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}
}
  • James HeffordS. Gogioso
  • Published 18 March 2020
  • Computer Science
  • Electronic Proceedings in Theoretical Computer Science
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… 
[PDF] Semantic Reader
5 Citations
Background Citations
1

5 Citations

Compositional resource theories of coherence

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.

A no-go theorem on the nature of the gravitational field beyond quantum theory

Recently, table-top experiments involving massive quantum systems have been proposed to test the interface of quantum theory and gravity. In particular, the crucial point of the debate is whether it…

Post-quantum steering is a stronger-than-quantum resource for information processing

We present the first instance where post-quantum steering is a stronger-than-quantum resource for information processing – remote state preparation. In addition, we show that the phenomenon of…

Computation in a general physical setting

The computational abilities of theories within the generalised probabilistic theory framework has been the subject of much recent study. Such investigations aim to gain an understanding of the…

CPM Categories for Galois Extensions

By considering a generalisation of the CPM construction, we develop an infinite hierarchy of probabilistic theories, exhibiting compositional decoherence structures which generalise the traditional…

References

SHOWING 1-10 OF 26 REFERENCES

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

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

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

  • S. Gogioso
  • Mathematics
    Electronic 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

  • Ciarán M. LeeJohn H. Selby
  • Philosophy, Physics
    Proceedings 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

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

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

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

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

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

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.