuits in the ancilla-free case, in some cases yielding up to 50% improvement.

### Quantum mechanics as quantum measure theory

- Physics
- 1994

The additivity of classical probabilities is only the first in a hierarchy of possible sum rules, each of which implies its successor. The first and most restrictive sum rule of the hierarchy yields…

### Higher-Order Interference in Extensions of Quantum Theory

- Physics
- 2015

Quantum interference, manifest in the two slit experiment, lies at the heart of several quantum computational speed-ups and provides a striking example of a quantum phenomenon with no classical…

### Interacting quantum observables: categorical algebra and diagrammatics

- MathematicsArXiv
- 2009

The ZX-calculus is introduced, an intuitive and universal graphical calculus for multi-qubit systems, which greatly simplifies derivations in the area of quantum computation and information and axiomatize phase shifts within this framework.